diff --git a/source-code/Poisson-Graphs/Blockchain.py b/source-code/Poisson-Graphs/Blockchain.py
index c580717..f0e23c5 100644
--- a/source-code/Poisson-Graphs/Blockchain.py
+++ b/source-code/Poisson-Graphs/Blockchain.py
@@ -51,9 +51,49 @@ class Blockchain(object):
             elif tempCumDiff == maxCumDiff:
                 self.miningIdents.append(ident)
             #print("leaf ident = ", str(ident), ", and tempCumDiff = ", str(tempCumDiff), " and maxCumDiff = ", str(maxCumDiff))
-            
+        assert len(self.miningIdents) > 0
            
 class Test_Blockchain(unittest.TestCase):
+    def test_addBlock(self):
+        bill = Blockchain([], verbosity=True)
+        
+        name = newIdent(0)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        
+        self.assertEqual(genesis.ident,name)
+        self.assertEqual(genesis.discoTimestamp,t)
+        self.assertEqual(genesis.arrivTimestamp,s)
+        self.assertTrue(genesis.parent is None)
+        self.assertEqual(genesis.diff,diff)
+        
+        bill.addBlock(genesis)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.ident in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(genesis.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),1)
+        
+        name = newIdent(1)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
+        blockA = Block(params)
+        bill.addBlock(blockA)
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        self.assertTrue(genesis.ident not in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(blockA.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),2)
+        
+        
     def test_bc(self):
         bill = Blockchain([], verbosity=True)
         
@@ -115,7 +155,7 @@ class Test_Blockchain(unittest.TestCase):
         self.assertTrue(bill.blocks[genesis.ident].parent is None)
         
         bill.whichLeaf()
-        print(bill.miningIdents)
+        #print(bill.miningIdents)
         
         self.assertEqual(type(bill.miningIdents), type([]))
         self.assertTrue(len(bill.miningIdents), 2)
diff --git a/source-code/Poisson-Graphs/Node.py b/source-code/Poisson-Graphs/Node.py
index 2866283..25447b2 100644
--- a/source-code/Poisson-Graphs/Node.py
+++ b/source-code/Poisson-Graphs/Node.py
@@ -1,4 +1,5 @@
 from Blockchain import *
+import copy
 
 class Node(object):
     '''
@@ -17,12 +18,9 @@ class Node(object):
             self.edges = {}
         
     def updateBlockchain(self, incBlocks, diffUpdateRate=1, mode="Nakamoto", targetRate=1.0/1209600.0):
-        # dataToUpdate shall be a dictionary of block identities (as keys) and their associated blocks (as values)
+        # incBlocks shall be a dictionary of block identities (as keys) and their associated blocks (as values)
         # to be added to the local data. We assume difficulty scores have been reported honestly for now.
         
-        # Stash a copy of incoming blocks so removing keys won't shrink the size of the dictionary over which
-        # we are looping.
-        
         if self.verbose:
             print("\t\t Updating blockchain.")
         
@@ -36,18 +34,19 @@ class Node(object):
         if self.verbose:
             print("\t\t Now tempData has " + str(len(tempData)) + " entries.")
             
-        for key in incBlocks.blocks:
+        for key in incBlocks:
             if key in self.data["blockchain"].blocks:
                 del tempData[key]
-            elif incBlocks.blocks[key].parent in self.data["blockchain"].blocks or incBlocks[key].parent is None:
-                self.data["blockchain"].addBlock(incBlocks.blocks[key])
+            elif incBlocks[key].parent in self.data["blockchain"].blocks or incBlocks[key].parent is None:
+                self.data["blockchain"].addBlock(incBlocks[key])
+                self.data["blockchain"].whichLeaf()
                 #if len(self.data["blockchain"]) % diffUpdateRate == 0:
                 #    self.updateDifficulty(mode, targetRate)
                 del tempData[key]
         incBlocks = copy.deepcopy(tempData)
         
         if self.verbose:
-            print("\t\t Now incBlocks has " + str(len(incBlocks.blocks)) + " entries.")
+            print("\t\t Now incBlocks has " + str(len(incBlocks)) + " entries.")
         
         if self.verbose:
             print("\t\tRemaining steps (while loop)")
@@ -58,8 +57,9 @@ class Node(object):
             for key in incBlocks:
                 if key in self.data["blockchain"].blocks:
                     del tempData[key]
-                elif incBlocks.blocks[key].parent in self.data["blockchain"].blocks:
-                        self.data["blockchain"].addBlock(incBlocks.blocks[key])
+                elif incBlocks[key].parent in self.data["blockchain"].blocks:
+                        self.data["blockchain"].addBlock(incBlocks[key])
+                        self.data["blockchain"].whichLeaf()
                         del tempData[key]
             incBlocks = copy.deepcopy(tempData)
             if self.verbose:
@@ -71,78 +71,118 @@ class Node(object):
         # Note for default, targetRate = two weeks/period, seven days/week, 24 hours/day, 60 minutes/hour, 60 seconds/minute) = 1209600 seconds/period
         if mode=="Nakamoto":
             # Use MLE estimate of poisson process, compare to targetRate, update by multiplying by resulting ratio.
+            if self.verbose:
+                print("Beginning update of difficulty with Nakamoto method")
             count = 2016
             bc = self.data["blockchain"]
-            ident = bc.miningIdent
-            topTime = copy.deepcopy(bc.blocks[ident].discoTimestamp)
-            parent = bc.blocks[ident].parent
-            count = count - 1
-            touched = False
-            while count > 0 and parent is not None:
-                ident = copy.deepcopy(parent)
+            if self.verbose:
+                print("Checking that blockchain is 2016*n blocks long and some mining identity has been set")
+            if len(bc.blocks) % 2016 == 0 and len(bc.miningIdents) > 0:
+                
+                ident = random.choice(bc.miningIdents)
+                topTime = copy.deepcopy(bc.blocks[ident].discoTimestamp)
                 parent = bc.blocks[ident].parent
                 count = count - 1
-                touched = True
-            if not touched:
-                mleDiscoRate = targetRate
-            else:
-                botTime = copy.deepcopy(bc.blocks[ident].discoTimestamp)
-            
-                # Algebra is okay:
-                assert 0 <= 2016 - count and 2016 - count < 2017
-                assert topTime != botTime
-                # MLE estimate of arrivals per second:
-                mleDiscoRate = float(2016 - count)/float(topTime - botTime)
-                mleDiscoRate = abs(mleDiscoRate) 
-                # Rate must be positive... so the MLE for block arrival rate
-                # assuming a Poisson process _is not even well-defined_ as
-                # an estimate for block arrival rate assuming timestamps are
-                # inaccurately reported!
+                touched = False
+                while count > 0 and parent is not None:
+                    ident = copy.deepcopy(parent)
+                    parent = bc.blocks[ident].parent
+                    count = count - 1
+                    touched = True
+                if not touched:
+                    mleDiscoRate = targetRate
+                else:
+                    botTime = copy.deepcopy(bc.blocks[ident].discoTimestamp)
                 
-                # We use it nonetheless.
+                    # Algebra is okay:
+                    assert topTime != botTime
+                    
+                    # MLE estimate of arrivals per second:
+                    mleDiscoRate = float(2015)/float(topTime - botTime)
+                    
+                    # Rates can't be negative, but this estimate could be (although it's highly unlikely given Bitcoin's standard choices
+                    # of difficulty update rate, etc.
+                    mleDiscoRate = abs(mleDiscoRate) 
+                    
+                    if self.verbose:
+                        print("MLE disco rate = " + str(mleDiscoRate) + " and targetRate = " + str(targetRate))
+                    # Rate must be positive... so the MLE for block arrival rate
+                    # assuming a Poisson process _is not even well-defined_ as
+                    # an estimate for block arrival rate assuming timestamps are
+                    # inaccurately reported!
+                    
+                    # We use it nonetheless.
+                
+                if self.verbose:
+                    print("MLE discovery rate = " + str(mleDiscoRate))
+                    print("Difficulty before adjustment = " + str(self.diff))
+                
+                # Update difficulty multiplicatively
+                self.diff = self.diff*mleDiscoRate/targetRate
+                
+                if self.verbose:
+                    print("Difficulty after adjustment = ", str(self.diff))
                 
-            # How much should difficulty change?
-            self.diff = self.diff*(mleDiscoRate/targetRate)
-            
         elif mode=="vanSaberhagen":
             # Similar to above, except use 1200 blocks, discard top 120 and bottom 120 after sorting.
             # 4 minute blocks in the original cryptonote, I believe... targetRate = 1.0/
             # 4 minutes/period, 60 seconds/minute ~ 240 seconds/period
-            assert targetRate==1.0/240.0
+            # assert targetRate==1.0/240.0
             count = 1200
-            ident = self.data.miningIdent
-            bl = []
-            bl.append(copy.deepcopy(self.data.blocks[ident].discoTimestamp))
-            parent = self.data.blocks[ident].parent
-            count = count - 1
-            while count > 0 and parent is not NOne:
-                ident = copy.deepcopy(parent)
-                bl.append(copy.deepcopy(self.data.blocks[ident].discoTimestamp))
-                parent = self.data.blocks[ident].parent
-                count = count-1
-            # sort    
-            bl = sorted(bl)
-            
-            # remove outliers
-            bl = bl[120:-120]
-            
-            # get topTime and botTime
-            topTime = bl[-1]
-            botTime = bl[0]
-            
-            # Assert algebra will work
-            assert 0 <= 960 - count and 960 - count < 961
-            assert topTime > botTime
-            
-            # Sort of the MLE: # blocks/difference in reported times
-            # But not the MLE, since the reported times may not be 
-            # the actual times, the "difference in reported times" != 
-            # "ground truth difference in block discoery times" in general 
-            naiveDiscoRate = (960 - count)/(topTime - botTime)
-            
-            # How much should difficulty change?
-            self.diff = self.diff*(naiveDiscoRate/targetRate)
-            
+            bc = self.data["blockchain"]
+            bc.whichLeaf()
+            assert self.diff != 0.0
+            if len(bc.blocks) > 120:
+                assert type(bc.miningIdents)==type([])
+                assert len(bc.miningIdents) > 0
+                ident = random.choice(bc.miningIdents)
+                bl = []
+                bl.append(copy.deepcopy(bc.blocks[ident].discoTimestamp))
+                parent = bc.blocks[ident].parent
+                count = count - 1
+                while count > 0 and parent is not None:
+                    ident = copy.deepcopy(parent)
+                    bl.append(copy.deepcopy(bc.blocks[ident].discoTimestamp))
+                    parent = bc.blocks[ident].parent
+                    count = count-1
+                # sort    
+                bl = sorted(bl)
+                assert len(bl)<=1200
+                
+                #print("Sample size = " + str(len(bl)))
+                # remove 10 and 90 %-iles
+                numOutliers = round(len(bl)/5)//2
+                assert numOutliers <= 120
+                #print("Number of outliers = " + str(numOutliers))
+                if numOutliers > 0:
+                    bl = bl[numOutliers:-numOutliers]
+                #print("New Sample Size = " + str(len(bl)))
+                    
+                
+                # get topTime and botTime
+                if self.verbose:
+                    print("bl[0] = " + str(bl[0]) + ",\tbl[-1] = " + str(bl[-1]))
+                topTime = bl[-1]
+                botTime = bl[0]
+                if self.verbose:
+                    print("list of timestamps = " + str(bl))
+                    print("topTime = " + str(bl[-1]))
+                    print("botTime = " + str(bl[0]))
+                
+                # Assert algebra will work
+                # 1200 - 2*120 = 1200 - 240 = 960
+                assert 0 < len(bl) and len(bl) < 961
+                assert topTime - botTime >= 0.0
+                
+                # Sort of the MLE: # blocks/difference in reported times
+                # But not the MLE, since the reported times may not be 
+                # the actual times, the "difference in reported times" != 
+                # "ground truth difference in block discoery times" in general 
+                naiveDiscoRate = (960 - count)/(topTime - botTime)
+                
+                # How much should difficulty change?
+                self.diff = self.diff*(naiveDiscoRate/targetRate)
+                
         elif mode=="MOM:expModGauss":
             # Similar to "vanSaberhagen" except with 2-minute blocks and
             # we attempt to take into account that "difference in timestamps" 
@@ -158,20 +198,26 @@ class Node(object):
             #       lambda ~ (1.0/(stdev))*(2/skewness)**(1.0/3.0)
             assert targetRate==1.0/120.0
             count = 1200
-            ident = self.data.miningIdent
+            bc = self.data["blockchain"]
+            if len(bc.miningIdents) > 0:
+                ident = random.choice(bc.miningIdents)
+            
             bl = []
-            bl.append(copy.deepcopy(self.data.blocks[ident].discoTimestamp))
-            parent = self.data.blocks[ident].parent
+            bl.append(copy.deepcopy(bc.blocks[ident].discoTimestamp))
+            parent = bc.blocks[ident].parent
             count = count - 1
-            while count > 0 and parent is not NOne:
+            while count > 0 and parent is not None:
                 ident = copy.deepcopy(parent)
-                bl.append(copy.deepcopy(self.data.blocks[ident].discoTimestamp))
-                parent = self.data.blocks[ident].parent
+                bl.append(copy.deepcopy(bc.blocks[ident].discoTimestamp))
+                parent = bc.blocks[ident].parent
                 count = count-1
-            sk   = skew(bl)
-            va   = var(bl)
-            stdv = sqrt(va)
-            lam  = (1.0/stdv)*(2.0/sk)**(1.0/3.0)
+            if len(bl) > 120:
+                sk   = skew(bl)
+                va   = var(bl)
+                stdv = sqrt(va)
+                lam  = (1.0/stdv)*(2.0/sk)**(1.0/3.0)
+            else:
+                lam = targetRate # we will not change difficulty unless we have at least 120 blocks of data (arbitrarily selected)
             self.diff = self.diff*(lam/targetRate)
         else:
             print("Error, invalid difficulty mode entered.")
@@ -193,77 +239,701 @@ class Node(object):
        
 
 class Test_Node(unittest.TestCase):
-    def test_node(self):
-        verbose = True
-        nellyIdent = newIdent(0)
-        bill = Blockchain([], verbosity=verbose)
+    # TODO test each method separately
+    '''def test_nakamoto(self):
+        print("Beginning test of Nakamoto difficulty adjustment")
+        print("Setting initial values")
+        target = 100.0 # rate = blocks/s
+        verbose = False
+        deltaT = 1.0/target # forced wait time
+        arrivalList = []
+        mode="Nakamoto"
         
+        print("Generating node")
+        nellyIdent = newIdent(0)
+        offset = random.random()
+        intensity = random.random()
+        
+        print("Generating initial blockchain")
+        # Create a new initial blockchain object
+        bill = Blockchain([], verbosity=verbose)
         name = newIdent(0)
         t = time.time()
-        s = t+1
+        t += offset
+        arrivalList.append(t)
+        s = t+random.random()
+        diff = 1.0
+        oldDiff = copy.deepcopy(diff)
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        print("Adding block")
+        bill.addBlock(genesis)
+        bill.whichLeaf()
+        
+        # Check that it consists only of the genesis block
+        self.assertTrue(len(bill.blocks)==1)
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.parent is None)
+        
+        print("Finish creating node")
+        # Create node with this blockchain.
+        nodeData = {"blockchain":bill, "intensity":intensity, "offset":offset}
+        params = {"ident":nellyIdent, "data":nodeData, "diff":diff, "verbose":verbose}
+        nelly = Node(params)
+        
+        # Check node creation worked
+        self.assertEqual(nelly.ident, nellyIdent)
+        self.assertEqual(nelly.data["blockchain"], bill)
+        self.assertEqual(nelly.diff, diff)
+        self.assertEqual(nelly.data["intensity"], intensity)
+        self.assertEqual(nelly.data["offset"], offset)
+        
+        # Sleep and add a block on top of genesis
+        if verbose:
+            print("sleeping")
+        time.sleep(deltaT)
+        
+        print("Giving genesis block a child")
+        name = newIdent(1)
+        t = time.time()
+        t += nelly.data["offset"]
+        arrivalList.append(t)
+        s = t+random.random()
+        diff = oldDiff
+        params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
+        blockA = Block(params)
+        nelly.updateBlockchain({blockA.ident:blockA})
+        oldIdent = blockA.ident
+        
+        # Check this worked
+        self.assertEqual(len(nelly.data["blockchain"].blocks),2)
+        self.assertTrue(blockA.ident in nelly.data["blockchain"].blocks)
+        self.assertTrue(genesis.ident in nelly.data["blockchain"].blocks)
+        self.assertEqual(genesis.ident, nelly.data["blockchain"].blocks[blockA.ident].parent)
+        
+        print("Updating difficulty")
+        # Update the difficulty score
+        nelly.updateDifficulty(mode, targetRate = target) # With only two blocks, nothing should change.
+        self.assertEqual(nelly.diff, oldDiff)
+        
+        # Print regardless of verbosity:
+        print("Now generating first difficulty adjustment period.")
+        
+        # Now we are going to fast forward to right before the first difficulty adjustment.
+        N = len(nelly.data["blockchain"].blocks)
+        while(N < 2015):
+            if N % 100 == 0:
+                print("\tN=" + str(N))
+            name = newIdent(N)
+            t = time.time()
+            t += nelly.data["offset"]
+            arrivalList.append(t)
+            s = t+random.random()
+            diff = nelly.diff
+            oldDiff = diff
+            params = {"ident":name, "disco":t, "arriv":s, "parent":oldIdent, "diff":diff}
+            oldIdent = copy.deepcopy(name)
+            block = Block(params)
+            nelly.updateBlockchain({block.ident:block})
+            
+            # Check this worked
+            self.assertEqual(len(nelly.data["blockchain"].blocks),N+1)
+            self.assertTrue(block.ident in nelly.data["blockchain"].blocks)
+            
+            # Update the difficulty score
+            nelly.updateDifficulty(mode, targetRate = target) # With N < 2016, nothing should change.
+            self.assertEqual(nelly.diff, oldDiff)
+            N = len(nelly.data["blockchain"].blocks)
+            time.sleep(deltaT)
+            
+        name = newIdent(N)
+        t = time.time()
+        t += nelly.data["offset"]
+        arrivalList.append(t)
+        s = t+random.random()
+        diff = oldDiff
+        params = {"ident":name, "disco":t, "arriv":s, "parent":oldIdent, "diff":diff}
+        block = Block(params)
+        nelly.updateBlockchain({block.ident:block})
+        
+        # Check this worked
+        self.assertEqual(len(nelly.data["blockchain"].blocks),N+1)
+        self.assertTrue(block.ident in nelly.data["blockchain"].blocks)
+        
+        # Update the difficulty score
+        nelly.updateDifficulty(mode, targetRate = target) # With N < 2016, nothing should change.
+        # Note: 2016 blocks is 2015 block inter-arrival times.
+        expRatioNumerator = float(2015)/(arrivalList[-1] - arrivalList[-2016])
+        expRatio = expRatioNumerator/target
+        expDiff = oldDiff*expRatio
+        self.assertEqual(nelly.diff, expDiff)
+        
+        # The following should fail, because our sample size is incorrect.
+        expRatioNumerator = float(2016)/(arrivalList[-1] - arrivalList[-2016])
+        expRatio = expRatioNumerator/target
+        expDiff = oldDiff*expRatio
+        self.assertFalse(nelly.diff - expDiff == 0.0)
+        
+        
+        # Print regardless of verbosity:
+        print("Now generating second difficulty adjustment period.")
+        
+        # Now we are going to fast forward to right before the next difficulty adjustment.
+        # This time, though, we are going to re-set the block inter-arrival time deltaT
+        # to half. This should drive difficulty up.
+        lastDifficultyScore = copy.deepcopy(nelly.diff)
+        N = len(nelly.data["blockchain"].blocks)
+        while(N < 4031):
+            if N % 100 == 0:
+                print("\tN=" + str(N))
+            name = newIdent(N)
+            t = time.time()
+            t += nelly.data["offset"]
+            arrivalList.append(t)
+            s = t+random.random()
+            diff = nelly.diff
+            oldDiff = diff
+            params = {"ident":name, "disco":t, "arriv":s, "parent":oldIdent, "diff":diff}
+            oldIdent = copy.deepcopy(name)
+            block = Block(params)
+            nelly.updateBlockchain({block.ident:block})
+            
+            # Check this worked
+            self.assertEqual(len(nelly.data["blockchain"].blocks),N+1)
+            self.assertTrue(block.ident in nelly.data["blockchain"].blocks)
+            
+            # Update the difficulty score
+            nelly.updateDifficulty(mode, targetRate = target) # With N < 2016, nothing should change.
+            self.assertEqual(nelly.diff, oldDiff)
+            N = len(nelly.data["blockchain"].blocks)
+            time.sleep(0.01*deltaT)
+            
+        # Now if we add a single new block, we should trigger difficulty adjustment.
+        name = newIdent(N)
+        t = time.time()
+        t += nelly.data["offset"]
+        arrivalList.append(t)
+        s = t+random.random()
+        diff = oldDiff
+        params = {"ident":name, "disco":t, "arriv":s, "parent":oldIdent, "diff":diff}
+        block = Block(params)
+        nelly.updateBlockchain({block.ident:block})
+        
+        # Check this worked
+        self.assertEqual(len(nelly.data["blockchain"].blocks),N+1)
+        self.assertTrue(block.ident in nelly.data["blockchain"].blocks)
+        
+        # Update the difficulty score. 
+        nelly.updateDifficulty(mode, targetRate = target)
+        expRatioNumerator = float(2015)/(arrivalList[-1] - arrivalList[-2016])
+        expRatio = expRatioNumerator/target
+        expDiff = oldDiff*expRatio
+        print("expRatio = " + str(expRatio) + ", lastDifficultyScore = " + str(lastDifficultyScore) + ", new difficulty = " + str(nelly.diff))
+        self.assertEqual(nelly.diff, expDiff)
+        '''
+        
+        
+        
+        
+    def test_vs(self):
+        print("Beginning test of vanSaberhagen difficulty adjustment.")
+        print("Setting initial values")
+        target = 10.0 # 1.0/240.0 # rate = blocks/s
+        verbose = False
+        deltaT = 1.0/target # forced wait time
+        arrivalList = []
+        mode="vanSaberhagen"
+        
+        print("Instantiating new node")
+        nellyIdent = newIdent(0)
+        offset = random.random()
+        intensity = random.random()
+        
+        print("Creating new blockchain for new node")
+        # Create a new initial blockchain object
+        bill = Blockchain([], verbosity=verbose)
+        name = newIdent(0)
+        t = time.time()
+        t += offset
+        arrivalList.append(t)
+        s = t+random.random()
         diff = 1.0
         params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
         genesis = Block(params)
+        print("Adding genesis block")
         bill.addBlock(genesis)
+        bill.whichLeaf()
         
-        time.sleep(10)
+        # Check that it consists only of the genesis block
+        self.assertTrue(len(bill.blocks)==1)
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.parent is None)
+        self.assertTrue(genesis.ident in bill.leaves)
         
+        print("Making node")
+        # Create node with this blockchain.
+        nodeData = {"blockchain":bill, "intensity":intensity, "offset":offset}
+        params = {"ident":nellyIdent, "data":nodeData, "diff":diff, "verbose":verbose}
+        nelly = Node(params)
+        
+        # Check node creation worked
+        self.assertEqual(nelly.ident, nellyIdent)
+        self.assertEqual(nelly.data["blockchain"], bill)
+        self.assertEqual(nelly.diff, diff)
+        self.assertEqual(nelly.data["intensity"], intensity)
+        self.assertEqual(nelly.data["offset"], offset)
+        
+        # Sleep and add a block on top of genesis
+        if verbose:
+            print("sleeping")
+        time.sleep(deltaT)
+        
+        print("Give genesis a child")
         name = newIdent(1)
         t = time.time()
-        s = t+1
-        diff = 1.0
+        t += nelly.data["offset"]
+        arrivalList.append(t)
+        s = t+random.random()
+        oldDiff = copy.deepcopy(diff)
+        diff = copy.deepcopy(nelly.diff)
+        assert diff != 0.0
         params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
         blockA = Block(params)
-        bill.addBlock(blockA)
+        nelly.updateBlockchain({blockA.ident:blockA})
+        oldIdent = blockA.ident
         
-        # Nodes need an identity and a blockchain object and verbosity and difficulty
-        nodeData = {"blockchain":bill, "intensity":random.random(), "offset":random.random()}
-        params = {"ident":name, "data":nodeData, "diff":diff, "verbose":verbose}
-        nelly = Node(params)
-        nelly.updateDifficulty(mode="Nakamoto")
+        # Check this worked
+        self.assertEqual(len(nelly.data["blockchain"].blocks),2)
+        self.assertTrue(blockA.ident in nelly.data["blockchain"].blocks)
+        self.assertTrue(genesis.ident in nelly.data["blockchain"].blocks)
+        self.assertEqual(genesis.ident, nelly.data["blockchain"].blocks[blockA.ident].parent)
         
-        time.sleep(9)
+        # Update the difficulty score
+        nelly.updateDifficulty(mode, targetRate = target) # With only two blocks, nothing should change.
+        assert nelly.diff != 0.0
+        self.assertEqual(nelly.diff, oldDiff)
+        self.assertFalse(nelly.diff == -0.0)
         
-        name = newIdent(len(nelly.data))
+        # Print regardless of verbosity:
+        print("Now generating fulls sample size.")
+        
+        # Now we are going to fast forward to a "full sample size" period of time.
+        N = len(nelly.data["blockchain"].blocks)
+        while(N < 1200):
+            name = newIdent(N)
+            if N % 100 == 0:
+                print("\tNow adding block N=" + str(N))
+            t = time.time()
+            t += nelly.data["offset"]
+            arrivalList.append(t)
+            s = t+random.random()
+            oldDiff = copy.deepcopy(diff)
+            diff = copy.deepcopy(nelly.diff)
+            assert diff != 0.0
+            params = {"ident":name, "disco":t, "arriv":s, "parent":oldIdent, "diff":diff}
+            oldIdent = copy.deepcopy(name)
+            block = Block(params)
+            nelly.updateBlockchain({block.ident:block})
+            
+            # Check this worked
+            self.assertEqual(len(nelly.data["blockchain"].blocks),N+1)
+            self.assertTrue(block.ident in nelly.data["blockchain"].blocks)
+            
+            # Update the difficulty score
+            nelly.updateDifficulty(mode, targetRate = target) # With N < 100, nothing should change.
+            if N < 100:
+                self.assertEqual(nelly.diff, oldDiff)
+            N = len(nelly.data["blockchain"].blocks)
+            time.sleep(0.5*deltaT)
+            
+        print("Adding one more block")
+        name = newIdent(N)
         t = time.time()
-        s = t + 1
-        params = {"ident":name, "disco":t, "arriv":s, "parent":blockA.ident, "diff":diff}
-        blockB = Block(params)
-        nelly.updateBlockchain({blockB.ident:blockB})
+        t += nelly.data["offset"]
+        arrivalList.append(t)
+        s = t+random.random()
+        oldDiff = diff
+        diff = nelly.diff
+        assert diff != 0.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":oldIdent, "diff":nelly.diff}
+        block = Block(params)
+        nelly.updateBlockchain({block.ident:block})
         
-        time.sleep(8)
+        # Check this worked
+        self.assertEqual(len(nelly.data["blockchain"].blocks),N+1)
+        self.assertTrue(block.ident in nelly.data["blockchain"].blocks)
         
-        name = newIdent(len(nelly.data))
+        # Update the difficulty score
+        nelly.updateDifficulty(mode, targetRate = target) # With N < 2016, nothing should change.
+        # Note: 2016 blocks is 2015 block inter-arrival times.
+        print(str(arrivalList[-120]) + ", " + str(arrivalList[-1080]) + ", " + str(arrivalList[-120]-arrivalList[-1080]) + ", " + str(float(959)/(arrivalList[-120]-arrivalList[-1080]))+ ", " + str(float(float(959)/(arrivalList[-120]-arrivalList[-1080]))/float(target)))
+        expRatioNumerator = float(959)/(arrivalList[-120] - arrivalList[-1080])
+        expRatio = expRatioNumerator/target
+        print(expRatio)
+        expDiff = oldDiff*expRatio
+        print(expDiff)
+        print("expDiff = " + str(expDiff) + " and nelly.diff = " + str(nelly.diff))
+        self.assertEqual(nelly.diff, expDiff)
+        
+        
+        # Print regardless of verbosity:
+        print("Now fast forwarding past the tail end of the last period..")
+        # Now we are going to fast forward to right before the next difficulty adjustment.
+        # This time, though, we are going to re-set the block inter-arrival time deltaT
+        # to half. This should drive difficulty up.
+        lastDifficultyScore = copy.deepcopy(nelly.diff)
+        N = len(nelly.data["blockchain"].blocks)
+        while(N < 1700):
+            name = newIdent(N)
+            t = time.time()
+            t += nelly.data["offset"]
+            arrivalList.append(t)
+            s = t+random.random()
+            diff = nelly.diff
+            oldDiff = diff
+            params = {"ident":name, "disco":t, "arriv":s, "parent":oldIdent, "diff":diff}
+            oldIdent = copy.deepcopy(name)
+            block = Block(params)
+            nelly.updateBlockchain({block.ident:block})
+            
+            # Check this worked
+            self.assertEqual(len(nelly.data["blockchain"].blocks),N+1)
+            self.assertTrue(block.ident in nelly.data["blockchain"].blocks)
+            
+            # Update the difficulty score
+            nelly.updateDifficulty(mode, targetRate = target) # With N < 2016, nothing should change.
+            self.assertEqual(nelly.diff, oldDiff)
+            N = len(nelly.data["blockchain"].blocks)
+            time.sleep(0.01*deltaT)
+            
+        # Now if we add a single new block, we should trigger difficulty adjustment.
+        name = newIdent(N)
         t = time.time()
-        s = t + 1
-        params = {"ident":name, "disco":t, "arriv":s, "parent":blockA.ident, "diff":diff}
-        blockC = Block(params)
-        nelly.updateBlockchain({blockC.ident:blockC})
+        t += nelly.data["offset"]
+        arrivalList.append(t)
+        s = t+random.random()
+        diff = oldDiff
+        params = {"ident":name, "disco":t, "arriv":s, "parent":oldIdent, "diff":diff}
+        block = Block(params)
+        nelly.updateBlockchain({block.ident:block})
         
-        time.sleep(1)
-        name = newIdent(len(nelly.data))
-        t = time.time()
-        s = t + 1
-        params = {"ident":name, "disco":t, "arriv":s, "parent":blockC.ident, "diff":diff}
-        blockD = Block(params)
-        nelly.updateBlockchain({blockD.ident:blockD})
+        # Check this worked
+        self.assertEqual(len(nelly.data["blockchain"].blocks),N+1)
+        self.assertTrue(block.ident in nelly.data["blockchain"].blocks)
         
-        time.sleep(7)
-        name = newIdent(len(nelly.data))
-        t = time.time()
-        s = t + 1
-        params = {"ident":name, "disco":t, "arriv":s, "parent":blockD.ident, "diff":diff}
-        blockE = Block(params)
-        nelly.updateBlockchain({blockE.ident:blockE})
+        # Update the difficulty score. 
+        nelly.updateDifficulty(mode, targetRate = target)
+        expRatioNumerator = float(959)/(arrivalList[-120] - arrivalList[-1080])
+        expRatio = expRatioNumerator/target
+        expDiff = oldDiff*expRatio
+        print("expRatio = " + str(expRatio) + ", lastDifficultyScore = " + str(lastDifficultyScore) + ", new difficulty = " + str(nelly.diff))
+        self.assertEqual(nelly.diff, expDiff)
         
         
-        time.sleep(6)
-        name = newIdent(len(nelly.data))
-        t = time.time()
-        s = t + 1
-        params = {"ident":name, "disco":t, "arriv":s, "parent":blockE.ident, "diff":diff}
-        blockF = Block(params)
-        nelly.updateBlockchain({blockF.ident:blockF})
+        
+    def test_modexp(self):
+        pass
+        
+    '''# Check this worked
+        if mode == "Nakamoto":
+            # In this case we take simple MLE estimate
+            ratio = 1.0/abs(t1-t)
+            print("Nakamoto mle = " + str(ratio))
+            ratio = ratio/target
+            print("Normalized = " + str(ratio))
+            print("New diff = " + str(ratio*oldDiff))
+            self.assertEqual(nelly.diff, ratio*oldDiff)
+        elif mode == "vanSaberhagen":
+            # In this case, with only 2 blocks, we just use simple MLE again
+            ratio = 1.0/abs(t1-t)
+            ratio = ratio/target
+            self.assertEqual(nelly.diff, ratio*oldDiff)
+        elif mode == "MOM:expModGauss":
+            self.assertEqual(nelly.diff, 1.0)
+            # With at least 120 blocks of data...
+            #sk   = skew(bl)
+            #va   = var(bl)
+            #stdv = sqrt(va)
+            #lam  = (1.0/stdv)*(2.0/sk)**(1.0/3.0)
+            #self.diff = self.diff*(lam/targetRate)
+            # Otherwise, set to 1.0
+        else:
+            print("what world are you living in?")
+        
+        if verbose:
+            print("sleeping 1 seconds")
+        time.sleep(deltaT/5.0)
+        
+        listOfTimes = [copy.deepcopy(t), copy.deepcopy(t1)]
+        listOfBlocks = []
+        
+        N = len(nelly.data["blockchain"].blocks)
+        lastIdent = blockA.ident
+        
+        bail = False
+        while N < 10 and not bail:
+            # Generate new block
+            name = newIdent(N)
+            t = time.time()
+            t += nelly.data["offset"]
+            s = t+random.random()
+            oldDiff = copy.deepcopy(nelly.diff)
+            print("Current difficulty = ", oldDiff)
+            params = {"ident":name, "disco":t, "arriv":s, "parent":lastIdent, "diff":oldDiff}
+            newBlock = Block(params)
+            
+            # Append new block to running list along with creation time
+            listOfBlocks.append(newBlock)
+            listOfTimes.append(copy.deepcopy(t))
+            
+            # Update nelly's blockchain with newBlock
+            nelly.updateBlockchain({newBlock.ident:newBlock})
+            lastIdent = name
+            
+            # Quick check that this worked:
+            self.assertTrue(name in nelly.data["blockchain"].blocks)
+            self.assertEqual(len(nelly.data["blockchain"].blocks), N+1)
+            N = len(nelly.data["blockchain"].blocks)
+        
+            # Update difficulty
+            nelly.updateDifficulty(mode, targetRate = 100.0)
+            
+            # Quick check that this worked:
+            if mode == "Nakamoto":
+                # In this case we take use top block and genesis block
+                ratio = float(len(nelly.data["blockchain"].blocks) - 1)/(listOfTimes[-1] - listOfTimes[0])
+                ratio = ratio / target
+                self.assertEqual(nelly.diff, ratio*oldDiff)
+                print("Hoped for difficulty = " + str(oldDiff*ratio) + ", and computed = " + str(nelly.diff))
+            elif mode == "vanSaberhagen":
+                # This case coincides with nakamoto until block 10
+                ratio = float( len(nelly.data["blockchain"].blocks) - 1)/(listOfTimes[-1] - listOfTimes[0])
+                ratio = ratio / target
+                self.assertEqual(nelly.diff, ratio*oldDiff)
+            elif mode == "MOM:expModGauss":
+                self.assertEqual(nelly.diff, 1.0)
+                # With at least 120 blocks of data...
+                #sk   = skew(bl)
+                #va   = var(bl)
+                #stdv = sqrt(va)
+                #lam  = (1.0/stdv)*(2.0/sk)**(1.0/3.0)
+                #self.diff = self.diff*(lam/targetRate)
+                # Otherwise, set to 1.0
+            else:
+                print("what world are you living in?")
+            
+            # Sleep a random time
+            print("Sleeping a random sub-second, working on block " + str(N))
+            deltaT = deltaT*ratio
+            time.sleep(deltaT/5.0)
+            
+        while N < 120 and not bail:
+            # Generate new block
+            name = newIdent(N)
+            t = time.time()
+            t += nelly.data["offset"]
+            s = t+random.random()
+            oldDiff = copy.deepcopy(nelly.diff)
+            params = {"ident":name, "disco":t, "arriv":s, "parent":lastIdent, "diff":oldDiff}
+            newBlock = Block(params)
+            
+            # Append new block to running list along with creation time
+            listOfBlocks.append(newBlock)
+            listOfTimes.append(copy.deepcopy(t))
+            
+            # Update nelly's blockchain with newBlock
+            nelly.updateBlockchain({newBlock.ident:newBlock})
+            lastIdent = name
+            
+            # Quick check that this worked:
+            self.assertTrue(name in nelly.data["blockchain"].blocks)
+            self.assertEqual(len(nelly.data["blockchain"].blocks), N+1)
+            N = len(nelly.data["blockchain"].blocks)
+        
+            # Update difficulty
+            nelly.updateDifficulty(mode, targetRate = 100.0)
+            
+            # Quick check that this worked:
+            if mode == "Nakamoto":
+                # In this case we take use top block and genesis block
+                ratio = float(len(nelly.data["blockchain"].blocks)-1)/(listOfTimes[-1] - listOfTimes[0])
+                ratio = ratio / target
+                self.assertEqual(nelly.diff, oldDiff*ratio)
+                print("Hoped for difficulty = " + str(oldDiff*ratio) + ", and computed = " + str(nelly.diff))
+            elif mode == "vanSaberhagen":
+                # This case no longer coincides with Nakamoto...
+                numOutliers = len(nelly.data["blockchain"].blocks)//10
+                numOutliers = min(numOutliers, 120)
+                ratio = float(len(nelly.data["blockchain"].blocks) - 2*numOutliers - 1)/(listOfTimes[-numOutliers] - listOfTimes[numOutliers])
+                ratio = ratio / target
+                self.assertEqual(nelly.diff, oldDiff*ratio)
+            elif mode == "MOM:expModGauss":
+                # With at least 120 blocks of data...
+                count = 1200
+                bl = []
+                bl.append(copy.deepcopy(bc.blocks[lastIdent].discoTimestamp))
+                parent = bc.blocks[lastIdent].parent
+                count = count - 1
+                while count > 0 and parent is not None:
+                    ident = copy.deepcopy(parent)
+                    bl.append(copy.deepcopy(bc.blocks[ident].discoTimestamp))
+                    parent = bc.blocks[ident].parent
+                    count = count-1
+                if len(bl) > 120:
+                    sk   = skew(bl)
+                    va   = var(bl)
+                    stdv = sqrt(va)
+                    lam  = (1.0/stdv)*(2.0/sk)**(1.0/3.0)
+                else:
+                    lam = target
+                ratio = lam/target
+                self.assertEqual(nelly.diff, oldDiff*ratio)
+                
+            else:
+                print("what world are you living in?")
+            
+            # Sleep a random time
+            print("Sleeping a random sub-second, working on block " + str(N))
+            deltaT = deltaT*ratio
+            time.sleep(deltaT/5.0)
+          
+        while N < 2400 and not bail:
+            # Generate new block
+            name = newIdent(N)
+            t = time.time()
+            t += nelly.data["offset"]
+            s = t+random.random()
+            oldDiff = copy.deepcopy(nelly.diff)
+            params = {"ident":name, "disco":t, "arriv":s, "parent":lastIdent, "diff":oldDiff}
+            newBlock = Block(params)
+            
+            # Append new block to running list along with creation time
+            listOfBlocks.append(newBlock)
+            listOfTimes.append(copy.deepcopy(t))
+            
+            # Update nelly's blockchain with newBlock
+            nelly.updateBlockchain({newBlock.ident:newBlock})
+            lastIdent = name
+            
+            # Quick check that this worked:
+            self.assertTrue(name in nelly.data["blockchain"].blocks)
+            self.assertEqual(len(nelly.data["blockchain"].blocks), N+1)
+            N = len(nelly.data["blockchain"].blocks)
+        
+            # Update difficulty
+            nelly.updateDifficulty(mode, targetRate = 100.0)
+            
+            # Quick check that this worked:
+            if mode == "Nakamoto":
+                # In this case we take use top block and genesis block
+                ratio = float(len(nelly.data["blockchain"].blocks)-1)/(listOfTimes[-1] - listOfTimes[0])
+                ratio = ratio / target
+                self.assertEqual(nelly.diff, oldDiff*ratio)
+                print("Hoped for difficulty = " + str(oldDiff*ratio) + ", and computed = " + str(nelly.diff))
+            elif mode == "vanSaberhagen":
+                # This case no longer coincides with Nakamoto...
+                numOutliers = len(nelly.data["blockchain"].blocks)//10
+                numOutliers = min(numOutliers, 120)
+                ratio = float(len(nelly.data["blockchain"].blocks) - 2*numOutliers - 1)/(listOfTimes[-numOutliers] - listOfTimes[numOutliers])
+                ratio = ratio / target
+                self.assertEqual(nelly.diff, ratio*oldDiff)
+            elif mode == "MOM:expModGauss":
+                # With at least 120 blocks of data...
+                count = 1200
+                bl = []
+                bl.append(copy.deepcopy(bc.blocks[lastIdent].discoTimestamp))
+                parent = bc.blocks[lastIdent].parent
+                count = count - 1
+                while count > 0 and parent is not None:
+                    ident = copy.deepcopy(parent)
+                    bl.append(copy.deepcopy(bc.blocks[ident].discoTimestamp))
+                    parent = bc.blocks[ident].parent
+                    count = count-1
+                if len(bl) > 120:
+                    sk   = skew(bl)
+                    va   = var(bl)
+                    stdv = sqrt(va)
+                    lam  = (1.0/stdv)*(2.0/sk)**(1.0/3.0)
+                else:
+                    lam = targetRate 
+                ratio = lam/targetRate
+                self.assertEqual(nelly.diff, ratio*oldDiff)
+                
+            else:
+                print("what world are you living in?")
+            
+            # Sleep a random time
+            print("Sleeping a random sub-second, working on block " + str(N))
+            deltaT = deltaT*ratio
+            time.sleep(deltaT/5.0)
+            
+                   
+        while N < 3600 and not bail:
+            # Generate new block
+            name = newIdent(N)
+            t = time.time()
+            t += nelly.data["offset"]
+            s = t+random.random()
+            oldDiff = nelly.diff
+            params = {"ident":name, "disco":t, "arriv":s, "parent":lastIdent, "diff":oldDiff}
+            newBlock = Block(params)
+            
+            # Append new block to running list along with creation time
+            listOfBlocks.append(newBlock)
+            listOfTimes.append(copy.deepcopy(t))
+            
+            # Update nelly's blockchain with newBlock
+            nelly.updateBlockchain({newBlock.ident:newBlock})
+            lastIdent = name
+            
+            # Quick check that this worked:
+            self.assertTrue(name in nelly.data["blockchain"].blocks)
+            self.assertEqual(len(nelly.data["blockchain"].blocks), N+1)
+            N = len(nelly.data["blockchain"].blocks)
+        
+            # Update difficulty
+            nelly.updateDifficulty(mode, targetRate = 100.0)
+            
+            # Quick check that this worked:
+            if mode == "Nakamoto":
+                # In this case we take use top block and genesis block
+                ratio = float(2400)/(listOfTimes[-1] - listOfTimes[-2400])
+                self.assertEqual(nelly.diff, ratio*oldDiff)
+            elif mode == "vanSaberhagen":
+                # This case no longer coincides with Nakamoto...
+                numOutliers = len(nelly.data["blockchain"].blocks)//10
+                numOutliers = min(numOutliers, 120)
+                ratio = float(len(nelly.data["blockchain"].blocks) - 2*numOutliers)/(listOfTimes[-numOutliers] - listOfTimes[numOutliers])
+                self.assertEqual(nelly.diff, ratio*oldDiff)
+            elif mode == "MOM:expModGauss":
+                # With at least 120 blocks of data...
+                count = 1200
+                bl = []
+                bl.append(copy.deepcopy(bc.blocks[lastIdent].discoTimestamp))
+                parent = bc.blocks[lastIdent].parent
+                count = count - 1
+                while count > 0 and parent is not None:
+                    ident = copy.deepcopy(parent)
+                    bl.append(copy.deepcopy(bc.blocks[ident].discoTimestamp))
+                    parent = bc.blocks[ident].parent
+                    count = count-1
+                if len(bl) > 120:
+                    sk   = skew(bl)
+                    va   = var(bl)
+                    stdv = sqrt(va)
+                    lam  = (1.0/stdv)*(2.0/sk)**(1.0/3.0)
+                else:
+                    lam = targetRate 
+                ratio = lam/targetRate
+                self.assertEqual(nelly.diff, ratio*oldDiff)
+                
+            else:
+                print("what world are you living in?")
+            
+            # Sleep a random time
+            print("Sleeping a random sub-second, working on block " + str(N))
+            deltaT = deltaT*ratio
+            time.sleep(deltaT/5.0)'''
         
         
 suite = unittest.TestLoader().loadTestsFromTestCase(Test_Node)
diff --git a/source-code/Poisson-Graphs/new/Block.py b/source-code/Poisson-Graphs/new/Block.py
new file mode 100644
index 0000000..dece697
--- /dev/null
+++ b/source-code/Poisson-Graphs/new/Block.py
@@ -0,0 +1,46 @@
+import unittest, random, time
+
+def newIdent(params):
+    nonce = params
+    # Generate new random identity.
+    return hash(str(nonce) + str(random.random()))
+ #### #### #### #### #### #### #### #### #### #### #### #### #### #### #### ####
+class Block(object):
+    '''
+    Each block has: an identity, a timestamp of discovery (possibly false), 
+    has a timestamp of arrival at the local node (possibly unnecessary), a 
+    parent block's identity, and a difficulty score.
+    '''
+    def __init__(self, params={}):
+        self.ident = None
+        self.discoTimestamp = None
+        self.arrivTimestamp = None
+        self.parent = None
+        self.diff = None
+        try:
+            assert len(params)==5
+        except AssertionError:
+            print("Error in Block(): Tried to add a malformed block. We received params = " + str(params) + ", but should have had something of the form {\"ident\":ident, \"disco\":disco, \"arriv\":arriv, \"parent\":parent, \"diff\":diff}.")
+        self.ident = params["ident"]
+        self.discoTimestamp = params["disco"]
+        self.arrivTimestamp = params["arriv"]
+        self.parent = params["parent"]
+        self.diff = params["diff"]
+        
+class Test_Block(unittest.TestCase):
+    def test_b(self):
+        #bill = Block()
+        name = newIdent(0)
+        t = time.time()
+        s = t+1
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        bill = Block(params)
+        self.assertEqual(bill.ident,name)
+        self.assertEqual(bill.discoTimestamp,t)
+        self.assertEqual(bill.arrivTimestamp,t+1)
+        self.assertTrue(bill.parent is None)
+        self.assertEqual(bill.diff,diff)
+        
+suite = unittest.TestLoader().loadTestsFromTestCase(Test_Block)
+unittest.TextTestRunner(verbosity=1).run(suite)
diff --git a/source-code/Poisson-Graphs/new/Block.py~ b/source-code/Poisson-Graphs/new/Block.py~
new file mode 100644
index 0000000..dece697
--- /dev/null
+++ b/source-code/Poisson-Graphs/new/Block.py~
@@ -0,0 +1,46 @@
+import unittest, random, time
+
+def newIdent(params):
+    nonce = params
+    # Generate new random identity.
+    return hash(str(nonce) + str(random.random()))
+ #### #### #### #### #### #### #### #### #### #### #### #### #### #### #### ####
+class Block(object):
+    '''
+    Each block has: an identity, a timestamp of discovery (possibly false), 
+    has a timestamp of arrival at the local node (possibly unnecessary), a 
+    parent block's identity, and a difficulty score.
+    '''
+    def __init__(self, params={}):
+        self.ident = None
+        self.discoTimestamp = None
+        self.arrivTimestamp = None
+        self.parent = None
+        self.diff = None
+        try:
+            assert len(params)==5
+        except AssertionError:
+            print("Error in Block(): Tried to add a malformed block. We received params = " + str(params) + ", but should have had something of the form {\"ident\":ident, \"disco\":disco, \"arriv\":arriv, \"parent\":parent, \"diff\":diff}.")
+        self.ident = params["ident"]
+        self.discoTimestamp = params["disco"]
+        self.arrivTimestamp = params["arriv"]
+        self.parent = params["parent"]
+        self.diff = params["diff"]
+        
+class Test_Block(unittest.TestCase):
+    def test_b(self):
+        #bill = Block()
+        name = newIdent(0)
+        t = time.time()
+        s = t+1
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        bill = Block(params)
+        self.assertEqual(bill.ident,name)
+        self.assertEqual(bill.discoTimestamp,t)
+        self.assertEqual(bill.arrivTimestamp,t+1)
+        self.assertTrue(bill.parent is None)
+        self.assertEqual(bill.diff,diff)
+        
+suite = unittest.TestLoader().loadTestsFromTestCase(Test_Block)
+unittest.TextTestRunner(verbosity=1).run(suite)
diff --git a/source-code/Poisson-Graphs/new/Blockchain.py b/source-code/Poisson-Graphs/new/Blockchain.py
new file mode 100644
index 0000000..97a3ba2
--- /dev/null
+++ b/source-code/Poisson-Graphs/new/Blockchain.py
@@ -0,0 +1,1142 @@
+from Block import *
+import math
+from scipy.stats import *
+from numpy import *
+from copy import deepcopy
+
+class Blockchain(object):
+    ''' 
+    Not a true blockchain, of course, but tracks block objects (timestamps) as above.
+    Each node should be responsible for finding the chain with most cumulative work.
+    Right now we assume Nakamoto consensus (konsensnakamoto).
+    '''
+    def __init__(self, params=[], verbosity=True):
+        self.blocks = {}
+        self.leaves = {}
+        self.miningIdents = None
+        self.mIdent = None
+        self.verbose = verbosity
+        self.diff = None
+        self.targetRate = None
+                
+    def addBlock(self, blockToAdd, mode="Nakamoto", targetRate=1.0/600000.0):
+        # In our model we assume difficulty scores of blocks are correct (otherwise they would
+        # be rejected in the real life network, and we aren't trying to model spam attacks).
+        assert blockToAdd.ident not in self.blocks
+        if len(self.blocks)==0:
+            # In this case, blockToAdd is a genesis block, so we set difficulty
+            self.diff = deepcopy(blockToAdd.diff)
+            
+        self.blocks.update({blockToAdd.ident:blockToAdd})
+        self.leaves.update({blockToAdd.ident:blockToAdd})
+        if blockToAdd.parent in self.leaves:
+            del self.leaves[blockToAdd.parent]
+        self.whichLeaf()
+        return self.computeDifficulty(mode, targetRate)
+            
+    def whichLeaf(self):
+        # Determine which leaf shall be the parent leaf.
+        # If the chain has forked *ever* this will not be the case.
+        maxCumDiff = 0.0
+        self.miningIdents = []
+        for ident in self.leaves:
+            tempCumDiff = 0.0
+            thisBlockIdent = ident
+            tempCumDiff += self.blocks[thisBlockIdent].diff
+            while self.blocks[thisBlockIdent].parent is not None:
+                thisBlockIdent = self.blocks[thisBlockIdent].parent
+                tempCumDiff += self.blocks[thisBlockIdent].diff
+            if tempCumDiff > maxCumDiff:
+                # If more than one leaf ties for maxCumDiff, each node in the 
+                # network should pick one of these two arbitrarily. Since we 
+                # are storing each blockchain in a hash table (unordered!), for 
+                # each node in the network that observes a tie, each possible leaf
+                # is equally likely to have been the first one found! So
+                # we don't need to do anything for the node to select which chain
+                # to work off of.
+                self.miningIdents = [ident]
+                maxCumDiff = tempCumDiff
+            elif tempCumDiff == maxCumDiff:
+                self.miningIdents.append(ident)
+            #print("leaf ident = ", str(ident), ", and tempCumDiff = ", str(tempCumDiff), " and maxCumDiff = ", str(maxCumDiff))
+        assert len(self.miningIdents) > 0
+        self.mIdent = random.choice(self.miningIdents)
+        
+    
+    # 1 block in 6*10^5 milliseconds=10min
+    def computeDifficulty(self, mode="Nakamoto", targetRate=1.0/600000.0):
+        result = None
+        if mode=="Nakamoto":
+            # Use MLE estimate of poisson process, compare to targetRate, update by multiplying by resulting ratio.
+            #if self.verbose:
+            #    print("Beginning update of difficulty with Nakamoto method")
+            count = 2016
+            #if self.verbose:
+            #    print("Checking that blockchain is 2016*n blocks long and some mining identity has been set")
+            if len(self.blocks) % 2016 == 0 and len(self.miningIdents) > 0:
+                ident = self.mIdent
+                topTime = deepcopy(self.blocks[ident].discoTimestamp)
+                parent = self.blocks[ident].parent
+                count = count - 1
+                touched = False
+                while count > 0 and parent is not None:
+                    ident = deepcopy(parent)
+                    parent = self.blocks[ident].parent
+                    count = count - 1
+                    touched = True
+                if not touched:
+                    mleDiscoRate = targetRate
+                else:
+                    botTime = deepcopy(self.blocks[ident].discoTimestamp)
+                
+                    # Algebra is okay:
+                    assert topTime != botTime
+                    
+                    # MLE estimate of arrivals per second:
+                    mleDiscoRate = float(2015)/float(topTime - botTime)
+                    
+                    # Rates can't be negative, but this estimate could be (although it's highly unlikely given Bitcoin's standard choices
+                    # of difficulty update rate, etc.
+                    mleDiscoRate = abs(mleDiscoRate) 
+                    
+                    if self.verbose:
+                        print("MLE disco rate = " + str(mleDiscoRate) + " and targetRate = " + str(targetRate))
+                    # Rate must be positive... so the MLE for block arrival rate
+                    # assuming a Poisson process _is not even well-defined_ as
+                    # an estimate for block arrival rate assuming timestamps are
+                    # inaccurately reported!
+                    
+                    # We use it nonetheless.
+                
+                if self.verbose:
+                    print("MLE discovery rate = " + str(mleDiscoRate))
+                    print("Difficulty before adjustment = " + str(self.diff))
+                
+                # Update difficulty multiplicatively
+                self.diff = self.diff*mleDiscoRate/targetRate
+                
+                if self.verbose:
+                    print("Difficulty after adjustment = ", str(self.diff))
+                
+        elif mode=="vanSaberhagen":
+            # Similar to above, except use 1200 blocks, discard top 120 and bottom 120 after sorting.
+            # 4 minute blocks in the original cryptonote, I believe... targetRate = 1.0/
+            # 4 minutes/period, 60 seconds/minute ~ 240 seconds/period
+            # assert targetRate==1.0/240.0
+            count = 1200
+            #print(self.diff)
+            assert self.diff != 0.0
+            if len(self.blocks) > 120 and len(self.miningIdents) > 0:
+                ident = self.mIdent
+                bl = []
+                bl.append(deepcopy(self.blocks[ident].discoTimestamp))
+                parent = self.blocks[ident].parent
+                count = count - 1
+                while count > 0 and parent is not None:
+                    ident = deepcopy(parent)
+                    bl.append(deepcopy(self.blocks[ident].discoTimestamp))
+                    parent = self.blocks[ident].parent
+                    count = count-1
+                # sort    
+                bl = sorted(bl)
+                assert len(bl)<=1200
+                
+                #print("Sample size = " + str(len(bl)))
+                # remove 10 and 90 %-iles
+                numOutliers = math.ceil(float(len(bl))/float(10))
+                assert numOutliers <= 120
+                #print("Number of outliers = " + str(numOutliers))
+                oldBL = deepcopy(bl)
+                if numOutliers > 0:
+                    bl = bl[numOutliers:-numOutliers]
+                #if numOutliers == 120:
+                #    print("\n\nSORTED TS LIST = " + str(oldBL) + "\nModified list = " + str(bl))
+                    
+                
+                # get topTime and botTime
+                #if self.verbose:
+                #    print("bl[0] = " + str(bl[0]) + ",\tbl[-1] = " + str(bl[-1]))
+                topTime = bl[-1]
+                botTime = bl[0]
+                result = [float(topTime - botTime)]
+                #print(topTime - botTime)
+                #if self.verbose:
+                #    print("list of timestamps = " + str(bl))
+                #    print("topTime = " + str(bl[-1]))
+                #    print("botTime = " + str(bl[0]))
+                
+                # Assert algebra will work
+                # 1200 - 2*120 = 1200 - 240 = 960
+                assert 0 < len(bl) and len(bl) < 961
+                assert topTime - botTime >= 0.0
+                result.append(len(bl)-1)
+                # Sort of the MLE: # blocks/difference in reported times
+                # But not the MLE, since the reported times may not be 
+                # the actual times, the "difference in reported times" != 
+                # "ground truth difference in block discoery times" in general
+                if len(bl)==0:
+                    print("WOOP WOOP NO TIMESTAMPS WTF? We have " + str(len(self.blocks)) + " blocks available, and we are counting " + str(2*numOutliers) + " as outliers. bl = " + str(bl)) 
+                naiveDiscoRate = float(len(bl)-1)/float(topTime - botTime)
+                
+                # How much should difficulty change?
+                assert naiveDiscoRate != 0.0
+                assert targetRate != 0.0 
+                assert self.diff != 0.0
+                self.diff = self.diff*naiveDiscoRate/targetRate
+                
+        elif mode=="MOM:expModGauss":
+            # Similar to "vanSaberhagen" except with 2-minute blocks and
+            # we attempt to take into account that "difference in timestamps" 
+            # can be negative by:
+            # 1) insisting that the ordering induced by the blockchain and
+            # 2) modeling timestamps as exponentially modified gaussian.
+            # If timestamps are T = X + Z where X is exponentially dist-
+            # ributed with parameter lambda and Z is some Gaussian 
+            # noise with average mu and variance sigma2, then we can est-
+            # imate sigma2, mu, and lambda:
+            #       mu     ~ mean - stdev*(skewness/2)**(1.0/3.0)
+            #       sigma2 ~ variance*(1-(skewness/2)**(2.0/3.0))
+            #       lambda ~ (1.0/(stdev))*(2/skewness)**(1.0/3.0)
+            #assert targetRate==1.0/120.0
+            
+            # Really a trash metric unless sample sizes are huge.
+            count = 1200
+            ident = self.mIdent
+            bl = []
+            bl.append(deepcopy(self.blocks[ident].discoTimestamp))
+            parent = self.blocks[ident].parent
+            count = count - 1
+            while count > 0 and parent is not None:
+                ident = deepcopy(parent)
+                bl.append(deepcopy(self.blocks[ident].discoTimestamp))
+                parent = self.blocks[ident].parent
+                count = count-1
+            if len(bl) > 120:
+                sk   = abs(skew(bl))
+                va   = var(bl)
+                stdv = sqrt(va)
+                lam  = (1.0/stdv)*(2.0/sk)**(1.0/3.0)
+            else:
+                lam = targetRate # we will not change difficulty unless we have at least 120 blocks of data (arbitrarily selected)
+            self.diff = self.diff*(lam/targetRate)
+        elif mode=="reciprocalOfMedian":
+            # In this mode we use a bitcoin-style metric except instead of 1/average inter-arrival time
+            # we use 1/median magnitude of inter-arrival time.
+            # And updated each block like with monero instead of every 2016 blocks like bitcoin.
+            # We assume a sample size of only 600 blocks for now
+            count = 600
+            interArrivals = []
+            if len(self.blocks) < count:
+                estDiscoRate = targetRate
+            elif len(self.miningIdents) > 0:
+                ident = self.mIdent
+                parent = self.blocks[ident].parent
+                if parent is not None:
+                    dT = abs(self.blocks[ident].discoTimestamp - self.blocks[parent].discoTimestamp)
+                    interArrivals.append(dT)
+                count = count - 1
+                touched = False
+                while count > 0 and parent is not None:
+                    ident = deepcopy(parent)
+                    parent = self.blocks[ident].parent
+                    if parent is not None:
+                        dT = abs(self.blocks[ident].discoTimestamp - self.blocks[parent].discoTimestamp)
+                        interArrivals.append(dT)
+                    count = count - 1
+                    touched = True
+                if not touched:
+                    estDiscoRate = targetRate
+                else:
+                    estDiscoRate = 1.0/median(interArrivals)
+                    if self.verbose:
+                        print("Est disco rate = " + str(estDiscoRate) + " and targetRate = " + str(targetRate))
+                    
+                
+                if self.verbose:
+                    print("MLE discovery rate = " + str(estDiscoRate))
+                    print("Difficulty before adjustment = " + str(self.diff))
+                
+                # Update difficulty multiplicatively
+                self.diff = self.diff*estDiscoRate/targetRate
+                
+                if self.verbose:
+                    print("Difficulty after adjustment = ", str(self.diff))
+        else:
+            print("Error, invalid difficulty mode entered.")
+        return result
+           
+class Test_Blockchain(unittest.TestCase):
+    def test_addBlock(self):
+        bill = Blockchain([], verbosity=True)
+        mode="Nakamoto"
+        tr = 1.0/100.0
+        bill.targetRate = tr
+        
+        name = newIdent(0)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        
+        self.assertEqual(genesis.ident,name)
+        self.assertEqual(genesis.discoTimestamp,t)
+        self.assertEqual(genesis.arrivTimestamp,s)
+        self.assertTrue(genesis.parent is None)
+        self.assertEqual(genesis.diff,diff)
+        
+        bill.addBlock(genesis, mode, tr)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.ident in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(genesis.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),1)
+        
+        name = newIdent(1)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
+        blockA = Block(params)
+        bill.addBlock(blockA, mode, tr)
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        self.assertTrue(genesis.ident not in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(blockA.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),2)
+        
+        
+        
+        
+        
+        bill = Blockchain([], verbosity=True)
+        mode="vanSaberhagen"
+        tr = 1.0/100.0
+        bill.targetRate = tr
+        
+        name = newIdent(0)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        
+        self.assertEqual(genesis.ident,name)
+        self.assertEqual(genesis.discoTimestamp,t)
+        self.assertEqual(genesis.arrivTimestamp,s)
+        self.assertTrue(genesis.parent is None)
+        self.assertEqual(genesis.diff,diff)
+        
+        bill.addBlock(genesis, mode, tr)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.ident in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(genesis.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),1)
+        
+        name = newIdent(1)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
+        blockA = Block(params)
+        bill.addBlock(blockA, mode, tr)
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        self.assertTrue(genesis.ident not in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(blockA.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),2)
+        
+        
+        
+        
+        
+        bill = Blockchain([], verbosity=True)
+        mode="MOM:expModGauss"
+        tr = 1.0/100.0
+        bill.targetRate = tr
+        
+        name = newIdent(0)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        
+        self.assertEqual(genesis.ident,name)
+        self.assertEqual(genesis.discoTimestamp,t)
+        self.assertEqual(genesis.arrivTimestamp,s)
+        self.assertTrue(genesis.parent is None)
+        self.assertEqual(genesis.diff,diff)
+        
+        bill.addBlock(genesis, mode, tr)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.ident in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(genesis.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),1)
+        
+        name = newIdent(1)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
+        blockA = Block(params)
+        bill.addBlock(blockA, mode, tr)
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        self.assertTrue(genesis.ident not in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(blockA.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),2)
+        
+        
+    def test_bc(self):
+        bill = Blockchain([], verbosity=True)
+        mode="Nakamoto"
+        tr = 1.0/100.0
+        bill.targetRate = tr
+        
+        name = newIdent(0)
+        t = time.time()
+        s = t+1
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        
+        self.assertEqual(genesis.ident,name)
+        self.assertEqual(genesis.discoTimestamp,t)
+        self.assertEqual(genesis.arrivTimestamp,t+1)
+        self.assertTrue(genesis.parent is None)
+        self.assertEqual(genesis.diff,diff)
+        
+        bill.addBlock(genesis, mode, tr)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.ident in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(genesis.ident, bill.miningIdents[0])
+        
+        name = newIdent(1)
+        t = time.time()
+        s = t+1
+        diff = 2.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
+        blockA = Block(params)
+        bill.addBlock(blockA, mode, tr)
+        
+        #bill.whichLeaf()
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        self.assertFalse(genesis.ident in bill.leaves)
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(blockA.ident, bill.miningIdents[0])
+        
+        name = newIdent(1)
+        t = time.time()
+        s = t+1
+        diff = 2.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
+        blockB = Block(params)
+        bill.addBlock(blockB, mode, tr)
+        
+        self.assertTrue(blockB.ident in bill.blocks)
+        self.assertTrue(blockB.ident in bill.leaves)
+        self.assertEqual(bill.blocks[blockB.ident].parent, genesis.ident)
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        self.assertEqual(bill.blocks[blockA.ident].parent, genesis.ident)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertFalse(genesis.ident in bill.leaves)
+        self.assertTrue(bill.blocks[genesis.ident].parent is None)
+        
+        #bill.whichLeaf()
+        #print(bill.miningIdents)
+        
+        self.assertEqual(type(bill.miningIdents), type([]))
+        self.assertTrue(len(bill.miningIdents), 2)
+        
+        name = newIdent(2)
+        t = time.time()
+        diff = 3.14159
+        params = {"ident":name, "disco":t, "arriv":s, "parent":blockB.ident, "diff":diff}
+        blockC = Block(params)
+        bill.addBlock(blockC, mode, tr)
+        
+        self.assertTrue(blockC.ident in bill.blocks)
+        self.assertTrue(blockC.ident in bill.leaves)
+        
+        self.assertTrue(blockB.ident in bill.blocks)
+        self.assertFalse(blockB.ident in bill.leaves)
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertFalse(genesis.ident in bill.leaves)
+        
+        #bill.whichLeaf()
+        
+        #for blockIdent in bill.blocks:
+        #    ident = bill.blocks[blockIdent].ident
+        #    disco = bill.blocks[blockIdent].discoTimestamp
+        #    arriv = bill.blocks[blockIdent].arrivTimestamp
+        #    parent = bill.blocks[blockIdent].parent
+        #    diff = bill.blocks[blockIdent].diff
+        #    print(str(ident) + ", " + str(disco) + ", " + str(arriv) + ", " + str(parent) + ", " + str(diff) + ", " + str() + "\n")
+        #print(bill.miningIdents)
+        self.assertEqual(len(bill.miningIdents), 1)
+        self.assertEqual(bill.miningIdents[0], blockC.ident)
+    '''  
+    def test_median(self):
+        # TODO: everything.
+        mode = "reciprocalOfMedian"
+        tr = 1.0 # one block per millisecond why not
+        deltaT = 1.0 # let's just make this easy
+        bill = Blockchain([], verbosity=True)
+        bill.targetRate = tr
+        
+        with open("outputM.txt", "w") as writeFile:
+            # We will send (t, a, diff) to writeFile.
+            writeFile.write("time,rateConstant,difficulty\n")
+            name = newIdent(0)
+            t = 0.0
+            s = 0.0
+            diff = 1.0
+            params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+            genesis = Block(params)
+            
+            self.assertEqual(genesis.ident,name)
+            self.assertEqual(genesis.discoTimestamp,t)
+            self.assertEqual(genesis.arrivTimestamp,s)
+            self.assertTrue(genesis.parent is None)
+            self.assertEqual(genesis.diff,diff)
+            
+            bill.addBlock(genesis, mode, tr)
+            a = 1.0
+            b = 1.0/a
+            
+            writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")
+            
+            self.assertTrue(genesis.ident in bill.blocks)
+            self.assertTrue(genesis.ident in bill.leaves)
+            self.assertEqual(len(bill.miningIdents),1)
+            self.assertEqual(genesis.ident, bill.miningIdents[0])
+            
+            parent = genesis.ident
+            oldDiff = bill.diff
+            
+            while len(bill.blocks)<601:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                self.assertEqual(bill.diff, oldDiff)
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                bill.addBlock(newBlock, mode, tr)
+                
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")   
+                parent = newName
+                oldDiff = bill.diff
+            
+            a = 1.01 # slightly slower blocks, median won't change until half the data is corrupted!
+            b = 1.0/a
+            while len(bill.blocks)<899:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                self.assertEqual(bill.diff, oldDiff)
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                bill.addBlock(newBlock, mode, tr)
+                self.assertEqual(bill.diff, oldDiff)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")   
+                parent = newName
+                oldDiff = bill.diff
+                
+            # One more block and our median inter-arrival time is deltaT*(1.0+a)/2.0 
+            # and so estRate = 1/median = (2.0/(1.0+a))/deltaT, whereas before it was just
+            # 1/deltaT. So estRate/targetRate = 2.0/(1.0+a)
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            self.assertEqual(bill.diff, oldDiff)
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr)
+            err = bill.diff - oldDiff*2.0/(1.0+a)
+            self.assertTrue(err*err < 10**-15)
+            writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")   
+            parent = newName
+            oldDiff = bill.diff
+                
+            # One more block and our median inter-arrival time is deltaT*a 
+            # and so estRate = 1/median = (1.0/a)/deltaT, whereas before it was just
+            # 1/deltaT. So estRate/targetRate = 1.0/a = b
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            self.assertEqual(bill.diff, oldDiff)
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr)
+            err = bill.diff - oldDiff*b
+            self.assertTrue(err*err < 10**-15)
+            writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")   
+            parent = newName
+            oldDiff = bill.diff
+            
+            # Note that until the median changes again, this estimated block arrival rate
+            # does not change. This may be true even if a lot of new data has come in. 
+            # It is possible that the same pair of blocks remain the median inter-arrival
+            # magnitude for the entire time both blocks are in the sample size.
+            # During this period of time, difficulty will update multiplicatively, so
+            # will either exponentially grow or shrink.
+            # In other words, this model can be looked at as: exponential change over
+            # time with a rate proportional to the deviation between the median and
+            # the target inter-arrival rates.
+            
+            
+                
+              
+    
+    def test_mine(self):
+        # TODO: everything.
+        mode = "MOM:expModGauss"
+        tr = 1.0/120000.0 # one block per two minutes
+        deltaT = 120000.0
+        bill = Blockchain([], verbosity=True)
+        bill.targetRate = tr
+        
+        with open("outputM.txt", "w") as writeFile:
+            # We will send (t, a, diff, ratio, awayFromOne) to writeFile.
+            writeFile.write("time,rateConstant,difficulty\n")
+            name = newIdent(0)
+            t = 0.0
+            s = 0.0
+            diff = 1.0
+            params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+            genesis = Block(params)
+            
+            self.assertEqual(genesis.ident,name)
+            self.assertEqual(genesis.discoTimestamp,t)
+            self.assertEqual(genesis.arrivTimestamp,s)
+            self.assertTrue(genesis.parent is None)
+            self.assertEqual(genesis.diff,diff)
+            
+            bill.addBlock(genesis, mode, tr)
+            a = 1.0
+            b = 1.0/a
+            
+            writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")
+            
+            self.assertTrue(genesis.ident in bill.blocks)
+            self.assertTrue(genesis.ident in bill.leaves)
+            self.assertEqual(len(bill.miningIdents),1)
+            self.assertEqual(genesis.ident, bill.miningIdents[0])
+            
+            parent = genesis.ident
+            oldDiff = bill.diff
+            
+            while len(bill.blocks)<120:
+                # Our metric divides by skewness. In reality, this is zero with
+                # probability zero. But for our tests, it's assured. So we
+                # will perturb each arrival by a small, up-to-half-percent
+                # variation to ensure a nonzero skewness without altering things
+                # too much.
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a*(1.0 + (2.0*random.random() - 1.0)/100.0)
+                s += deltaT*a*(1.0 + (2.0*random.random() - 1.0)/100.0)
+                self.assertEqual(bill.diff, oldDiff)
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                bill.addBlock(newBlock, mode, tr)
+                
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")   
+                parent = newName
+                oldDiff = bill.diff
+                
+            # Just one more block and difficulty should be computed for the first time.
+            print("Just one more block and difficulty should be computed for the first time.")
+            self.assertEqual(bill.diff, oldDiff)
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a*(1.0 + (2.0*random.random() - 1.0)/100.0)
+            s += deltaT*a*(1.0 + (2.0*random.random() - 1.0)/100.0)
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr) 
+            writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")
+            parent = newName
+            #self.assertEqual(bill.diff, oldDiff)
+              
+            oldDiff = bill.diff
+            
+            # what if we add a bunch of blocks this way?
+            # In the case of a static hash rate, I suppose we hope to not
+            # vary too far from a multiplicative factor of 1.0, or rather
+            # a constant difficulty.
+            
+            while len(bill.blocks)<200:
+                # Our metric divides by skewness. In reality, this is zero with
+                # probability zero. But for our tests, it's assured. So we
+                # will perturb each arrival by a small, up-to-half-percent
+                # variation to ensure a nonzero skewness without altering things
+                # too much.
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a*(1.0 + (2.0*random.random() - 1.0)/100.0)
+                s += deltaT*a*(1.0 + (2.0*random.random() - 1.0)/100.0)
+                self.assertEqual(bill.diff, oldDiff)
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                bill.addBlock(newBlock, mode, tr)
+                
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")   
+                parent = newName
+                oldDiff = bill.diff
+              
+       
+    
+    def test_vs(self):
+        # TODO: Still must test that outliers are being removed "appropriately" according to specifications
+        # TODO: Test that scrambled lists of timestamps produce the same difficulty estimate.
+        # TODO: Show that in the case of homogeneous poisson processes, unusual estimates are a little
+        # more common than in the Nakamoto difficulty (which must be the case because Nakamoto uses
+        # the UMVUE).
+        mode = "vanSaberhagen"
+        tr = 1.0/60000.0 # one block per minute
+        deltaT = 60000.0
+        bill = Blockchain([], verbosity=True)
+        bill.targetRate = tr
+        
+        with open("output.txt", "w") as writeFile:
+            # We will send (t, a, diff, ratio, awayFromOne) to writeFile.
+            writeFile.write("time,rateConstant,difficulty,ratio\n")
+            name = newIdent(0)
+            t = 0.0
+            s = 0.0
+            diff = 1.0
+            params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+            genesis = Block(params)
+            
+            self.assertEqual(genesis.ident,name)
+            self.assertEqual(genesis.discoTimestamp,t)
+            self.assertEqual(genesis.arrivTimestamp,s)
+            self.assertTrue(genesis.parent is None)
+            self.assertEqual(genesis.diff,diff)
+            
+            bill.addBlock(genesis, mode, tr)
+            writeFile.write(str(t) + ",1.0," + str(bill.diff) + ",1.0\n")
+            
+            self.assertTrue(genesis.ident in bill.blocks)
+            self.assertTrue(genesis.ident in bill.leaves)
+            self.assertEqual(len(bill.miningIdents),1)
+            self.assertEqual(genesis.ident, bill.miningIdents[0])
+            self.assertEqual(bill.diff, 1.0)
+            
+            parent = genesis.ident
+            oldDiff = bill.diff
+            a = 1.0
+            b = 1.0/a
+            
+            while len(bill.blocks)<120:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                self.assertEqual(bill.diff, oldDiff)
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                bill.addBlock(newBlock, mode, tr)
+                
+                writeFile.write(str(t) + ",1.0," + str(bill.diff) + ",1.0\n")   
+                parent = newName
+                oldDiff = bill.diff
+                
+            # Just one more block and difficulty should be computed for the first time.
+            print("Just one more block and difficulty should be computed for the first time.")
+            self.assertEqual(bill.diff, oldDiff)
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr) 
+            writeFile.write(str(t) + ",1.0," + str(bill.diff) + ",1.0\n")
+            parent = newName
+            self.assertEqual(bill.diff, oldDiff)
+              
+            oldDiff = bill.diff
+            
+            print("Let's add more blocks at the same rate.")
+            a = 1.0
+            b = 1.0/a
+            
+            while len(bill.blocks)<1200:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + ",1.0," + str(bill.diff) + ",1.0\n")
+                parent = newName
+                self.assertEqual(bill.diff, oldDiff)
+                oldDiff = bill.diff
+            
+            print("Let's add more blocks at a slower rate.")
+            a = 1.1
+            b = 1.0/a
+            
+            # If blocks arrive slightly further apart, difficulty should drop.
+            # However, since vanSaberhagen discards top 10% and bottom 10% of
+            # timestamps, it will take 120 blocks for this change to register
+            # in difficulty.
+            print("If blocks arrive slightly further apart, difficulty should drop. However, since vanSaberhagen discards top 10% and bottom 10% of timestamps, it will take 120 blocks for this change to register in difficulty.")
+            while len(bill.blocks)<1320:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+                parent = newName
+                self.assertEqual(bill.diff, oldDiff)
+                oldDiff = bill.diff
+                
+            print("One more block and difficulty should register a change.")
+            self.assertEqual(bill.diff, oldDiff)
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr) 
+            writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+            parent = newName
+            self.assertTrue(bill.diff < oldDiff)
+            oldDiff = bill.diff
+            
+            # Let's add another fifty blocks at this same rate and verify that difficulty continually
+            # drops.
+            print("Let's add another fifty blocks at this same rate and verify that difficulty continually drops.")
+            a = 1.1
+            b = 1.0/a
+            
+            while len(bill.blocks)<1370:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+                parent = newName
+                self.assertTrue(bill.diff < oldDiff)
+                oldDiff = bill.diff
+                
+            # Now we go back to the target rate. We have 170 slow blocks in the queue and 50 in the sample size. Difficulty will continue to drop for another 120 blocks...
+            print("Now we go back to the target rate. We have 170 slow blocks in the queue and 50 in the sample size. Difficulty will continue to drop for another 120 blocks...")
+            a = 1.0
+            b = 1.0/a
+            
+            while len(bill.blocks)<1490:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+                parent = newName
+                self.assertTrue(bill.diff < oldDiff)
+                oldRatio = bill.diff/oldDiff
+                oldDiff = bill.diff
+                #print(str(result) + ", " + str(bill.diff) + ", " + str(oldDiff))
+                
+            # Now all 170 slow blocks are not only in the queue but in our sample. The *multiplicative factor* between timesteps should be identical for the next 790 blocks.. leading to AN EXPONENTIAL DECAY OF DIFFICULTY.
+            print("Now all 170 slow blocks are not only in the queue but in our sample. The *multiplicative factor* between timesteps should be identical for the next 790 blocks.. leading to AN EXPONENTIAL DECAY OF DIFFICULTY.")
+            a = 1.0
+            b = 1.0/a
+            while len(bill.blocks)<2279:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT
+                s += deltaT
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+                ratio = bill.diff/oldDiff
+                parent = newName
+                err = ratio - oldRatio
+                #print("Difference between last ratio and next ratio:" + str(err))
+                self.assertTrue(err*err < 10**-15)
+                oldDiff = bill.diff
+                oldRatio = ratio
+                
+            print("Now adding a single new block will cause our 170 slow blocks to start dropping out of our sample, so the ratio should start returning to 1.0.")
+            oldAwayFromOne = abs(oldRatio - 1.0) # Ratio should be returning to 1.0 so this difference should go to zero
+            oldAwayFromOne = oldAwayFromOne*oldAwayFromOne
+                
+            # For the next 170 blocks as our perturbed blocks drop out of our sample, our 
+            # estimated block arrival rate will return to "normal" so the multiplicative
+            # difference in difficulty should return to 1.0.
+            print("For the next 170 blocks as our perturbed blocks drop out of our sample, ourestimated block arrival rate will return to normal so the multiplicative difference in difficulty should return to 1.0.")
+            a = 1.0
+            b = 1.0/a
+            while len(bill.blocks)<2449:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+                ratio = bill.diff/oldDiff
+                #print("New ratio = " + str(ratio) + " and oldRatio = " + str(oldRatio))
+                self.assertTrue(ratio > oldRatio)
+                awayFromOne = abs(ratio - 1.0) # Ratio should be returning to 1.0 so this difference should go to zero
+                awayFromOne = awayFromOne*awayFromOne
+                self.assertTrue(awayFromOne < oldAwayFromOne) # This return will be monotonic in our manufactured example.
+                parent = newName
+                oldDiff = bill.diff
+                oldRatio = ratio
+                oldAwayFromOne = awayFromOne
+            
+            
+            # Now difficulty should remain frozen for as long as we like.
+            
+            a = 1.0
+            b = 1.0/a
+            while len(bill.blocks)<2500:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+                parent = newName
+                self.assertEqual(bill.diff, oldDiff)
+                oldDiff = bill.diff
+                
+        
+         
+     
+    def test_nak(self):
+        # Since Nakamoto difficulty is derived from the MLE of the block arrival rate,
+        # we already know how it "should" behave in a poisson process, etc.
+        # TODO: Generate N samples of MLEs of Poisson rates compared to known homog. 
+        # poisson rate, show that the resulting code does not result in unusual measurements
+        # more often than expected.
+        mode = "Nakamoto"
+        tr = 1.0/600000.0
+        deltaT = 600000.0
+        bill = Blockchain([], verbosity=True)
+        bill.targetRate = tr
+        # Bitcoin updating at 1 block per 10 minutes
+        
+        name = newIdent(0)
+        t = 0.0
+        s = 0.0
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        
+        self.assertEqual(genesis.ident,name)
+        self.assertEqual(genesis.discoTimestamp,t)
+        self.assertEqual(genesis.arrivTimestamp,s)
+        self.assertTrue(genesis.parent is None)
+        self.assertEqual(genesis.diff,diff)
+        
+        bill.addBlock(genesis, mode, tr)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.ident in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(genesis.ident, bill.miningIdents[0])
+        self.assertEqual(bill.diff, 1.0)
+        
+        parent = genesis.ident
+        oldDiff = bill.diff
+        i = 1
+        
+        while len(bill.blocks)<2016*i-1:
+            newName = newIdent(len(bill.blocks))
+            t += deltaT
+            s += deltaT
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr)
+            parent = newName
+            
+        # Just one more block and difficulty should recompute.
+        print("Just one more block and difficulty should recompute.")
+        self.assertEqual(bill.diff, oldDiff)
+        newName = newIdent(len(bill.blocks))
+        t += deltaT
+        s += deltaT
+        diff = bill.diff
+        params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+        newBlock = Block(params)
+        bill.addBlock(newBlock, mode, tr) 
+        parent = newName
+        self.assertEqual(bill.diff, oldDiff)
+          
+        oldDiff = bill.diff
+        i += 1
+        
+        while len(bill.blocks)<2016*i-1:
+            newName = newIdent(len(bill.blocks))
+            t += deltaT
+            s += deltaT
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            
+            bill.addBlock(newBlock, mode, tr)
+            parent = newName
+        
+        # Just one more block and difficulty should recompute.
+        print("Just one more block and difficulty should again recompute.")
+        self.assertEqual(bill.diff, oldDiff)
+        newName = newIdent(len(bill.blocks))
+        t += deltaT
+        s += deltaT
+        diff = bill.diff
+        params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+        newBlock = Block(params)
+        bill.addBlock(newBlock, mode, tr) 
+        parent = newName
+        self.assertEqual(bill.diff, oldDiff)
+          
+        oldDiff = bill.diff
+        i += 1
+        a = 1.1
+        b = 1.0/a
+        
+        # If blocks arrive slightly further apart, difficulty should drop.
+        while len(bill.blocks)<2016*i-1:
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            
+            bill.addBlock(newBlock, mode, tr)
+            parent = newName
+            
+        print("Just one more block and difficulty will go down.")
+        
+        self.assertEqual(bill.diff, oldDiff)
+        newName = newIdent(len(bill.blocks))
+        t += deltaT*a
+        s += deltaT*a
+        diff = bill.diff
+        params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+        newBlock = Block(params)
+        bill.addBlock(newBlock, mode, tr) 
+        parent = newName
+        err = abs(bill.diff - oldDiff*b)
+        self.assertTrue(err*err < 10**-15)
+        oldDiff = bill.diff
+        i += 1
+            
+         
+        # If blocks then arrive on target, difficulty should freeze.
+        a = 1.0
+        b = 1.0/a
+        while len(bill.blocks)<2016*i-1:
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            
+            bill.addBlock(newBlock, mode, tr)
+            parent = newName
+            
+        self.assertEqual(bill.diff, oldDiff)
+        newName = newIdent(len(bill.blocks))
+        t += deltaT*a
+        s += deltaT*a
+        diff = bill.diff
+        params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+        newBlock = Block(params)
+        bill.addBlock(newBlock, mode, tr) 
+        parent = newName
+        self.assertEqual(bill.diff, oldDiff)
+        oldDiff = bill.diff
+        i += 1
+        
+        # If blocks arrive too close together, difficulty should increase.
+        a = 0.9
+        b = 1.0/a
+        while len(bill.blocks)<2016*i-1:
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            
+            bill.addBlock(newBlock, mode, tr)
+            parent = newName
+            
+        print("Just one more block and difficulty should go up.")
+        self.assertEqual(bill.diff, oldDiff)
+        newName = newIdent(len(bill.blocks))
+        t += deltaT*a
+        s += deltaT*a
+        diff = bill.diff
+        params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+        newBlock = Block(params)
+        bill.addBlock(newBlock, mode, tr) 
+        parent = newName
+        err = abs(bill.diff - oldDiff*b)
+        self.assertTrue(err*err < 10**-15)
+    '''
+            
+        
+       
+        
+suite = unittest.TestLoader().loadTestsFromTestCase(Test_Blockchain)
+unittest.TextTestRunner(verbosity=1).run(suite)
diff --git a/source-code/Poisson-Graphs/new/Blockchain.py~ b/source-code/Poisson-Graphs/new/Blockchain.py~
new file mode 100644
index 0000000..97a3ba2
--- /dev/null
+++ b/source-code/Poisson-Graphs/new/Blockchain.py~
@@ -0,0 +1,1142 @@
+from Block import *
+import math
+from scipy.stats import *
+from numpy import *
+from copy import deepcopy
+
+class Blockchain(object):
+    ''' 
+    Not a true blockchain, of course, but tracks block objects (timestamps) as above.
+    Each node should be responsible for finding the chain with most cumulative work.
+    Right now we assume Nakamoto consensus (konsensnakamoto).
+    '''
+    def __init__(self, params=[], verbosity=True):
+        self.blocks = {}
+        self.leaves = {}
+        self.miningIdents = None
+        self.mIdent = None
+        self.verbose = verbosity
+        self.diff = None
+        self.targetRate = None
+                
+    def addBlock(self, blockToAdd, mode="Nakamoto", targetRate=1.0/600000.0):
+        # In our model we assume difficulty scores of blocks are correct (otherwise they would
+        # be rejected in the real life network, and we aren't trying to model spam attacks).
+        assert blockToAdd.ident not in self.blocks
+        if len(self.blocks)==0:
+            # In this case, blockToAdd is a genesis block, so we set difficulty
+            self.diff = deepcopy(blockToAdd.diff)
+            
+        self.blocks.update({blockToAdd.ident:blockToAdd})
+        self.leaves.update({blockToAdd.ident:blockToAdd})
+        if blockToAdd.parent in self.leaves:
+            del self.leaves[blockToAdd.parent]
+        self.whichLeaf()
+        return self.computeDifficulty(mode, targetRate)
+            
+    def whichLeaf(self):
+        # Determine which leaf shall be the parent leaf.
+        # If the chain has forked *ever* this will not be the case.
+        maxCumDiff = 0.0
+        self.miningIdents = []
+        for ident in self.leaves:
+            tempCumDiff = 0.0
+            thisBlockIdent = ident
+            tempCumDiff += self.blocks[thisBlockIdent].diff
+            while self.blocks[thisBlockIdent].parent is not None:
+                thisBlockIdent = self.blocks[thisBlockIdent].parent
+                tempCumDiff += self.blocks[thisBlockIdent].diff
+            if tempCumDiff > maxCumDiff:
+                # If more than one leaf ties for maxCumDiff, each node in the 
+                # network should pick one of these two arbitrarily. Since we 
+                # are storing each blockchain in a hash table (unordered!), for 
+                # each node in the network that observes a tie, each possible leaf
+                # is equally likely to have been the first one found! So
+                # we don't need to do anything for the node to select which chain
+                # to work off of.
+                self.miningIdents = [ident]
+                maxCumDiff = tempCumDiff
+            elif tempCumDiff == maxCumDiff:
+                self.miningIdents.append(ident)
+            #print("leaf ident = ", str(ident), ", and tempCumDiff = ", str(tempCumDiff), " and maxCumDiff = ", str(maxCumDiff))
+        assert len(self.miningIdents) > 0
+        self.mIdent = random.choice(self.miningIdents)
+        
+    
+    # 1 block in 6*10^5 milliseconds=10min
+    def computeDifficulty(self, mode="Nakamoto", targetRate=1.0/600000.0):
+        result = None
+        if mode=="Nakamoto":
+            # Use MLE estimate of poisson process, compare to targetRate, update by multiplying by resulting ratio.
+            #if self.verbose:
+            #    print("Beginning update of difficulty with Nakamoto method")
+            count = 2016
+            #if self.verbose:
+            #    print("Checking that blockchain is 2016*n blocks long and some mining identity has been set")
+            if len(self.blocks) % 2016 == 0 and len(self.miningIdents) > 0:
+                ident = self.mIdent
+                topTime = deepcopy(self.blocks[ident].discoTimestamp)
+                parent = self.blocks[ident].parent
+                count = count - 1
+                touched = False
+                while count > 0 and parent is not None:
+                    ident = deepcopy(parent)
+                    parent = self.blocks[ident].parent
+                    count = count - 1
+                    touched = True
+                if not touched:
+                    mleDiscoRate = targetRate
+                else:
+                    botTime = deepcopy(self.blocks[ident].discoTimestamp)
+                
+                    # Algebra is okay:
+                    assert topTime != botTime
+                    
+                    # MLE estimate of arrivals per second:
+                    mleDiscoRate = float(2015)/float(topTime - botTime)
+                    
+                    # Rates can't be negative, but this estimate could be (although it's highly unlikely given Bitcoin's standard choices
+                    # of difficulty update rate, etc.
+                    mleDiscoRate = abs(mleDiscoRate) 
+                    
+                    if self.verbose:
+                        print("MLE disco rate = " + str(mleDiscoRate) + " and targetRate = " + str(targetRate))
+                    # Rate must be positive... so the MLE for block arrival rate
+                    # assuming a Poisson process _is not even well-defined_ as
+                    # an estimate for block arrival rate assuming timestamps are
+                    # inaccurately reported!
+                    
+                    # We use it nonetheless.
+                
+                if self.verbose:
+                    print("MLE discovery rate = " + str(mleDiscoRate))
+                    print("Difficulty before adjustment = " + str(self.diff))
+                
+                # Update difficulty multiplicatively
+                self.diff = self.diff*mleDiscoRate/targetRate
+                
+                if self.verbose:
+                    print("Difficulty after adjustment = ", str(self.diff))
+                
+        elif mode=="vanSaberhagen":
+            # Similar to above, except use 1200 blocks, discard top 120 and bottom 120 after sorting.
+            # 4 minute blocks in the original cryptonote, I believe... targetRate = 1.0/
+            # 4 minutes/period, 60 seconds/minute ~ 240 seconds/period
+            # assert targetRate==1.0/240.0
+            count = 1200
+            #print(self.diff)
+            assert self.diff != 0.0
+            if len(self.blocks) > 120 and len(self.miningIdents) > 0:
+                ident = self.mIdent
+                bl = []
+                bl.append(deepcopy(self.blocks[ident].discoTimestamp))
+                parent = self.blocks[ident].parent
+                count = count - 1
+                while count > 0 and parent is not None:
+                    ident = deepcopy(parent)
+                    bl.append(deepcopy(self.blocks[ident].discoTimestamp))
+                    parent = self.blocks[ident].parent
+                    count = count-1
+                # sort    
+                bl = sorted(bl)
+                assert len(bl)<=1200
+                
+                #print("Sample size = " + str(len(bl)))
+                # remove 10 and 90 %-iles
+                numOutliers = math.ceil(float(len(bl))/float(10))
+                assert numOutliers <= 120
+                #print("Number of outliers = " + str(numOutliers))
+                oldBL = deepcopy(bl)
+                if numOutliers > 0:
+                    bl = bl[numOutliers:-numOutliers]
+                #if numOutliers == 120:
+                #    print("\n\nSORTED TS LIST = " + str(oldBL) + "\nModified list = " + str(bl))
+                    
+                
+                # get topTime and botTime
+                #if self.verbose:
+                #    print("bl[0] = " + str(bl[0]) + ",\tbl[-1] = " + str(bl[-1]))
+                topTime = bl[-1]
+                botTime = bl[0]
+                result = [float(topTime - botTime)]
+                #print(topTime - botTime)
+                #if self.verbose:
+                #    print("list of timestamps = " + str(bl))
+                #    print("topTime = " + str(bl[-1]))
+                #    print("botTime = " + str(bl[0]))
+                
+                # Assert algebra will work
+                # 1200 - 2*120 = 1200 - 240 = 960
+                assert 0 < len(bl) and len(bl) < 961
+                assert topTime - botTime >= 0.0
+                result.append(len(bl)-1)
+                # Sort of the MLE: # blocks/difference in reported times
+                # But not the MLE, since the reported times may not be 
+                # the actual times, the "difference in reported times" != 
+                # "ground truth difference in block discoery times" in general
+                if len(bl)==0:
+                    print("WOOP WOOP NO TIMESTAMPS WTF? We have " + str(len(self.blocks)) + " blocks available, and we are counting " + str(2*numOutliers) + " as outliers. bl = " + str(bl)) 
+                naiveDiscoRate = float(len(bl)-1)/float(topTime - botTime)
+                
+                # How much should difficulty change?
+                assert naiveDiscoRate != 0.0
+                assert targetRate != 0.0 
+                assert self.diff != 0.0
+                self.diff = self.diff*naiveDiscoRate/targetRate
+                
+        elif mode=="MOM:expModGauss":
+            # Similar to "vanSaberhagen" except with 2-minute blocks and
+            # we attempt to take into account that "difference in timestamps" 
+            # can be negative by:
+            # 1) insisting that the ordering induced by the blockchain and
+            # 2) modeling timestamps as exponentially modified gaussian.
+            # If timestamps are T = X + Z where X is exponentially dist-
+            # ributed with parameter lambda and Z is some Gaussian 
+            # noise with average mu and variance sigma2, then we can est-
+            # imate sigma2, mu, and lambda:
+            #       mu     ~ mean - stdev*(skewness/2)**(1.0/3.0)
+            #       sigma2 ~ variance*(1-(skewness/2)**(2.0/3.0))
+            #       lambda ~ (1.0/(stdev))*(2/skewness)**(1.0/3.0)
+            #assert targetRate==1.0/120.0
+            
+            # Really a trash metric unless sample sizes are huge.
+            count = 1200
+            ident = self.mIdent
+            bl = []
+            bl.append(deepcopy(self.blocks[ident].discoTimestamp))
+            parent = self.blocks[ident].parent
+            count = count - 1
+            while count > 0 and parent is not None:
+                ident = deepcopy(parent)
+                bl.append(deepcopy(self.blocks[ident].discoTimestamp))
+                parent = self.blocks[ident].parent
+                count = count-1
+            if len(bl) > 120:
+                sk   = abs(skew(bl))
+                va   = var(bl)
+                stdv = sqrt(va)
+                lam  = (1.0/stdv)*(2.0/sk)**(1.0/3.0)
+            else:
+                lam = targetRate # we will not change difficulty unless we have at least 120 blocks of data (arbitrarily selected)
+            self.diff = self.diff*(lam/targetRate)
+        elif mode=="reciprocalOfMedian":
+            # In this mode we use a bitcoin-style metric except instead of 1/average inter-arrival time
+            # we use 1/median magnitude of inter-arrival time.
+            # And updated each block like with monero instead of every 2016 blocks like bitcoin.
+            # We assume a sample size of only 600 blocks for now
+            count = 600
+            interArrivals = []
+            if len(self.blocks) < count:
+                estDiscoRate = targetRate
+            elif len(self.miningIdents) > 0:
+                ident = self.mIdent
+                parent = self.blocks[ident].parent
+                if parent is not None:
+                    dT = abs(self.blocks[ident].discoTimestamp - self.blocks[parent].discoTimestamp)
+                    interArrivals.append(dT)
+                count = count - 1
+                touched = False
+                while count > 0 and parent is not None:
+                    ident = deepcopy(parent)
+                    parent = self.blocks[ident].parent
+                    if parent is not None:
+                        dT = abs(self.blocks[ident].discoTimestamp - self.blocks[parent].discoTimestamp)
+                        interArrivals.append(dT)
+                    count = count - 1
+                    touched = True
+                if not touched:
+                    estDiscoRate = targetRate
+                else:
+                    estDiscoRate = 1.0/median(interArrivals)
+                    if self.verbose:
+                        print("Est disco rate = " + str(estDiscoRate) + " and targetRate = " + str(targetRate))
+                    
+                
+                if self.verbose:
+                    print("MLE discovery rate = " + str(estDiscoRate))
+                    print("Difficulty before adjustment = " + str(self.diff))
+                
+                # Update difficulty multiplicatively
+                self.diff = self.diff*estDiscoRate/targetRate
+                
+                if self.verbose:
+                    print("Difficulty after adjustment = ", str(self.diff))
+        else:
+            print("Error, invalid difficulty mode entered.")
+        return result
+           
+class Test_Blockchain(unittest.TestCase):
+    def test_addBlock(self):
+        bill = Blockchain([], verbosity=True)
+        mode="Nakamoto"
+        tr = 1.0/100.0
+        bill.targetRate = tr
+        
+        name = newIdent(0)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        
+        self.assertEqual(genesis.ident,name)
+        self.assertEqual(genesis.discoTimestamp,t)
+        self.assertEqual(genesis.arrivTimestamp,s)
+        self.assertTrue(genesis.parent is None)
+        self.assertEqual(genesis.diff,diff)
+        
+        bill.addBlock(genesis, mode, tr)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.ident in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(genesis.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),1)
+        
+        name = newIdent(1)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
+        blockA = Block(params)
+        bill.addBlock(blockA, mode, tr)
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        self.assertTrue(genesis.ident not in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(blockA.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),2)
+        
+        
+        
+        
+        
+        bill = Blockchain([], verbosity=True)
+        mode="vanSaberhagen"
+        tr = 1.0/100.0
+        bill.targetRate = tr
+        
+        name = newIdent(0)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        
+        self.assertEqual(genesis.ident,name)
+        self.assertEqual(genesis.discoTimestamp,t)
+        self.assertEqual(genesis.arrivTimestamp,s)
+        self.assertTrue(genesis.parent is None)
+        self.assertEqual(genesis.diff,diff)
+        
+        bill.addBlock(genesis, mode, tr)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.ident in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(genesis.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),1)
+        
+        name = newIdent(1)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
+        blockA = Block(params)
+        bill.addBlock(blockA, mode, tr)
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        self.assertTrue(genesis.ident not in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(blockA.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),2)
+        
+        
+        
+        
+        
+        bill = Blockchain([], verbosity=True)
+        mode="MOM:expModGauss"
+        tr = 1.0/100.0
+        bill.targetRate = tr
+        
+        name = newIdent(0)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        
+        self.assertEqual(genesis.ident,name)
+        self.assertEqual(genesis.discoTimestamp,t)
+        self.assertEqual(genesis.arrivTimestamp,s)
+        self.assertTrue(genesis.parent is None)
+        self.assertEqual(genesis.diff,diff)
+        
+        bill.addBlock(genesis, mode, tr)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.ident in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(genesis.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),1)
+        
+        name = newIdent(1)
+        t = time.time()
+        s = t+random.random()
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
+        blockA = Block(params)
+        bill.addBlock(blockA, mode, tr)
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        self.assertTrue(genesis.ident not in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(blockA.ident, bill.miningIdents[0])
+        self.assertEqual(len(bill.blocks),2)
+        
+        
+    def test_bc(self):
+        bill = Blockchain([], verbosity=True)
+        mode="Nakamoto"
+        tr = 1.0/100.0
+        bill.targetRate = tr
+        
+        name = newIdent(0)
+        t = time.time()
+        s = t+1
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        
+        self.assertEqual(genesis.ident,name)
+        self.assertEqual(genesis.discoTimestamp,t)
+        self.assertEqual(genesis.arrivTimestamp,t+1)
+        self.assertTrue(genesis.parent is None)
+        self.assertEqual(genesis.diff,diff)
+        
+        bill.addBlock(genesis, mode, tr)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.ident in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(genesis.ident, bill.miningIdents[0])
+        
+        name = newIdent(1)
+        t = time.time()
+        s = t+1
+        diff = 2.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
+        blockA = Block(params)
+        bill.addBlock(blockA, mode, tr)
+        
+        #bill.whichLeaf()
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        self.assertFalse(genesis.ident in bill.leaves)
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(blockA.ident, bill.miningIdents[0])
+        
+        name = newIdent(1)
+        t = time.time()
+        s = t+1
+        diff = 2.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":genesis.ident, "diff":diff}
+        blockB = Block(params)
+        bill.addBlock(blockB, mode, tr)
+        
+        self.assertTrue(blockB.ident in bill.blocks)
+        self.assertTrue(blockB.ident in bill.leaves)
+        self.assertEqual(bill.blocks[blockB.ident].parent, genesis.ident)
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        self.assertEqual(bill.blocks[blockA.ident].parent, genesis.ident)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertFalse(genesis.ident in bill.leaves)
+        self.assertTrue(bill.blocks[genesis.ident].parent is None)
+        
+        #bill.whichLeaf()
+        #print(bill.miningIdents)
+        
+        self.assertEqual(type(bill.miningIdents), type([]))
+        self.assertTrue(len(bill.miningIdents), 2)
+        
+        name = newIdent(2)
+        t = time.time()
+        diff = 3.14159
+        params = {"ident":name, "disco":t, "arriv":s, "parent":blockB.ident, "diff":diff}
+        blockC = Block(params)
+        bill.addBlock(blockC, mode, tr)
+        
+        self.assertTrue(blockC.ident in bill.blocks)
+        self.assertTrue(blockC.ident in bill.leaves)
+        
+        self.assertTrue(blockB.ident in bill.blocks)
+        self.assertFalse(blockB.ident in bill.leaves)
+        
+        self.assertTrue(blockA.ident in bill.blocks)
+        self.assertTrue(blockA.ident in bill.leaves)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertFalse(genesis.ident in bill.leaves)
+        
+        #bill.whichLeaf()
+        
+        #for blockIdent in bill.blocks:
+        #    ident = bill.blocks[blockIdent].ident
+        #    disco = bill.blocks[blockIdent].discoTimestamp
+        #    arriv = bill.blocks[blockIdent].arrivTimestamp
+        #    parent = bill.blocks[blockIdent].parent
+        #    diff = bill.blocks[blockIdent].diff
+        #    print(str(ident) + ", " + str(disco) + ", " + str(arriv) + ", " + str(parent) + ", " + str(diff) + ", " + str() + "\n")
+        #print(bill.miningIdents)
+        self.assertEqual(len(bill.miningIdents), 1)
+        self.assertEqual(bill.miningIdents[0], blockC.ident)
+    '''  
+    def test_median(self):
+        # TODO: everything.
+        mode = "reciprocalOfMedian"
+        tr = 1.0 # one block per millisecond why not
+        deltaT = 1.0 # let's just make this easy
+        bill = Blockchain([], verbosity=True)
+        bill.targetRate = tr
+        
+        with open("outputM.txt", "w") as writeFile:
+            # We will send (t, a, diff) to writeFile.
+            writeFile.write("time,rateConstant,difficulty\n")
+            name = newIdent(0)
+            t = 0.0
+            s = 0.0
+            diff = 1.0
+            params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+            genesis = Block(params)
+            
+            self.assertEqual(genesis.ident,name)
+            self.assertEqual(genesis.discoTimestamp,t)
+            self.assertEqual(genesis.arrivTimestamp,s)
+            self.assertTrue(genesis.parent is None)
+            self.assertEqual(genesis.diff,diff)
+            
+            bill.addBlock(genesis, mode, tr)
+            a = 1.0
+            b = 1.0/a
+            
+            writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")
+            
+            self.assertTrue(genesis.ident in bill.blocks)
+            self.assertTrue(genesis.ident in bill.leaves)
+            self.assertEqual(len(bill.miningIdents),1)
+            self.assertEqual(genesis.ident, bill.miningIdents[0])
+            
+            parent = genesis.ident
+            oldDiff = bill.diff
+            
+            while len(bill.blocks)<601:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                self.assertEqual(bill.diff, oldDiff)
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                bill.addBlock(newBlock, mode, tr)
+                
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")   
+                parent = newName
+                oldDiff = bill.diff
+            
+            a = 1.01 # slightly slower blocks, median won't change until half the data is corrupted!
+            b = 1.0/a
+            while len(bill.blocks)<899:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                self.assertEqual(bill.diff, oldDiff)
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                bill.addBlock(newBlock, mode, tr)
+                self.assertEqual(bill.diff, oldDiff)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")   
+                parent = newName
+                oldDiff = bill.diff
+                
+            # One more block and our median inter-arrival time is deltaT*(1.0+a)/2.0 
+            # and so estRate = 1/median = (2.0/(1.0+a))/deltaT, whereas before it was just
+            # 1/deltaT. So estRate/targetRate = 2.0/(1.0+a)
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            self.assertEqual(bill.diff, oldDiff)
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr)
+            err = bill.diff - oldDiff*2.0/(1.0+a)
+            self.assertTrue(err*err < 10**-15)
+            writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")   
+            parent = newName
+            oldDiff = bill.diff
+                
+            # One more block and our median inter-arrival time is deltaT*a 
+            # and so estRate = 1/median = (1.0/a)/deltaT, whereas before it was just
+            # 1/deltaT. So estRate/targetRate = 1.0/a = b
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            self.assertEqual(bill.diff, oldDiff)
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr)
+            err = bill.diff - oldDiff*b
+            self.assertTrue(err*err < 10**-15)
+            writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")   
+            parent = newName
+            oldDiff = bill.diff
+            
+            # Note that until the median changes again, this estimated block arrival rate
+            # does not change. This may be true even if a lot of new data has come in. 
+            # It is possible that the same pair of blocks remain the median inter-arrival
+            # magnitude for the entire time both blocks are in the sample size.
+            # During this period of time, difficulty will update multiplicatively, so
+            # will either exponentially grow or shrink.
+            # In other words, this model can be looked at as: exponential change over
+            # time with a rate proportional to the deviation between the median and
+            # the target inter-arrival rates.
+            
+            
+                
+              
+    
+    def test_mine(self):
+        # TODO: everything.
+        mode = "MOM:expModGauss"
+        tr = 1.0/120000.0 # one block per two minutes
+        deltaT = 120000.0
+        bill = Blockchain([], verbosity=True)
+        bill.targetRate = tr
+        
+        with open("outputM.txt", "w") as writeFile:
+            # We will send (t, a, diff, ratio, awayFromOne) to writeFile.
+            writeFile.write("time,rateConstant,difficulty\n")
+            name = newIdent(0)
+            t = 0.0
+            s = 0.0
+            diff = 1.0
+            params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+            genesis = Block(params)
+            
+            self.assertEqual(genesis.ident,name)
+            self.assertEqual(genesis.discoTimestamp,t)
+            self.assertEqual(genesis.arrivTimestamp,s)
+            self.assertTrue(genesis.parent is None)
+            self.assertEqual(genesis.diff,diff)
+            
+            bill.addBlock(genesis, mode, tr)
+            a = 1.0
+            b = 1.0/a
+            
+            writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")
+            
+            self.assertTrue(genesis.ident in bill.blocks)
+            self.assertTrue(genesis.ident in bill.leaves)
+            self.assertEqual(len(bill.miningIdents),1)
+            self.assertEqual(genesis.ident, bill.miningIdents[0])
+            
+            parent = genesis.ident
+            oldDiff = bill.diff
+            
+            while len(bill.blocks)<120:
+                # Our metric divides by skewness. In reality, this is zero with
+                # probability zero. But for our tests, it's assured. So we
+                # will perturb each arrival by a small, up-to-half-percent
+                # variation to ensure a nonzero skewness without altering things
+                # too much.
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a*(1.0 + (2.0*random.random() - 1.0)/100.0)
+                s += deltaT*a*(1.0 + (2.0*random.random() - 1.0)/100.0)
+                self.assertEqual(bill.diff, oldDiff)
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                bill.addBlock(newBlock, mode, tr)
+                
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")   
+                parent = newName
+                oldDiff = bill.diff
+                
+            # Just one more block and difficulty should be computed for the first time.
+            print("Just one more block and difficulty should be computed for the first time.")
+            self.assertEqual(bill.diff, oldDiff)
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a*(1.0 + (2.0*random.random() - 1.0)/100.0)
+            s += deltaT*a*(1.0 + (2.0*random.random() - 1.0)/100.0)
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr) 
+            writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")
+            parent = newName
+            #self.assertEqual(bill.diff, oldDiff)
+              
+            oldDiff = bill.diff
+            
+            # what if we add a bunch of blocks this way?
+            # In the case of a static hash rate, I suppose we hope to not
+            # vary too far from a multiplicative factor of 1.0, or rather
+            # a constant difficulty.
+            
+            while len(bill.blocks)<200:
+                # Our metric divides by skewness. In reality, this is zero with
+                # probability zero. But for our tests, it's assured. So we
+                # will perturb each arrival by a small, up-to-half-percent
+                # variation to ensure a nonzero skewness without altering things
+                # too much.
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a*(1.0 + (2.0*random.random() - 1.0)/100.0)
+                s += deltaT*a*(1.0 + (2.0*random.random() - 1.0)/100.0)
+                self.assertEqual(bill.diff, oldDiff)
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                bill.addBlock(newBlock, mode, tr)
+                
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "\n")   
+                parent = newName
+                oldDiff = bill.diff
+              
+       
+    
+    def test_vs(self):
+        # TODO: Still must test that outliers are being removed "appropriately" according to specifications
+        # TODO: Test that scrambled lists of timestamps produce the same difficulty estimate.
+        # TODO: Show that in the case of homogeneous poisson processes, unusual estimates are a little
+        # more common than in the Nakamoto difficulty (which must be the case because Nakamoto uses
+        # the UMVUE).
+        mode = "vanSaberhagen"
+        tr = 1.0/60000.0 # one block per minute
+        deltaT = 60000.0
+        bill = Blockchain([], verbosity=True)
+        bill.targetRate = tr
+        
+        with open("output.txt", "w") as writeFile:
+            # We will send (t, a, diff, ratio, awayFromOne) to writeFile.
+            writeFile.write("time,rateConstant,difficulty,ratio\n")
+            name = newIdent(0)
+            t = 0.0
+            s = 0.0
+            diff = 1.0
+            params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+            genesis = Block(params)
+            
+            self.assertEqual(genesis.ident,name)
+            self.assertEqual(genesis.discoTimestamp,t)
+            self.assertEqual(genesis.arrivTimestamp,s)
+            self.assertTrue(genesis.parent is None)
+            self.assertEqual(genesis.diff,diff)
+            
+            bill.addBlock(genesis, mode, tr)
+            writeFile.write(str(t) + ",1.0," + str(bill.diff) + ",1.0\n")
+            
+            self.assertTrue(genesis.ident in bill.blocks)
+            self.assertTrue(genesis.ident in bill.leaves)
+            self.assertEqual(len(bill.miningIdents),1)
+            self.assertEqual(genesis.ident, bill.miningIdents[0])
+            self.assertEqual(bill.diff, 1.0)
+            
+            parent = genesis.ident
+            oldDiff = bill.diff
+            a = 1.0
+            b = 1.0/a
+            
+            while len(bill.blocks)<120:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                self.assertEqual(bill.diff, oldDiff)
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                bill.addBlock(newBlock, mode, tr)
+                
+                writeFile.write(str(t) + ",1.0," + str(bill.diff) + ",1.0\n")   
+                parent = newName
+                oldDiff = bill.diff
+                
+            # Just one more block and difficulty should be computed for the first time.
+            print("Just one more block and difficulty should be computed for the first time.")
+            self.assertEqual(bill.diff, oldDiff)
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr) 
+            writeFile.write(str(t) + ",1.0," + str(bill.diff) + ",1.0\n")
+            parent = newName
+            self.assertEqual(bill.diff, oldDiff)
+              
+            oldDiff = bill.diff
+            
+            print("Let's add more blocks at the same rate.")
+            a = 1.0
+            b = 1.0/a
+            
+            while len(bill.blocks)<1200:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + ",1.0," + str(bill.diff) + ",1.0\n")
+                parent = newName
+                self.assertEqual(bill.diff, oldDiff)
+                oldDiff = bill.diff
+            
+            print("Let's add more blocks at a slower rate.")
+            a = 1.1
+            b = 1.0/a
+            
+            # If blocks arrive slightly further apart, difficulty should drop.
+            # However, since vanSaberhagen discards top 10% and bottom 10% of
+            # timestamps, it will take 120 blocks for this change to register
+            # in difficulty.
+            print("If blocks arrive slightly further apart, difficulty should drop. However, since vanSaberhagen discards top 10% and bottom 10% of timestamps, it will take 120 blocks for this change to register in difficulty.")
+            while len(bill.blocks)<1320:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+                parent = newName
+                self.assertEqual(bill.diff, oldDiff)
+                oldDiff = bill.diff
+                
+            print("One more block and difficulty should register a change.")
+            self.assertEqual(bill.diff, oldDiff)
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr) 
+            writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+            parent = newName
+            self.assertTrue(bill.diff < oldDiff)
+            oldDiff = bill.diff
+            
+            # Let's add another fifty blocks at this same rate and verify that difficulty continually
+            # drops.
+            print("Let's add another fifty blocks at this same rate and verify that difficulty continually drops.")
+            a = 1.1
+            b = 1.0/a
+            
+            while len(bill.blocks)<1370:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+                parent = newName
+                self.assertTrue(bill.diff < oldDiff)
+                oldDiff = bill.diff
+                
+            # Now we go back to the target rate. We have 170 slow blocks in the queue and 50 in the sample size. Difficulty will continue to drop for another 120 blocks...
+            print("Now we go back to the target rate. We have 170 slow blocks in the queue and 50 in the sample size. Difficulty will continue to drop for another 120 blocks...")
+            a = 1.0
+            b = 1.0/a
+            
+            while len(bill.blocks)<1490:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+                parent = newName
+                self.assertTrue(bill.diff < oldDiff)
+                oldRatio = bill.diff/oldDiff
+                oldDiff = bill.diff
+                #print(str(result) + ", " + str(bill.diff) + ", " + str(oldDiff))
+                
+            # Now all 170 slow blocks are not only in the queue but in our sample. The *multiplicative factor* between timesteps should be identical for the next 790 blocks.. leading to AN EXPONENTIAL DECAY OF DIFFICULTY.
+            print("Now all 170 slow blocks are not only in the queue but in our sample. The *multiplicative factor* between timesteps should be identical for the next 790 blocks.. leading to AN EXPONENTIAL DECAY OF DIFFICULTY.")
+            a = 1.0
+            b = 1.0/a
+            while len(bill.blocks)<2279:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT
+                s += deltaT
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+                ratio = bill.diff/oldDiff
+                parent = newName
+                err = ratio - oldRatio
+                #print("Difference between last ratio and next ratio:" + str(err))
+                self.assertTrue(err*err < 10**-15)
+                oldDiff = bill.diff
+                oldRatio = ratio
+                
+            print("Now adding a single new block will cause our 170 slow blocks to start dropping out of our sample, so the ratio should start returning to 1.0.")
+            oldAwayFromOne = abs(oldRatio - 1.0) # Ratio should be returning to 1.0 so this difference should go to zero
+            oldAwayFromOne = oldAwayFromOne*oldAwayFromOne
+                
+            # For the next 170 blocks as our perturbed blocks drop out of our sample, our 
+            # estimated block arrival rate will return to "normal" so the multiplicative
+            # difference in difficulty should return to 1.0.
+            print("For the next 170 blocks as our perturbed blocks drop out of our sample, ourestimated block arrival rate will return to normal so the multiplicative difference in difficulty should return to 1.0.")
+            a = 1.0
+            b = 1.0/a
+            while len(bill.blocks)<2449:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+                ratio = bill.diff/oldDiff
+                #print("New ratio = " + str(ratio) + " and oldRatio = " + str(oldRatio))
+                self.assertTrue(ratio > oldRatio)
+                awayFromOne = abs(ratio - 1.0) # Ratio should be returning to 1.0 so this difference should go to zero
+                awayFromOne = awayFromOne*awayFromOne
+                self.assertTrue(awayFromOne < oldAwayFromOne) # This return will be monotonic in our manufactured example.
+                parent = newName
+                oldDiff = bill.diff
+                oldRatio = ratio
+                oldAwayFromOne = awayFromOne
+            
+            
+            # Now difficulty should remain frozen for as long as we like.
+            
+            a = 1.0
+            b = 1.0/a
+            while len(bill.blocks)<2500:
+                newName = newIdent(len(bill.blocks))
+                t += deltaT*a
+                s += deltaT*a
+                diff = bill.diff
+                params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+                newBlock = Block(params)
+                
+                bill.addBlock(newBlock, mode, tr)
+                writeFile.write(str(t) + "," + str(a) + "," + str(bill.diff) + "," + str(bill.diff/oldDiff) + "\n")
+                parent = newName
+                self.assertEqual(bill.diff, oldDiff)
+                oldDiff = bill.diff
+                
+        
+         
+     
+    def test_nak(self):
+        # Since Nakamoto difficulty is derived from the MLE of the block arrival rate,
+        # we already know how it "should" behave in a poisson process, etc.
+        # TODO: Generate N samples of MLEs of Poisson rates compared to known homog. 
+        # poisson rate, show that the resulting code does not result in unusual measurements
+        # more often than expected.
+        mode = "Nakamoto"
+        tr = 1.0/600000.0
+        deltaT = 600000.0
+        bill = Blockchain([], verbosity=True)
+        bill.targetRate = tr
+        # Bitcoin updating at 1 block per 10 minutes
+        
+        name = newIdent(0)
+        t = 0.0
+        s = 0.0
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        
+        self.assertEqual(genesis.ident,name)
+        self.assertEqual(genesis.discoTimestamp,t)
+        self.assertEqual(genesis.arrivTimestamp,s)
+        self.assertTrue(genesis.parent is None)
+        self.assertEqual(genesis.diff,diff)
+        
+        bill.addBlock(genesis, mode, tr)
+        
+        self.assertTrue(genesis.ident in bill.blocks)
+        self.assertTrue(genesis.ident in bill.leaves)
+        self.assertEqual(len(bill.miningIdents),1)
+        self.assertEqual(genesis.ident, bill.miningIdents[0])
+        self.assertEqual(bill.diff, 1.0)
+        
+        parent = genesis.ident
+        oldDiff = bill.diff
+        i = 1
+        
+        while len(bill.blocks)<2016*i-1:
+            newName = newIdent(len(bill.blocks))
+            t += deltaT
+            s += deltaT
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr)
+            parent = newName
+            
+        # Just one more block and difficulty should recompute.
+        print("Just one more block and difficulty should recompute.")
+        self.assertEqual(bill.diff, oldDiff)
+        newName = newIdent(len(bill.blocks))
+        t += deltaT
+        s += deltaT
+        diff = bill.diff
+        params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+        newBlock = Block(params)
+        bill.addBlock(newBlock, mode, tr) 
+        parent = newName
+        self.assertEqual(bill.diff, oldDiff)
+          
+        oldDiff = bill.diff
+        i += 1
+        
+        while len(bill.blocks)<2016*i-1:
+            newName = newIdent(len(bill.blocks))
+            t += deltaT
+            s += deltaT
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            
+            bill.addBlock(newBlock, mode, tr)
+            parent = newName
+        
+        # Just one more block and difficulty should recompute.
+        print("Just one more block and difficulty should again recompute.")
+        self.assertEqual(bill.diff, oldDiff)
+        newName = newIdent(len(bill.blocks))
+        t += deltaT
+        s += deltaT
+        diff = bill.diff
+        params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+        newBlock = Block(params)
+        bill.addBlock(newBlock, mode, tr) 
+        parent = newName
+        self.assertEqual(bill.diff, oldDiff)
+          
+        oldDiff = bill.diff
+        i += 1
+        a = 1.1
+        b = 1.0/a
+        
+        # If blocks arrive slightly further apart, difficulty should drop.
+        while len(bill.blocks)<2016*i-1:
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            
+            bill.addBlock(newBlock, mode, tr)
+            parent = newName
+            
+        print("Just one more block and difficulty will go down.")
+        
+        self.assertEqual(bill.diff, oldDiff)
+        newName = newIdent(len(bill.blocks))
+        t += deltaT*a
+        s += deltaT*a
+        diff = bill.diff
+        params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+        newBlock = Block(params)
+        bill.addBlock(newBlock, mode, tr) 
+        parent = newName
+        err = abs(bill.diff - oldDiff*b)
+        self.assertTrue(err*err < 10**-15)
+        oldDiff = bill.diff
+        i += 1
+            
+         
+        # If blocks then arrive on target, difficulty should freeze.
+        a = 1.0
+        b = 1.0/a
+        while len(bill.blocks)<2016*i-1:
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            
+            bill.addBlock(newBlock, mode, tr)
+            parent = newName
+            
+        self.assertEqual(bill.diff, oldDiff)
+        newName = newIdent(len(bill.blocks))
+        t += deltaT*a
+        s += deltaT*a
+        diff = bill.diff
+        params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+        newBlock = Block(params)
+        bill.addBlock(newBlock, mode, tr) 
+        parent = newName
+        self.assertEqual(bill.diff, oldDiff)
+        oldDiff = bill.diff
+        i += 1
+        
+        # If blocks arrive too close together, difficulty should increase.
+        a = 0.9
+        b = 1.0/a
+        while len(bill.blocks)<2016*i-1:
+            newName = newIdent(len(bill.blocks))
+            t += deltaT*a
+            s += deltaT*a
+            diff = bill.diff
+            params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            
+            bill.addBlock(newBlock, mode, tr)
+            parent = newName
+            
+        print("Just one more block and difficulty should go up.")
+        self.assertEqual(bill.diff, oldDiff)
+        newName = newIdent(len(bill.blocks))
+        t += deltaT*a
+        s += deltaT*a
+        diff = bill.diff
+        params = {"ident":newName, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+        newBlock = Block(params)
+        bill.addBlock(newBlock, mode, tr) 
+        parent = newName
+        err = abs(bill.diff - oldDiff*b)
+        self.assertTrue(err*err < 10**-15)
+    '''
+            
+        
+       
+        
+suite = unittest.TestLoader().loadTestsFromTestCase(Test_Blockchain)
+unittest.TextTestRunner(verbosity=1).run(suite)
diff --git a/source-code/Poisson-Graphs/new/Node.py b/source-code/Poisson-Graphs/new/Node.py
new file mode 100644
index 0000000..716fe4f
--- /dev/null
+++ b/source-code/Poisson-Graphs/new/Node.py
@@ -0,0 +1,116 @@
+from Blockchain import *
+
+class Node(object):
+    '''
+    Node object. params [identity, blockchain (data), verbosity, difficulty]
+    '''
+    def __init__(self, params={}):
+        try:
+            assert len(params)==5
+        except AssertionError:
+            print("Error, Tried to create malformed node.")
+        else:
+            self.ident = params["ident"]
+            self.data = params["data"]
+            self.verbose = params["verbose"]
+            self.edges = {}
+            self.mode = params["mode"]
+            self.targetRate = params["targetRate"]
+            
+    def generateBlock(self, discoTime, nonce):
+        newName = newIdent(nonce)
+        t = discoTime
+        s = t+self.data["offset"]
+        diff = self.data["blockchain"].diff
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        newBlock = Block(params)
+        self.data["blockchain"].addBlock(newBlock, mode, tr)
+        return newName
+        
+    def updateBlockchain(self, incBlocks):
+        # incBlocks shall be a dictionary of block identities (as keys) and their associated blocks (as values)
+        # to be added to the local data. We assume difficulty scores have been reported honestly for now.
+        
+        tempData = copy.deepcopy(incBlocks)
+        for key in incBlocks:
+            if key in self.data["blockchain"].blocks:
+                del tempData[key]
+            elif incBlocks[key].parent in self.data["blockchain"].blocks or incBlocks[key].parent is None:
+                self.data["blockchain"].addBlock(incBlocks[key], self.mode, self.targetRate)
+                del tempData[key]
+        incBlocks = copy.deepcopy(tempData)
+        while len(incBlocks)>0:
+            for key in incBlocks:
+                if key in self.data["blockchain"].blocks:
+                    del tempData[key]
+                elif incBlocks[key].parent in self.data["blockchain"].blocks:
+                    self.data["blockchain"].addBlock(incBlocks[key], self.mode, self.targetRate)
+                    del tempData[key]
+            incBlocks = copy.deepcopy(tempData)
+            
+    def propagate(self, timeOfProp, blockIdent):
+        for edgeIdent in self.edges:
+            edge = self.edges[edgeIdent]
+            length = e.data["length"]
+            timeOfArrival = timeOfProp + length
+            otherIdent = e.getNeighbor(self.ident)
+            other = e.nodes[otherIdent]
+            bc = other.data["blockchain"]
+            if blockIdent not in bc.blocks:
+                pB = e.data["pendingBlocks"]
+                pendingIdent = newIdent(len(pB))
+                mybc = self.data["blockchain"]
+                blockToProp = mybc.blocks[blockIdent]
+                pendingDat = {"timeOfArrival":timeOfArrival, "destIdent":otherIdent, "block":blockToProp}
+                pB.update({pendingIdent:pendingDat})
+       
+
+class Test_Node(unittest.TestCase):
+    # TODO test each method separately
+    def test_all(self):
+        bill = Blockchain([], verbosity=True)
+        mode="Nakamoto"
+        tr = 1.0/600000.0
+        deltaT = 600000.0
+        bill.targetRate = tr
+        
+        name = newIdent(0)
+        t = 0.0
+        s = t
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        bill.addBlock(genesis, mode, tr)
+        
+        parent = genesis.ident
+        
+        nellyname = newIdent(time.time())
+        mode = "Nakamoto"
+        targetRate = 1.0/600000.0
+        params = {"ident":nellyname, "data":{"offset":0.0, "intensity":1.0, "blockchain":bill}, "verbose":True, "mode":mode, "targetRate":targetRate}
+        nelly = Node(params)
+        
+        while len(nelly.data["blockchain"].blocks) < 2015:
+            name = newIdent(0)
+            diff = nelly.data["blockchain"].diff
+            t += deltaT*diff*(2.0*random.random()-1.0)
+            s = t
+            params = {"ident":name, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr)
+            parent = name
+            
+            
+        while len(nelly.data["blockchain"].blocks) < 5000:
+            name = newIdent(0)
+            diff = nelly.data["blockchain"].diff
+            t += deltaT*diff
+            s = t
+            params = {"ident":name, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr)
+            parent = name
+        
+suite = unittest.TestLoader().loadTestsFromTestCase(Test_Node)
+unittest.TextTestRunner(verbosity=1).run(suite)
+       
diff --git a/source-code/Poisson-Graphs/new/Node.py~ b/source-code/Poisson-Graphs/new/Node.py~
new file mode 100644
index 0000000..716fe4f
--- /dev/null
+++ b/source-code/Poisson-Graphs/new/Node.py~
@@ -0,0 +1,116 @@
+from Blockchain import *
+
+class Node(object):
+    '''
+    Node object. params [identity, blockchain (data), verbosity, difficulty]
+    '''
+    def __init__(self, params={}):
+        try:
+            assert len(params)==5
+        except AssertionError:
+            print("Error, Tried to create malformed node.")
+        else:
+            self.ident = params["ident"]
+            self.data = params["data"]
+            self.verbose = params["verbose"]
+            self.edges = {}
+            self.mode = params["mode"]
+            self.targetRate = params["targetRate"]
+            
+    def generateBlock(self, discoTime, nonce):
+        newName = newIdent(nonce)
+        t = discoTime
+        s = t+self.data["offset"]
+        diff = self.data["blockchain"].diff
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        newBlock = Block(params)
+        self.data["blockchain"].addBlock(newBlock, mode, tr)
+        return newName
+        
+    def updateBlockchain(self, incBlocks):
+        # incBlocks shall be a dictionary of block identities (as keys) and their associated blocks (as values)
+        # to be added to the local data. We assume difficulty scores have been reported honestly for now.
+        
+        tempData = copy.deepcopy(incBlocks)
+        for key in incBlocks:
+            if key in self.data["blockchain"].blocks:
+                del tempData[key]
+            elif incBlocks[key].parent in self.data["blockchain"].blocks or incBlocks[key].parent is None:
+                self.data["blockchain"].addBlock(incBlocks[key], self.mode, self.targetRate)
+                del tempData[key]
+        incBlocks = copy.deepcopy(tempData)
+        while len(incBlocks)>0:
+            for key in incBlocks:
+                if key in self.data["blockchain"].blocks:
+                    del tempData[key]
+                elif incBlocks[key].parent in self.data["blockchain"].blocks:
+                    self.data["blockchain"].addBlock(incBlocks[key], self.mode, self.targetRate)
+                    del tempData[key]
+            incBlocks = copy.deepcopy(tempData)
+            
+    def propagate(self, timeOfProp, blockIdent):
+        for edgeIdent in self.edges:
+            edge = self.edges[edgeIdent]
+            length = e.data["length"]
+            timeOfArrival = timeOfProp + length
+            otherIdent = e.getNeighbor(self.ident)
+            other = e.nodes[otherIdent]
+            bc = other.data["blockchain"]
+            if blockIdent not in bc.blocks:
+                pB = e.data["pendingBlocks"]
+                pendingIdent = newIdent(len(pB))
+                mybc = self.data["blockchain"]
+                blockToProp = mybc.blocks[blockIdent]
+                pendingDat = {"timeOfArrival":timeOfArrival, "destIdent":otherIdent, "block":blockToProp}
+                pB.update({pendingIdent:pendingDat})
+       
+
+class Test_Node(unittest.TestCase):
+    # TODO test each method separately
+    def test_all(self):
+        bill = Blockchain([], verbosity=True)
+        mode="Nakamoto"
+        tr = 1.0/600000.0
+        deltaT = 600000.0
+        bill.targetRate = tr
+        
+        name = newIdent(0)
+        t = 0.0
+        s = t
+        diff = 1.0
+        params = {"ident":name, "disco":t, "arriv":s, "parent":None, "diff":diff}
+        genesis = Block(params)
+        bill.addBlock(genesis, mode, tr)
+        
+        parent = genesis.ident
+        
+        nellyname = newIdent(time.time())
+        mode = "Nakamoto"
+        targetRate = 1.0/600000.0
+        params = {"ident":nellyname, "data":{"offset":0.0, "intensity":1.0, "blockchain":bill}, "verbose":True, "mode":mode, "targetRate":targetRate}
+        nelly = Node(params)
+        
+        while len(nelly.data["blockchain"].blocks) < 2015:
+            name = newIdent(0)
+            diff = nelly.data["blockchain"].diff
+            t += deltaT*diff*(2.0*random.random()-1.0)
+            s = t
+            params = {"ident":name, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr)
+            parent = name
+            
+            
+        while len(nelly.data["blockchain"].blocks) < 5000:
+            name = newIdent(0)
+            diff = nelly.data["blockchain"].diff
+            t += deltaT*diff
+            s = t
+            params = {"ident":name, "disco":t, "arriv":s, "parent":parent, "diff":diff}
+            newBlock = Block(params)
+            bill.addBlock(newBlock, mode, tr)
+            parent = name
+        
+suite = unittest.TestLoader().loadTestsFromTestCase(Test_Node)
+unittest.TextTestRunner(verbosity=1).run(suite)
+       
diff --git a/source-code/Poisson-Graphs/new/__pycache__/Block.cpython-35.pyc b/source-code/Poisson-Graphs/new/__pycache__/Block.cpython-35.pyc
new file mode 100644
index 0000000..62b87dd
Binary files /dev/null and b/source-code/Poisson-Graphs/new/__pycache__/Block.cpython-35.pyc differ
diff --git a/source-code/Poisson-Graphs/new/__pycache__/Blockchain.cpython-35.pyc b/source-code/Poisson-Graphs/new/__pycache__/Blockchain.cpython-35.pyc
new file mode 100644
index 0000000..9602d14
Binary files /dev/null and b/source-code/Poisson-Graphs/new/__pycache__/Blockchain.cpython-35.pyc differ
diff --git a/source-code/Poisson-Graphs/new/output.txt b/source-code/Poisson-Graphs/new/output.txt
new file mode 100644
index 0000000..776c5db
--- /dev/null
+++ b/source-code/Poisson-Graphs/new/output.txt
@@ -0,0 +1,2501 @@
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diff --git a/source-code/Poisson-Graphs/new/outputM.txt b/source-code/Poisson-Graphs/new/outputM.txt
new file mode 100644
index 0000000..99e4ad2
--- /dev/null
+++ b/source-code/Poisson-Graphs/new/outputM.txt
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diff --git a/source-code/Poisson-Graphs/new/outputM.txt~ b/source-code/Poisson-Graphs/new/outputM.txt~
new file mode 100644
index 0000000..7af84cc
--- /dev/null
+++ b/source-code/Poisson-Graphs/new/outputM.txt~
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