moneropedia: uniform structure of pedersen-commitment.md

_i18n/ar/resources/moneropedia/pedersen-commitment.md

@@ -1,23 +1,45 @@
 ---
+summary: 'Pedersen commitments are cryptographic algorithms that allow a prover to commit to a certain value without revealing it or being able to change it'
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments"]
-summary: "Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it"
 ---
 
 {% include disclaimer.html translated="no" translationOutdated="no" %}
+
 ### The Basics
 
-Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it.
+Pedersen commitments are cryptographic algorithms that allow a prover to
+commit to a certain value without revealing it or being able to change it.
 
-When you spend Monero, the value of the inputs that you are spending and the value of the outputs you are sending are encrypted and opaque to everyone except the recipient of each of those outputs. Pedersen commitments allow you to send Monero without revealing the value of the transactions. Pedersen commitments also make it possible for people to verify that transactions on the blockchain are valid and not creating Monero out of thin air.
+When you spend Monero, the value of the inputs that you are spending and the
+value of the outputs you are sending are encrypted and opaque to everyone
+except the recipient of each of those outputs. Pedersen commitments allow
+you to send Monero without revealing the value of the transactions. Pedersen
+commitments also make it possible for people to verify that transactions on
+the blockchain are valid and not creating Monero out of thin air.
 
 ### What It Means
 
-As long as the encrypted output amounts created, which include an output for the recipient and a change output back to the sender, and the unencrypted transaction fee is equal to the sum of the inputs that are being spent, it is a legitimate transaction and can be confirmed to not be creating Monero out of thin air.
+As long as the encrypted output amounts created, which include an output for
+the recipient and a change output back to the sender, and the unencrypted
+transaction fee is equal to the sum of the inputs that are being spent, it
+is a legitimate transaction and can be confirmed to not be creating Monero
+out of thin air.
 
-Pedersen commitments mean that the sums can be verified as being equal, but the Monero value of each of the sums and the Monero value of the inputs and outputs individually are undeterminable. Pedersen commitments also mean that even the ratio of one input to another, or one output to another is undeterminable.
+Pedersen commitments mean that the sums can be verified as being equal, but
+the Monero value of each of the sums and the Monero value of the inputs and
+outputs individually are undeterminable. Pedersen commitments also mean that
+even the ratio of one input to another, or one output to another is
+undeterminable.
 
-It is unclear which inputs are really being spent as the ring signature lists both the real inputs being spent and decoy inputs, therefore you don't actually know which input Pedersen commitments need to be summed. That's okay, because the @RingCT ring signature only has to prove that for one combination of the inputs the outputs are equal to the sum of the inputs. For mathematical reasons, this is impossible to forge.
+It is unclear which inputs are really being spent as the ring signature
+lists both the real inputs being spent and decoy inputs, therefore you don't
+actually know which input Pedersen commitments need to be summed. That's
+okay, because the @RingCT ring signature only has to prove that for one
+combination of the inputs the outputs are equal to the sum of the
+inputs. For mathematical reasons, this is impossible to forge.
 
 ### In-depth Information
 
-See information in [Ring Confidential Transactions paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero Research Lab.
+See information in [Ring Confidential Transactions
+paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero
+Research Lab.

_i18n/de/resources/moneropedia/pedersen-commitment.md

@@ -1,23 +1,49 @@
 ---
+summary: 'Pedersen-Commitments sind kryptografische Algorithmen, die es einer beweisenden Partei erlauben, sich auf einen bestimmten Wert festzulegen, ohne diesen zu offenbaren oder ändern zu können'
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments", "Pedersen-Commitment", "Pedersen-Commitments", "Commitment", "Commitments"]
-summary: "Pedersen-Commitments sind kryptografische Algorithmen, die es einer beweisenden Partei erlauben, sich auf einen bestimmten Wert festzulegen, ohne diesen zu offenbaren oder ändern zu können"
 ---
 
 {% include disclaimer.html translated="yes" translationOutdated="no" %}
+
 ### Grundlagen
 
-Pedersen-Commitments sind kryptografische Algorithmen, die es einer beweisenden Partei erlauben, sich auf einen bestimmten Wert festzulegen, ohne diesen zu offenbaren oder ändern zu können.
+Pedersen-Commitments sind kryptografische Algorithmen, die es einer
+beweisenden Partei erlauben, sich auf einen bestimmten Wert festzulegen,
+ohne diesen zu offenbaren oder ändern zu können.
 
-Wenn Monero ausgegeben werden, sind der Wert der ausgegebenen Inputs und der Wert der gesendeten Outputs verschlüsselt und, außer für die Empfänger dieser Outputs, für jeden verschleiert. Pedersen-Commitments erlauben das Senden von Monero, ohne den Wert der Transaktionen zu offenbaren. Zudem ermöglichen sie es Personen, zu verifizieren, dass Transaktionen auf der Blockchain valide sind und nicht etwa aus dem Nichts heraus Monero erschaffen.
+Wenn Monero ausgegeben werden, sind der Wert der ausgegebenen Inputs und der
+Wert der gesendeten Outputs verschlüsselt und, außer für die Empfänger
+dieser Outputs, für jeden verschleiert. Pedersen-Commitments erlauben das
+Senden von Monero, ohne den Wert der Transaktionen zu offenbaren. Zudem
+ermöglichen sie es Personen, zu verifizieren, dass Transaktionen auf der
+Blockchain valide sind und nicht etwa aus dem Nichts heraus Monero
+erschaffen.
 
 ### Was dies bedeutet
 
-Solange die erstellten (verschlüsselten) Output-Beträge (welche einen Output für den Empfänger und einen an den Sender zurückgehenden Wechselgeld-Output umfassen) und die (unverschlüsselte) Transaktionsgebühr mit der Summe der ausgegebenen Inputs übereinstimmen, handelt es sich um eine legitime Transaktion; es kann bestätigt werden, dass keine Monero aus dem Nichts heraus erschaffen werden.
+Solange die erstellten (verschlüsselten) Output-Beträge (welche einen Output
+für den Empfänger und einen an den Sender zurückgehenden Wechselgeld-Output
+umfassen) und die (unverschlüsselte) Transaktionsgebühr mit der Summe der
+ausgegebenen Inputs übereinstimmen, handelt es sich um eine legitime
+Transaktion; es kann bestätigt werden, dass keine Monero aus dem Nichts
+heraus erschaffen werden.
 
-Pedersen-Commitments bedeuten, dass zwar die Summen als übereinstimmend verifiziert werden können, die einzelnen Monero-Werte jeder Summe und der Inputs und Outputs jedoch unbestimmbar sind. Pedersen-Commitments bedeuten außerdem, dass selbst das Verhältnis eines Inputs zu einem anderen, oder eines Outputs zu einem anderen, nicht bestimmbar ist.
+Pedersen-Commitments bedeuten, dass zwar die Summen als übereinstimmend
+verifiziert werden können, die einzelnen Monero-Werte jeder Summe und der
+Inputs und Outputs jedoch unbestimmbar sind. Pedersen-Commitments bedeuten
+außerdem, dass selbst das Verhältnis eines Inputs zu einem anderen, oder
+eines Outputs zu einem anderen, nicht bestimmbar ist.
 
-Welche Inputs tatsächlich ausgegeben werden ist unklar, da die Ringsignatur sowohl die in echt ausgegebenen Inputs, als auch Input-Attrappen auflistet, und demnach nicht genau klar ist, welche Inputs zusammengezählt werden müssen. Dies ist aber okay, weil die Ringsignatur der @Ring-CT lediglich nachweisen muss, dass bei einer bestimmten Kombination der Inputs die Outputs mit der Summe dieser Inputs übereinstimmen. Aus mathematschen Gründen ist es unmöglich, das Ergebnis zu fälschen.
+Welche Inputs tatsächlich ausgegeben werden ist unklar, da die Ringsignatur
+sowohl die in echt ausgegebenen Inputs, als auch Input-Attrappen auflistet,
+und demnach nicht genau klar ist, welche Inputs zusammengezählt werden
+müssen. Dies ist aber okay, weil die Ringsignatur der @Ring-CT lediglich
+nachweisen muss, dass bei einer bestimmten Kombination der Inputs die
+Outputs mit der Summe dieser Inputs übereinstimmen. Aus mathematschen
+Gründen ist es unmöglich, das Ergebnis zu fälschen.
 
 ### Ausführliche Informationen
 
-Weitere Informationen finden sich im ["Ring Confidential Transactions"-Paper](https://eprint.iacr.org/2015/1098.pdf) von Shen Noether vom Monero-Research-Lab.
+Weitere Informationen finden sich im ["Ring Confidential
+Transactions"-Paper](https://eprint.iacr.org/2015/1098.pdf) von Shen Noether
+vom Monero-Research-Lab.

_i18n/en/resources/moneropedia/pedersen-commitment.md

@@ -4,6 +4,7 @@ summary: "Pedersen commitments are cryptographic algorithms that allow a prover
 ---
 
 {% include disclaimer.html translated="no" translationOutdated="no" %}
+
 ### The Basics
 
 Pedersen commitments are cryptographic algorithms that allow a prover to commit to a certain value without revealing it or being able to change it.

_i18n/es/resources/moneropedia/pedersen-commitment.md

@@ -1,23 +1,45 @@
 ---
+summary: 'Pedersen commitments are cryptographic algorithms that allow a prover to commit to a certain value without revealing it or being able to change it'
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments"]
-summary: "Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it"
 ---
 
 {% include disclaimer.html translated="no" translationOutdated="no" %}
+
 ### The Basics
 
-Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it.
+Pedersen commitments are cryptographic algorithms that allow a prover to
+commit to a certain value without revealing it or being able to change it.
 
-When you spend Monero, the value of the inputs that you are spending and the value of the outputs you are sending are encrypted and opaque to everyone except the recipient of each of those outputs. Pedersen commitments allow you to send Monero without revealing the value of the transactions. Pedersen commitments also make it possible for people to verify that transactions on the blockchain are valid and not creating Monero out of thin air.
+When you spend Monero, the value of the inputs that you are spending and the
+value of the outputs you are sending are encrypted and opaque to everyone
+except the recipient of each of those outputs. Pedersen commitments allow
+you to send Monero without revealing the value of the transactions. Pedersen
+commitments also make it possible for people to verify that transactions on
+the blockchain are valid and not creating Monero out of thin air.
 
 ### What It Means
 
-As long as the encrypted output amounts created, which include an output for the recipient and a change output back to the sender, and the unencrypted transaction fee is equal to the sum of the inputs that are being spent, it is a legitimate transaction and can be confirmed to not be creating Monero out of thin air.
+As long as the encrypted output amounts created, which include an output for
+the recipient and a change output back to the sender, and the unencrypted
+transaction fee is equal to the sum of the inputs that are being spent, it
+is a legitimate transaction and can be confirmed to not be creating Monero
+out of thin air.
 
-Pedersen commitments mean that the sums can be verified as being equal, but the Monero value of each of the sums and the Monero value of the inputs and outputs individually are undeterminable. Pedersen commitments also mean that even the ratio of one input to another, or one output to another is undeterminable.
+Pedersen commitments mean that the sums can be verified as being equal, but
+the Monero value of each of the sums and the Monero value of the inputs and
+outputs individually are undeterminable. Pedersen commitments also mean that
+even the ratio of one input to another, or one output to another is
+undeterminable.
 
-It is unclear which inputs are really being spent as the ring signature lists both the real inputs being spent and decoy inputs, therefore you don't actually know which input Pedersen commitments need to be summed. That's okay, because the @RingCT ring signature only has to prove that for one combination of the inputs the outputs are equal to the sum of the inputs. For mathematical reasons, this is impossible to forge.
+It is unclear which inputs are really being spent as the ring signature
+lists both the real inputs being spent and decoy inputs, therefore you don't
+actually know which input Pedersen commitments need to be summed. That's
+okay, because the @RingCT ring signature only has to prove that for one
+combination of the inputs the outputs are equal to the sum of the
+inputs. For mathematical reasons, this is impossible to forge.
 
 ### In-depth Information
 
-See information in [Ring Confidential Transactions paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero Research Lab.
+See information in [Ring Confidential Transactions
+paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero
+Research Lab.

_i18n/fr/resources/moneropedia/pedersen-commitment.md

@@ -1,23 +1,50 @@
 ---
+summary: "Les engagements de Pedersen sont des algorythmes de cryptographie qui permettent à un prouveur de s'engager sur une certaine valeur sans la révéler ou pouvoir la modifier."
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments", "engagement", "engagements", "engagement-de-pedersen", "engagements-de-pedersen"]
-summary: "Les engagements de Pedersen sont des algorythmes de cryptographie qui permettent à un prouveur de s'engager sur une certaine valeur sans la révéler ou pouvoir la modifier"
 ---
 
 {% include disclaimer.html translated="yes" translationOutdated="no" %}
+
 ### Les Bases
 
-Les engagements de Pedersen sont des algorythmes de cryptographie qui permettent à un prouveur de s'engager sur une certaine valeur sans la révéler ou pouvoir la modifier.
+Les engagements de Pedersen sont des algorythmes de cryptographie qui
+permettent à un prouveur de s'engager sur une certaine valeur sans la
+révéler ou pouvoir la modifier.
 
-Lorsque vous dépensez des Moneroj, la valeur des entrées que vous dépensez et la valeur des sorties que vous envoyez sont chiffrés et opaques pour tout le monde sauf le destinataire de chacune de ces sorties. Les engagements de Pedersen vous permettent d'envoyer des Moneroj sans révéler la valeur des transactions. Les engagements de Pedersen permettent également aux gens de vérifier que les transactions sur la chaîne de blocs sont valides et ne créent pas de Moneroj à partir de rien.
+Lorsque vous dépensez des Moneroj, la valeur des entrées que vous dépensez
+et la valeur des sorties que vous envoyez sont chiffrés et opaques pour tout
+le monde sauf le destinataire de chacune de ces sorties. Les engagements de
+Pedersen vous permettent d'envoyer des Moneroj sans révéler la valeur des
+transactions. Les engagements de Pedersen permettent également aux gens de
+vérifier que les transactions sur la chaîne de blocs sont valides et ne
+créent pas de Moneroj à partir de rien.
 
 ### Ce que cela signifie
 
-Tant que les montants de sortie chiffrés créés, qui comprennent une sortie pour le destinataire et une sortie de monnaie retournant à l'expéditeur, et que les frais de transaction non chiffrés sont égaux à la somme des entrées qui sont dépensées, il s'agit d'une transaction légitime et on peut confirmer qu'il n'y a pas de création de Moneroj à partir de rien.
+Tant que les montants de sortie chiffrés créés, qui comprennent une sortie
+pour le destinataire et une sortie de monnaie retournant à l'expéditeur, et
+que les frais de transaction non chiffrés sont égaux à la somme des entrées
+qui sont dépensées, il s'agit d'une transaction légitime et on peut
+confirmer qu'il n'y a pas de création de Moneroj à partir de rien.
 
-Les engagements de Pedersen signifient que les sommes peuvent être vérifiées comme étant égales, mais la valeur en Moneroj de chacune des sommes et les valeurs individuelles en Moneroj des entrées et sorties sont indéterminables. Les engagements de Pedersen signifient également que même le ratio d'une entrée à une autre ou d'une sortie à une autre est indéterminable.
+Les engagements de Pedersen signifient que les sommes peuvent être vérifiées
+comme étant égales, mais la valeur en Moneroj de chacune des sommes et les
+valeurs individuelles en Moneroj des entrées et sorties sont
+indéterminables. Les engagements de Pedersen signifient également que même
+le ratio d'une entrée à une autre ou d'une sortie à une autre est
+indéterminable.
 
-L'entrée exacte étant dépensée n'est pas clair, car les signatures de cercle listent à la fois les entrées réelles étant dépensées et les entrées de leurre, donc vous ne savez pas vraiment quelles entrées les engagements de Pedersen doivent additionner. Ce n'est pas un problème car les @transactions-confidentielles-de-cercle des signatures de cercle doivent uniquement prouver que pour une combinaison d'entrées les sorties sont égales à la somme de ces entrées. Pour des raisons mathématiques, c'est impossible à forger.
+L'entrée exacte étant dépensée n'est pas clair, car les signatures de cercle
+listent à la fois les entrées réelles étant dépensées et les entrées de
+leurre, donc vous ne savez pas vraiment quelles entrées les engagements de
+Pedersen doivent additionner. Ce n'est pas un problème car les
+@transactions-confidentielles-de-cercle des signatures de cercle doivent
+uniquement prouver que pour une combinaison d'entrées les sorties sont
+égales à la somme de ces entrées. Pour des raisons mathématiques, c'est
+impossible à forger.
 
 ### Informations détaillées
 
-Voir le document [Transactions confidentielles de cercle](https://eprint.iacr.org/2015/1098.pdf) de Shen Noether du Laboratoire de Recheche Monero.
+Voir le document [Transactions confidentielles de
+cercle](https://eprint.iacr.org/2015/1098.pdf) de Shen Noether du
+Laboratoire de Recheche Monero.

_i18n/it/resources/moneropedia/pedersen-commitment.md

@@ -1,23 +1,45 @@
 ---
+summary: 'Pedersen commitments are cryptographic algorithms that allow a prover to commit to a certain value without revealing it or being able to change it'
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments"]
-summary: "Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it"
 ---
 
 {% include disclaimer.html translated="no" translationOutdated="no" %}
+
 ### The Basics
 
-Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it.
+Pedersen commitments are cryptographic algorithms that allow a prover to
+commit to a certain value without revealing it or being able to change it.
 
-When you spend Monero, the value of the inputs that you are spending and the value of the outputs you are sending are encrypted and opaque to everyone except the recipient of each of those outputs. Pedersen commitments allow you to send Monero without revealing the value of the transactions. Pedersen commitments also make it possible for people to verify that transactions on the blockchain are valid and not creating Monero out of thin air.
+When you spend Monero, the value of the inputs that you are spending and the
+value of the outputs you are sending are encrypted and opaque to everyone
+except the recipient of each of those outputs. Pedersen commitments allow
+you to send Monero without revealing the value of the transactions. Pedersen
+commitments also make it possible for people to verify that transactions on
+the blockchain are valid and not creating Monero out of thin air.
 
 ### What It Means
 
-As long as the encrypted output amounts created, which include an output for the recipient and a change output back to the sender, and the unencrypted transaction fee is equal to the sum of the inputs that are being spent, it is a legitimate transaction and can be confirmed to not be creating Monero out of thin air.
+As long as the encrypted output amounts created, which include an output for
+the recipient and a change output back to the sender, and the unencrypted
+transaction fee is equal to the sum of the inputs that are being spent, it
+is a legitimate transaction and can be confirmed to not be creating Monero
+out of thin air.
 
-Pedersen commitments mean that the sums can be verified as being equal, but the Monero value of each of the sums and the Monero value of the inputs and outputs individually are undeterminable. Pedersen commitments also mean that even the ratio of one input to another, or one output to another is undeterminable.
+Pedersen commitments mean that the sums can be verified as being equal, but
+the Monero value of each of the sums and the Monero value of the inputs and
+outputs individually are undeterminable. Pedersen commitments also mean that
+even the ratio of one input to another, or one output to another is
+undeterminable.
 
-It is unclear which inputs are really being spent as the ring signature lists both the real inputs being spent and decoy inputs, therefore you don't actually know which input Pedersen commitments need to be summed. That's okay, because the @RingCT ring signature only has to prove that for one combination of the inputs the outputs are equal to the sum of the inputs. For mathematical reasons, this is impossible to forge.
+It is unclear which inputs are really being spent as the ring signature
+lists both the real inputs being spent and decoy inputs, therefore you don't
+actually know which input Pedersen commitments need to be summed. That's
+okay, because the @RingCT ring signature only has to prove that for one
+combination of the inputs the outputs are equal to the sum of the
+inputs. For mathematical reasons, this is impossible to forge.
 
 ### In-depth Information
 
-See information in [Ring Confidential Transactions paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero Research Lab.
+See information in [Ring Confidential Transactions
+paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero
+Research Lab.

_i18n/nb-no/resources/moneropedia/pedersen-commitment.md

@@ -1,23 +1,46 @@
 ---
+summary: 'Pedersen-forpliktelser er kryptografiske algoritmer som lar en beviser forplikte seg til en viss verdi uten å avsløre den eller kunne endre den'
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments", forpliktelse", "forpliktelser", "pedersen-forpliktelse", "pedersen-forpliktelser"]
-summary: "Pedersen-forpliktelser er kryptografiske algoritmer som lar en beviser forplikte seg til en viss verdi uten å avsløre den eller kunne endre den"
 ---
 
 {% include disclaimer.html translated="yes" translationOutdated="no" %}
+
 ### Det grunnleggende
 
-Pedersen-forpliktelser er kryptografiske algoritmer som lar en beviser forplikte seg til en viss verdi uten å avsløre den eller kunne endre den.
+Pedersen-forpliktelser er kryptografiske algoritmer som lar en beviser
+forplikte seg til en viss verdi uten å avsløre den eller kunne endre den.
 
-Når du forbruker Monero, er verdien på inndataene du bruker og verdien på utdataene du sender kryptert og ugjennomsiktig for alle, bortsett fra mottakeren av hver av utdataene. Pedersen-forpliktelser lar deg sende Monero uten å avsløre verdien på transaksjonene. Pedersen-forpliktelser gjør det også mulig for folk å verifisere at transaksjoner på blokkjeden er gyldige og at de ikke oppretter Monero ut av ingenting.
+Når du forbruker Monero, er verdien på inndataene du bruker og verdien på
+utdataene du sender kryptert og ugjennomsiktig for alle, bortsett fra
+mottakeren av hver av utdataene. Pedersen-forpliktelser lar deg sende Monero
+uten å avsløre verdien på transaksjonene. Pedersen-forpliktelser gjør det
+også mulig for folk å verifisere at transaksjoner på blokkjeden er gyldige
+og at de ikke oppretter Monero ut av ingenting.
 
 ### Hva det innebærer
 
-Så lenge de krypterte utdatabeløpene opprettes, som inkluderer en utdata for mottakeren og en veksel-utdata tilbake til senderen, og det ukrypterte transaksjonsgebyret er lik summen av inndataene som brukes, er det en legitim transaksjon, og det kan bekreftes at det ikke opprettes Monero ut av ingenting.
+Så lenge de krypterte utdatabeløpene opprettes, som inkluderer en utdata for
+mottakeren og en veksel-utdata tilbake til senderen, og det ukrypterte
+transaksjonsgebyret er lik summen av inndataene som brukes, er det en
+legitim transaksjon, og det kan bekreftes at det ikke opprettes Monero ut av
+ingenting.
 
-Pedersen-forpliktelser innebærer at summene kan verifiseres som like, men Monero-verdien av hver av summene og Monero-verdien av inndataene og utdataene hver for seg er ubestemte. Pedersen-forpliktelser innebærer også at til og med forholdet mellom én inndata og en annen, eller én utdata og en annen, er ubestemt.
+Pedersen-forpliktelser innebærer at summene kan verifiseres som like, men
+Monero-verdien av hver av summene og Monero-verdien av inndataene og
+utdataene hver for seg er ubestemte. Pedersen-forpliktelser innebærer også
+at til og med forholdet mellom én inndata og en annen, eller én utdata og en
+annen, er ubestemt.
 
-Det er uklart hvilke inndata som virkelig forbrukes i og med at ringsignaturen lister opp både ekte inndata som forbrukes og avledningsinndata, og derfor kan du ikke vite for hvilke inndata Pedersen-forpliktelsene må summeres. Men det er greit, fordi @RingCT-ringsignaturen må bare bevise at utdataene er like for summen av inndataene for én kombinasjon. Dette er, av matematiske årsaker, umulig å forfalske.
+Det er uklart hvilke inndata som virkelig forbrukes i og med at
+ringsignaturen lister opp både ekte inndata som forbrukes og
+avledningsinndata, og derfor kan du ikke vite for hvilke inndata
+Pedersen-forpliktelsene må summeres. Men det er greit, fordi
+@RingCT-ringsignaturen må bare bevise at utdataene er like for summen av
+inndataene for én kombinasjon. Dette er, av matematiske årsaker, umulig å
+forfalske.
 
 ### Inngående informasjon
 
-Se mer informasjon i [Ring Confidential Transactions-dokumentet](https://eprint.iacr.org/2015/1098.pdf), skrevet av Shen Noether i Monero Forskningslaben.
+Se mer informasjon i [Ring Confidential
+Transactions-dokumentet](https://eprint.iacr.org/2015/1098.pdf), skrevet av
+Shen Noether i Monero Forskningslaben.

_i18n/nl/resources/moneropedia/pedersen-commitment.md

@@ -1,23 +1,45 @@
 ---
+summary: 'Pedersen commitments are cryptographic algorithms that allow a prover to commit to a certain value without revealing it or being able to change it'
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments"]
-summary: "Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it"
 ---
 
 {% include disclaimer.html translated="no" translationOutdated="no" %}
+
 ### The Basics
 
-Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it.
+Pedersen commitments are cryptographic algorithms that allow a prover to
+commit to a certain value without revealing it or being able to change it.
 
-When you spend Monero, the value of the inputs that you are spending and the value of the outputs you are sending are encrypted and opaque to everyone except the recipient of each of those outputs. Pedersen commitments allow you to send Monero without revealing the value of the transactions. Pedersen commitments also make it possible for people to verify that transactions on the blockchain are valid and not creating Monero out of thin air.
+When you spend Monero, the value of the inputs that you are spending and the
+value of the outputs you are sending are encrypted and opaque to everyone
+except the recipient of each of those outputs. Pedersen commitments allow
+you to send Monero without revealing the value of the transactions. Pedersen
+commitments also make it possible for people to verify that transactions on
+the blockchain are valid and not creating Monero out of thin air.
 
 ### What It Means
 
-As long as the encrypted output amounts created, which include an output for the recipient and a change output back to the sender, and the unencrypted transaction fee is equal to the sum of the inputs that are being spent, it is a legitimate transaction and can be confirmed to not be creating Monero out of thin air.
+As long as the encrypted output amounts created, which include an output for
+the recipient and a change output back to the sender, and the unencrypted
+transaction fee is equal to the sum of the inputs that are being spent, it
+is a legitimate transaction and can be confirmed to not be creating Monero
+out of thin air.
 
-Pedersen commitments mean that the sums can be verified as being equal, but the Monero value of each of the sums and the Monero value of the inputs and outputs individually are undeterminable. Pedersen commitments also mean that even the ratio of one input to another, or one output to another is undeterminable.
+Pedersen commitments mean that the sums can be verified as being equal, but
+the Monero value of each of the sums and the Monero value of the inputs and
+outputs individually are undeterminable. Pedersen commitments also mean that
+even the ratio of one input to another, or one output to another is
+undeterminable.
 
-It is unclear which inputs are really being spent as the ring signature lists both the real inputs being spent and decoy inputs, therefore you don't actually know which input Pedersen commitments need to be summed. That's okay, because the @RingCT ring signature only has to prove that for one combination of the inputs the outputs are equal to the sum of the inputs. For mathematical reasons, this is impossible to forge.
+It is unclear which inputs are really being spent as the ring signature
+lists both the real inputs being spent and decoy inputs, therefore you don't
+actually know which input Pedersen commitments need to be summed. That's
+okay, because the @RingCT ring signature only has to prove that for one
+combination of the inputs the outputs are equal to the sum of the
+inputs. For mathematical reasons, this is impossible to forge.
 
 ### In-depth Information
 
-See information in [Ring Confidential Transactions paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero Research Lab.
+See information in [Ring Confidential Transactions
+paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero
+Research Lab.

_i18n/pl/resources/moneropedia/pedersen-commitment.md

@@ -1,23 +1,45 @@
 ---
+summary: 'Algorytmy kryptograficzne pozwalające osobie udowadniającej na zobowiązanie się do pewnej wartości bez ujawniania jej ani nie będąc w stanie jej zmienić'
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments", "zobowiązanie", "zobowiązania", "zobowiązaniu", "zobowiązaniom", "zobowiązanie-pedersena", "zobowiązaniu-pedersena", "zobowiązaniem-pedersena"]
-summary: "Algorytmy kryptograficzne pozwalające osobie udowadniającej na zobowiązanie się do pewnej wartości bez ujawniania jej ani nie będąc w stanie jej zmienić."
 ---
 
 {% include disclaimer.html translated="yes" translationOutdated="no" %}
+
 ### Podstawy
 
-Algorytmy kryptograficzne pozwalające osobie udowadniającej na zobowiązanie się do pewnej wartości bez ujawniania jej ani nie będąc w stanie jej zmienić.
+Algorytmy kryptograficzne pozwalające osobie udowadniającej na zobowiązanie
+się do pewnej wartości bez ujawniania jej ani nie będąc w stanie jej
+zmienić.
 
-Przy płatnościach Monero wartość wkładu, którą użytkownik wydaje, oraz wartość wyjściowa są zaszyfrowane i nieprzejrzyste dla wszystkich, z wyjątkiem odbiorcy każdego z wyjść. Zobowiązanie Pedersena pozwala na wysyłanie Monero bez ujawniania wartości transakcji. Umożliwia ono także weryfikację, czy transakcje w łańcuchu bloków są prawdziwe i nie tworzą monet z niczego.
+Przy płatnościach Monero wartość wkładu, którą użytkownik wydaje, oraz
+wartość wyjściowa są zaszyfrowane i nieprzejrzyste dla wszystkich, z
+wyjątkiem odbiorcy każdego z wyjść. Zobowiązanie Pedersena pozwala na
+wysyłanie Monero bez ujawniania wartości transakcji. Umożliwia ono także
+weryfikację, czy transakcje w łańcuchu bloków są prawdziwe i nie tworzą
+monet z niczego.
 
 ### Co to oznacza
 
-Dopóki zaszyfrowane wartości wyjściowe (w skład których wchodzi wyjście dla odbiorcy oraz @reszta zwracana nadawcy) razem z nieszyfrowanymi opłatami za transakcję są równe sumie wydanego wkładu, transakcja jest prawdziwa i może zostać potwierdzona, że nie wytworzyła Monero z niczego.
+Dopóki zaszyfrowane wartości wyjściowe (w skład których wchodzi wyjście dla
+odbiorcy oraz @reszta zwracana nadawcy) razem z nieszyfrowanymi opłatami za
+transakcję są równe sumie wydanego wkładu, transakcja jest prawdziwa i może
+zostać potwierdzona, że nie wytworzyła Monero z niczego.
 
-Zobowiązanie Pedersena oznacza, że sumy są potwierdzone jako równe, jednak wartość Monero każdej z sum oraz wkładu i wyjścia pozostają niemożliwe do określenia. Znaczy to także, że ukryty jest też stosunek jednego wkładu do drugiego lub jednego wyniku do drugiego.
+Zobowiązanie Pedersena oznacza, że sumy są potwierdzone jako równe, jednak
+wartość Monero każdej z sum oraz wkładu i wyjścia pozostają niemożliwe do
+określenia. Znaczy to także, że ukryty jest też stosunek jednego wkładu do
+drugiego lub jednego wyniku do drugiego.
 
-Mimo że pozostaje niejasne, czy wkłady faktycznie zostały wydane (@podpis-pierścieniowy zapisuje zarówno prawdziwe wkłady, jak i te fałszywe, stąd właściwie nie wiadomo, które wartości zobowiązanie Pedersena sumuje), nie jest to problemem, ponieważ podpisy pierścieniowe @poufnych-transakcji-pierścieniowych muszą udowodnić jedynie to, czy suma wyjść jednej kombinacji jest równa sumie wkładów w tej samej kombinacji. Z matematycznego punktu widzenia jest to niemożliwe do sfałszowania.
+Mimo że pozostaje niejasne, czy wkłady faktycznie zostały wydane
+(@podpis-pierścieniowy zapisuje zarówno prawdziwe wkłady, jak i te fałszywe,
+stąd właściwie nie wiadomo, które wartości zobowiązanie Pedersena sumuje),
+nie jest to problemem, ponieważ podpisy pierścieniowe
+@poufnych-transakcji-pierścieniowych muszą udowodnić jedynie to, czy suma
+wyjść jednej kombinacji jest równa sumie wkładów w tej samej kombinacji. Z
+matematycznego punktu widzenia jest to niemożliwe do sfałszowania.
 
 ### Szczegółowe informacje
 
-Przeczytaj więcej w dokumencie Shena Noethera z Laboratorium Badawczego Monero na temat [Poufnych Transakcji Pierścieniowych](https://eprint.iacr.org/2015/1098.pdf).
+Przeczytaj więcej w dokumencie Shena Noethera z Laboratorium Badawczego
+Monero na temat [Poufnych Transakcji
+Pierścieniowych](https://eprint.iacr.org/2015/1098.pdf).

_i18n/pt-br/resources/moneropedia/pedersen-commitment.md

@@ -1,23 +1,45 @@
 ---
+summary: 'Pedersen commitments are cryptographic algorithms that allow a prover to commit to a certain value without revealing it or being able to change it'
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments"]
-summary: "Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it"
 ---
 
 {% include disclaimer.html translated="no" translationOutdated="no" %}
+
 ### The Basics
 
-Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it.
+Pedersen commitments are cryptographic algorithms that allow a prover to
+commit to a certain value without revealing it or being able to change it.
 
-When you spend Monero, the value of the inputs that you are spending and the value of the outputs you are sending are encrypted and opaque to everyone except the recipient of each of those outputs. Pedersen commitments allow you to send Monero without revealing the value of the transactions. Pedersen commitments also make it possible for people to verify that transactions on the blockchain are valid and not creating Monero out of thin air.
+When you spend Monero, the value of the inputs that you are spending and the
+value of the outputs you are sending are encrypted and opaque to everyone
+except the recipient of each of those outputs. Pedersen commitments allow
+you to send Monero without revealing the value of the transactions. Pedersen
+commitments also make it possible for people to verify that transactions on
+the blockchain are valid and not creating Monero out of thin air.
 
 ### What It Means
 
-As long as the encrypted output amounts created, which include an output for the recipient and a change output back to the sender, and the unencrypted transaction fee is equal to the sum of the inputs that are being spent, it is a legitimate transaction and can be confirmed to not be creating Monero out of thin air.
+As long as the encrypted output amounts created, which include an output for
+the recipient and a change output back to the sender, and the unencrypted
+transaction fee is equal to the sum of the inputs that are being spent, it
+is a legitimate transaction and can be confirmed to not be creating Monero
+out of thin air.
 
-Pedersen commitments mean that the sums can be verified as being equal, but the Monero value of each of the sums and the Monero value of the inputs and outputs individually are undeterminable. Pedersen commitments also mean that even the ratio of one input to another, or one output to another is undeterminable.
+Pedersen commitments mean that the sums can be verified as being equal, but
+the Monero value of each of the sums and the Monero value of the inputs and
+outputs individually are undeterminable. Pedersen commitments also mean that
+even the ratio of one input to another, or one output to another is
+undeterminable.
 
-It is unclear which inputs are really being spent as the ring signature lists both the real inputs being spent and decoy inputs, therefore you don't actually know which input Pedersen commitments need to be summed. That's okay, because the @RingCT ring signature only has to prove that for one combination of the inputs the outputs are equal to the sum of the inputs. For mathematical reasons, this is impossible to forge.
+It is unclear which inputs are really being spent as the ring signature
+lists both the real inputs being spent and decoy inputs, therefore you don't
+actually know which input Pedersen commitments need to be summed. That's
+okay, because the @RingCT ring signature only has to prove that for one
+combination of the inputs the outputs are equal to the sum of the
+inputs. For mathematical reasons, this is impossible to forge.
 
 ### In-depth Information
 
-See information in [Ring Confidential Transactions paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero Research Lab.
+See information in [Ring Confidential Transactions
+paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero
+Research Lab.

_i18n/ru/resources/moneropedia/pedersen-commitment.md

@@ -1,23 +1,47 @@
 ---
+summary: 'Обязательства Педерсена представляют собой криптографические алгоритмы, которые позволяют доказывающему сделать расчет обязательства по сумме, не раскрывая её, и будучи не в состоянии её изменить'
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments", "обязательство-Педерсена", "обязательств-Педерсена"]
-summary: "Обязательства Педерсена представляют собой криптографические алгоритмы, которые позволяют доказывающему сделать расчет обязательство по сумме, не раскрывая её, и будучи не в состоянии её изменить"
 ---
 
 {% include disclaimer.html translated="yes" translationOutdated="no" %}
+
 ### Основная информация
 
-Обязательства Педерсена представляют собой криптографические алгоритмы, которые позволяют доказывающему сделать расчет обязательства по сумме, не раскрывая её, и будучи не в состоянии её изменить.
+Обязательства Педерсена представляют собой криптографические алгоритмы,
+которые позволяют доказывающему сделать расчет обязательства по сумме, не
+раскрывая её, и будучи не в состоянии её изменить.
 
-Когда вы тратите Monero, значение входов, которые вы тратите, и значение выходов, которые вы отправляете, шифруются и остаются скрытыми от всех, за исключением получателя каждого из этих выходов. Обязательства Педерсена позволяют отправлять Monero, не раскрывая суммы транзакций. Обязательства Педерсена также позволяют проверить действительность транзакций в блокчейне и не создавать Monero из воздуха.
+Когда вы тратите Monero, значение входов, которые вы тратите, и значение
+выходов, которые вы отправляете, шифруются и остаются скрытыми от всех, за
+исключением получателя каждого из этих выходов. Обязательства Педерсена
+позволяют отправлять Monero, не раскрывая суммы транзакций. Обязательства
+Педерсена также позволяют проверить действительность транзакций в блокчейне
+и не создавать Monero из воздуха.
 
 ### Что это значит
 
-Если создаются выходы с зашифрованными суммами, включая выход для получателя и выход со сдачей, который уходит обратно к отправителю, и зашифрованная комиссия за проведение транзакции равна сумме входов, которые тратятся, то транзакция является действительной, и подтверждается, что Monero создаются не из воздуха.
+Если создаются выходы с зашифрованными суммами, включая выход для получателя
+и выход со сдачей, который уходит обратно к отправителю, и зашифрованная
+комиссия за проведение транзакции равна сумме входов, которые тратятся, то
+транзакция является действительной, и подтверждается, что Monero создаются
+не из воздуха.
 
-Обязательства Педерсена означают, что суммы могут быть верифицированы как равные, но значение Monero в каждой сумме и значение Monero входов и выходов по отдельности определить невозможно. Обязательства Педерсена также означают, что отношение одного входа к другому или же отношение одного выхода к другому не поддаётся определению.
+Обязательства Педерсена означают, что суммы могут быть верифицированы как
+равные, но значение Monero в каждой сумме и значение Monero входов и выходов
+по отдельности определить невозможно. Обязательства Педерсена также
+означают, что отношение одного входа к другому или же отношение одного
+выхода к другому не поддаётся определению.
 
-Остаётся неясным, какие входы реально были потрачены, так как кольцевая подпись содержит как те входы, которые тратятся реально, так и ложные входы. Следовательно, по факту вам не известно, какие входы по обязательствам Педерсена необходимо суммировать. И это хорошо, так как кольцевая подпись @RingCT служит только для того, чтобы доказать, что одна комбинация входов и выходов равна сумме входов. Это невозможно подделать по математическим причинам.
+Остаётся неясным, какие входы реально были потрачены, так как кольцевая
+подпись содержит как те входы, которые тратятся реально, так и ложные
+входы. Следовательно, по факту вам не известно, какие входы по
+обязательствам Педерсена необходимо суммировать. И это хорошо, так как
+кольцевая подпись @RingCT служит только для того, чтобы доказать, что одна
+комбинация входов и выходов равна сумме входов. Это невозможно подделать по
+математическим причинам.
 
 ### Углублённая информация
 
-Ознакомьтесь с работой по [кольцевым конфиденциальным транзакциям](https://eprint.iacr.org/2015/1098.pdf) Шена Ноезера (Shen Noether) из лаборатории Monero Research Lab.
+Ознакомьтесь с работой по [кольцевым конфиденциальным
+транзакциям](https://eprint.iacr.org/2015/1098.pdf) Шена Ноезера (Shen
+Noether) из лаборатории Monero Research Lab.

_i18n/tr/resources/moneropedia/pedersen-commitment.md

@@ -1,23 +1,45 @@
 ---
+summary: 'Pedersen commitments are cryptographic algorithms that allow a prover to commit to a certain value without revealing it or being able to change it'
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments"]
-summary: "Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it"
 ---
 
 {% include disclaimer.html translated="no" translationOutdated="no" %}
+
 ### The Basics
 
-Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it.
+Pedersen commitments are cryptographic algorithms that allow a prover to
+commit to a certain value without revealing it or being able to change it.
 
-When you spend Monero, the value of the inputs that you are spending and the value of the outputs you are sending are encrypted and opaque to everyone except the recipient of each of those outputs. Pedersen commitments allow you to send Monero without revealing the value of the transactions. Pedersen commitments also make it possible for people to verify that transactions on the blockchain are valid and not creating Monero out of thin air.
+When you spend Monero, the value of the inputs that you are spending and the
+value of the outputs you are sending are encrypted and opaque to everyone
+except the recipient of each of those outputs. Pedersen commitments allow
+you to send Monero without revealing the value of the transactions. Pedersen
+commitments also make it possible for people to verify that transactions on
+the blockchain are valid and not creating Monero out of thin air.
 
 ### What It Means
 
-As long as the encrypted output amounts created, which include an output for the recipient and a change output back to the sender, and the unencrypted transaction fee is equal to the sum of the inputs that are being spent, it is a legitimate transaction and can be confirmed to not be creating Monero out of thin air.
+As long as the encrypted output amounts created, which include an output for
+the recipient and a change output back to the sender, and the unencrypted
+transaction fee is equal to the sum of the inputs that are being spent, it
+is a legitimate transaction and can be confirmed to not be creating Monero
+out of thin air.
 
-Pedersen commitments mean that the sums can be verified as being equal, but the Monero value of each of the sums and the Monero value of the inputs and outputs individually are undeterminable. Pedersen commitments also mean that even the ratio of one input to another, or one output to another is undeterminable.
+Pedersen commitments mean that the sums can be verified as being equal, but
+the Monero value of each of the sums and the Monero value of the inputs and
+outputs individually are undeterminable. Pedersen commitments also mean that
+even the ratio of one input to another, or one output to another is
+undeterminable.
 
-It is unclear which inputs are really being spent as the ring signature lists both the real inputs being spent and decoy inputs, therefore you don't actually know which input Pedersen commitments need to be summed. That's okay, because the @RingCT ring signature only has to prove that for one combination of the inputs the outputs are equal to the sum of the inputs. For mathematical reasons, this is impossible to forge.
+It is unclear which inputs are really being spent as the ring signature
+lists both the real inputs being spent and decoy inputs, therefore you don't
+actually know which input Pedersen commitments need to be summed. That's
+okay, because the @RingCT ring signature only has to prove that for one
+combination of the inputs the outputs are equal to the sum of the
+inputs. For mathematical reasons, this is impossible to forge.
 
 ### In-depth Information
 
-See information in [Ring Confidential Transactions paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero Research Lab.
+See information in [Ring Confidential Transactions
+paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero
+Research Lab.

_i18n/zh-cn/resources/moneropedia/pedersen-commitment.md

@@ -1,9 +1,10 @@
 ---
+summary: 佩德森承诺是一种密码算法，它允许验证者在不暴露或无法更改某个值的情况下提交该值。
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments"]
-summary: "Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it"
 ---
 
 {% include disclaimer.html translated="yes" translationOutdated="no" %}
+
 ### 基础知识
 
 佩德森承诺是一种密码算法，它允许验证者在不暴露或无法更改某个值的情况下提交该值。
@@ -20,4 +21,5 @@ summary: "Pedersen commitments are cryptographic algorythms that allow a prover
 
 ### 深度信息
 
-参见，门罗币研究实验室的 Shen Noether 撰写的[环机密交易论文](https://eprint.iacr.org/2015/1098.pdf)。
+参见，门罗币研究实验室的 Shen Noether
+撰写的[环机密交易论文](https://eprint.iacr.org/2015/1098.pdf)。

_i18n/zh-tw/resources/moneropedia/pedersen-commitment.md

@@ -1,23 +1,45 @@
 ---
+summary: 'Pedersen commitments are cryptographic algorithms that allow a prover to commit to a certain value without revealing it or being able to change it'
 terms: ["commitments", "commitment", "pedersen", "pedersen-commitment", "pedersen-commitments"]
-summary: "Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it"
 ---
 
 {% include disclaimer.html translated="no" translationOutdated="no" %}
+
 ### The Basics
 
-Pedersen commitments are cryptographic algorythms that allow a prover to commit to a certain value without revealing it or being able to change it.
+Pedersen commitments are cryptographic algorithms that allow a prover to
+commit to a certain value without revealing it or being able to change it.
 
-When you spend Monero, the value of the inputs that you are spending and the value of the outputs you are sending are encrypted and opaque to everyone except the recipient of each of those outputs. Pedersen commitments allow you to send Monero without revealing the value of the transactions. Pedersen commitments also make it possible for people to verify that transactions on the blockchain are valid and not creating Monero out of thin air.
+When you spend Monero, the value of the inputs that you are spending and the
+value of the outputs you are sending are encrypted and opaque to everyone
+except the recipient of each of those outputs. Pedersen commitments allow
+you to send Monero without revealing the value of the transactions. Pedersen
+commitments also make it possible for people to verify that transactions on
+the blockchain are valid and not creating Monero out of thin air.
 
 ### What It Means
 
-As long as the encrypted output amounts created, which include an output for the recipient and a change output back to the sender, and the unencrypted transaction fee is equal to the sum of the inputs that are being spent, it is a legitimate transaction and can be confirmed to not be creating Monero out of thin air.
+As long as the encrypted output amounts created, which include an output for
+the recipient and a change output back to the sender, and the unencrypted
+transaction fee is equal to the sum of the inputs that are being spent, it
+is a legitimate transaction and can be confirmed to not be creating Monero
+out of thin air.
 
-Pedersen commitments mean that the sums can be verified as being equal, but the Monero value of each of the sums and the Monero value of the inputs and outputs individually are undeterminable. Pedersen commitments also mean that even the ratio of one input to another, or one output to another is undeterminable.
+Pedersen commitments mean that the sums can be verified as being equal, but
+the Monero value of each of the sums and the Monero value of the inputs and
+outputs individually are undeterminable. Pedersen commitments also mean that
+even the ratio of one input to another, or one output to another is
+undeterminable.
 
-It is unclear which inputs are really being spent as the ring signature lists both the real inputs being spent and decoy inputs, therefore you don't actually know which input Pedersen commitments need to be summed. That's okay, because the @RingCT ring signature only has to prove that for one combination of the inputs the outputs are equal to the sum of the inputs. For mathematical reasons, this is impossible to forge.
+It is unclear which inputs are really being spent as the ring signature
+lists both the real inputs being spent and decoy inputs, therefore you don't
+actually know which input Pedersen commitments need to be summed. That's
+okay, because the @RingCT ring signature only has to prove that for one
+combination of the inputs the outputs are equal to the sum of the
+inputs. For mathematical reasons, this is impossible to forge.
 
 ### In-depth Information
 
-See information in [Ring Confidential Transactions paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero Research Lab.
+See information in [Ring Confidential Transactions
+paper](https://eprint.iacr.org/2015/1098.pdf) by Shen Noether of the Monero
+Research Lab.

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