Abstract: A method includes: accessing a transaction to execute a target blockchain object, the transaction defining a target object identifier, a target puzzle, and a solution representing a set of arguments associated with the target puzzle; generating a target puzzle hash based on the target puzzle; identifying a first blockchain object—in a set of blockchain objects—defining a first object identifier, and a first puzzle hash representing a first puzzle; generating an output in response to executing the target puzzle based on the solution; and, in response to detecting a match between the target object identifier and the first object identifier, in response to detecting a match between the target puzzle hash and the first puzzle hash, and in response to evaluating the output as true, generating a second blockchain object in the set of blockchain objects, and removing the first blockchain object from the set of blockchain objects.

Abstract: A method for extending a blockchain includes, at a space server in a distributed network: storing a plot file. The method also includes accessing a blockchain: during a current slot in the series of slots, accessing a proof-of-space challenge based on a current slot challenge associated with the current slot and a challenge chain signage point; in response to accessing the proof-of-space challenge, retrieving a proof-of-space based on the proof-of-space challenge and the plot file; calculating a quality-based number of iterations based on the quality of the proof-of-space; generating a block comprising the proof-of-space, the challenge chain signage point, and a reward chain signage point; and broadcasting the block to the distributed network.

Abstract: A method includes: generating a set of output entries based on a set of initial entries; identifying a matching pair of entries in the set of output entries; generating a first forward-propagated entry in a second set of entries based on the first matching pair of entries; identifying a second matching pair of entries in the second set of entries; identifying a group of initial entries associated with the second matching pair of entries; extracting a subset of bits, in a set of target bits, from each initial entry in the group of initial entries; generating a second forward-propagated entry—representing a proof fragment—in a third set of entries in a third table by encrypting the set of target bits; generating a plot file representing a set of tables including the third table; and storing the plot file.

Abstract: A method includes: accessing a transaction to execute a target blockchain object, the transaction defining a target object identifier, a target puzzle, and a solution representing a set of arguments associated with the target puzzle; generating a target puzzle hash based on the target puzzle; identifying a first blockchain object—in a set of blockchain objects—defining a first object identifier, and a first puzzle hash representing a first puzzle; generating an output in response to executing the target puzzle based on the solution; and, in response to detecting a match between the target object identifier and the first object identifier, in response to detecting a match between the target puzzle hash and the first puzzle hash, and in response to evaluating the output as true, generating a second blockchain object in the set of blockchain objects, and removing the first blockchain object from the set of blockchain objects.

Abstract: A method includes: generating a set of output entries based on a set of initial entries; identifying a matching pair of entries in the set of output entries; generating a first forward-propagated entry in a second set of entries based on the first matching pair of entries; identifying a second matching pair of entries in the second set of entries; identifying a group of initial entries associated with the second matching pair of entries; extracting a subset of bits, in a set of target bits, from each initial entry in the group of initial entries; generating a second forward-propagated entry—representing a proof fragment—in a third set of entries in a third table by encrypting the set of target bits; generating a plot file representing a set of tables including the third table; and storing the plot file.

Abstract: A method includes: generating a set of output entries based on a set of initial entries; identifying a matching pair of entries in the set of output entries; generating a first forward-propagated entry in a second set of entries based on the first matching pair of entries; identifying a second matching pair of entries in the second set of entries; identifying a group of initial entries associated with the second matching pair of entries; extracting a subset of bits, in a set of target bits, from each initial entry in the group of initial entries; generating a second forward-propagated entry—representing a proof fragment—in a third set of entries in a third table by encrypting the set of target bits; generating a plot file representing a set of tables including the third table; and storing the plot file.

Abstract: A method includes: generating a hash tree representing a structured data object including a data unit, the hash tree including a root hash and a data unit hash representing the data unit; submitting a first transaction to a distributed network, the first transaction configured to generate a blockchain object including the root hash, the blockchain object configured to generate an announcement representing membership of the data unit hash in the hash tree; and submitting a second transaction to the distributed network, the second transaction configured to trigger the blockchain object to generate the announcement based on a proof of inclusion of the data unit hash within the hash tree.

Abstract: A method includes: generating a first transaction configured to spend a first blockchain object representing a first asset, spend a second blockchain object representing a second asset, and generate a state channel object associated with an initial virtual object representing an initial state; transmitting the first transaction to a distributed network for inclusion in a first block of a blockchain; generating a second transaction configured to spend the initial virtual object and generate a first virtual object representing a first state; generating a third transaction configured to spend the state channel object associated with a target virtual object representing a target state, generate a third blockchain object representing a third asset based on the target state, and generate a fourth blockchain object representing a fourth asset based on the target state; and transmitting the third transaction to the distributed network for inclusion in a second block of the blockchain.

Abstract: A method for communicating data between a first blockchain and a second blockchain includes: accessing a message identifier for a message associated with the second blockchain; accessing signatures representing detection of the message, containing a representation of the message identifier, in a block in the second blockchain by validator nodes for the first blockchain; generating a transaction including the signatures and configured to trigger a portal object to generate a message object, associated with the first blockchain, representing the message in response to detecting the signatures; and transmitting the transaction to a distributed network associated with the first blockchain for commitment in a block in the first blockchain.

Abstract: A method for extending a blockchain comprises, at a space server: allocating an amount of drive storage for generating proofs-of-space; or accessing a first challenge based on a prior block of the blockchain, the prior block comprising a first proof-of-space and a first proof-of-time; in response to accessing the first challenge, generating a second proof-of-space based on the first challenge and the amount of drive storage, the second proof-of-space indicating allocation of the amount of drive storage; accessing a second proof-of-time based on the prior block and indicating a first time delay elapsed after extension of the blockchain with the prior block; generating a new block comprising the second proof-of-space and the second proof-of-time; and broadcasting the new block over a distributed network.

Abstract: A method includes, by a first node in a distributed network: generating a hash tree representing a structured data object including a data unit, the hash tree including a root hash and a data unit hash representing the data unit; accessing a non-interactive proof of inclusion representing membership of the data unit hash within the hash tree; generating a transaction configured to generate a blockchain object including the root hash; and transmitting the transaction and the non-interactive proof of inclusion to a second data node in the distributed network.

Abstract: A method includes, by a first node in a distributed network: generating a hash tree representing a structured data object including a data unit, the hash tree including a root hash and a data unit hash representing the data unit; accessing a non-interactive proof of inclusion representing membership of the data unit hash within the hash tree; generating a transaction configured to generate a blockchain object including the root hash; and transmitting the transaction and the non-interactive proof of inclusion to a second data node in the distributed network.

Abstract: A method includes: generating a first transaction configured to spend a first blockchain object representing a first asset, spend a second blockchain object representing a second asset, and generate a state channel object associated with an initial virtual object representing an initial state; transmitting the first transaction to a distributed network for inclusion in a first block of a blockchain; generating a second transaction configured to spend the initial virtual object and generate a first virtual object representing a first state; generating a third transaction configured to spend the state channel object associated with a target virtual object representing a target state, generate a third blockchain object representing a third asset based on the target state, and generate a fourth blockchain object representing a fourth asset based on the target state; and transmitting the third transaction to the distributed network for inclusion in a second block of the blockchain.

Abstract: A method for extending a blockchain comprises, at a space server: allocating an amount of drive storage for generating proofs-of-space; or accessing a first challenge based on a prior block of the blockchain, the prior block comprising a first proof-of-space and a first proof-of-time; in response to accessing the first challenge, generating a second proof-of-space based on the first challenge and the amount of drive storage, the second proof-of-space indicating allocation of the amount of drive storage; accessing a second proof-of-time based on the prior block and indicating a first time delay elapsed after extension of the blockchain with the prior block; generating a new block comprising the second proof-of-space and the second proof-of-time; and broadcasting the new block over a distributed network.

Abstract: A method for extending a blockchain includes, at a space server in a distributed network: storing a plot file. The method also includes accessing a blockchain: during a current slot in the series of slots, accessing a proof-of-space challenge based on a current slot challenge associated with the current slot and a challenge chain signage point; in response to accessing the proof-of-space challenge, retrieving a proof-of-space based on the proof-of-space challenge and the plot file; calculating a quality-based number of iterations based on the quality of the proof-of-space; generating a block comprising the proof-of-space, the challenge chain signage point, and a reward chain signage point; and broadcasting the block to the distributed network.

Abstract: A method includes: generating a first transaction configured to spend a first blockchain object representing a first asset, spend a second blockchain object representing a second asset, and generate a state channel object associated with an initial virtual object representing an initial state; transmitting the first transaction to a distributed network for inclusion in a first block of a blockchain; generating a second transaction configured to spend the initial virtual object and generate a first virtual object representing a first state; generating a third transaction configured to spend the state channel object associated with a target virtual object representing a target state, generate a third blockchain object representing a third asset based on the target state, and generate a fourth blockchain object representing a fourth asset based on the target state; and transmitting the third transaction to the distributed network for inclusion in a second block of the blockchain.

Abstract: A method for pooling and retrieving block rewards in a reward pool including an operator node and a set of member nodes in a distributed network extending a proof-of-space-based blockchain includes: submitting a transaction configured to generate a singleton in a set of singletons, the singleton including: an outer puzzle hash linking the singleton to a singleton puzzle hash; and an inner puzzle hash defining a pool address associated with the reward pool; generating a block including a proof-of-space and a block reward allocated to the singleton puzzle hash; detecting the block reward allocated to the singleton puzzle hash; identifying the singleton linked to the singleton puzzle hash; and submitting a transaction configured to: remove the singleton from the set of singletons; and transfer the block reward from the singleton puzzle hash to the pool address.

Abstract: A method for extending a blockchain comprises, at a space server: allocating an amount of drive storage for generating proofs-of-space; or accessing a first challenge based on a prior block of the blockchain, the prior block comprising a first proof-of-space and a first proof-of-time; in response to accessing the first challenge, generating a second proof-of-space based on the first challenge and the amount of drive storage, the second proof-of-space indicating allocation of the amount of drive storage; accessing a second proof-of-time based on the prior block and indicating a first time delay elapsed after extension of the blockchain with the prior block; generating a new block comprising the second proof-of-space and the second proof-of-time; and broadcasting the new block over a distributed network.

Abstract: A method for extending a blockchain includes, at a space server in a distributed network: storing a plot file. The method also includes accessing a blockchain: during a current slot in the series of slots, accessing a proof-of-space challenge based on a current slot challenge associated with the current slot and a challenge chain signage point; in response to accessing the proof-of-space challenge, retrieving a proof-of-space based on the proof-of-space challenge and the plot file; calculating a quality-based number of iterations based on the quality of the proof-of-space; generating a block comprising the proof-of-space, the challenge chain signage point, and a reward chain signage point; and broadcasting the block to the distributed network.

Abstract: A method for pooling and retrieving block rewards in a reward pool including an operator node and a set of member nodes in a distributed network extending a proof-of-space-based blockchain includes: submitting a transaction configured to generate a singleton in a set of singletons, the singleton including: an outer puzzle hash linking the singleton to a singleton puzzle hash; and an inner puzzle hash defining a pool address associated with the reward pool; generating a block including a proof-of-space and a block reward allocated to the singleton puzzle hash; detecting the block reward allocated to the singleton puzzle hash; identifying the singleton linked to the singleton puzzle hash; and submitting a transaction configured to: remove the singleton from the set of singletons; and transfer the block reward from the singleton puzzle hash to the pool address.