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 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 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 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.

Abstract: Disclosed are aspects of an untrusted decentralized computing platform that includes an untrusted decentralized database which participant computing systems within the platform reach consensus on an accepted representation thereof. Some aspects of the databased include one or more directed acyclic graphs, which may include cryptographic hash pointers. Some aspects include an untrusted decentralized database architecture that includes two constituent chains. Some aspects of a consensus layer of the untrusted decentralized computing platform alternate a proof of space with a verifiable delay function to reduce compute resource waste relative to systems reliant on compute sources for proofs of work. In some aspects of a consensus layer alternating the proof-of-space and the proof-of-time, a single difficulty factors may be determined by multiplying their difficulty factors together to generate a single variable which accounts for difficulty for both proofs.

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.

Abstract: Disclosed are aspects of an untrusted decentralized computing platform that includes an untrusted decentralized database which participant computing systems within the platform reach consensus on an accepted representation thereof. Some aspects of the databased include one or more directed acyclic graphs, which may include cryptographic hash pointers. Some aspects include an untrusted decentralized database architecture that includes two constituent chains. Some aspects of a consensus layer of the untrusted decentralized computing platform alternate a proof of space with a verifiable delay function to reduce compute resource waste relative to systems reliant on compute sources for proofs of work. In some aspects of a consensus layer alternating the proof-of-space and the proof-of-time, a single difficulty factors may be determined by multiplying their difficulty factors together to generate a single variable which accounts for difficulty for both proofs.

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: Disclosed are aspects of an untrusted decentralized computing platform that includes an untrusted decentralized database which participant computing systems within the platform reach consensus on an accepted representation thereof. Some aspects of the databased include one or more directed acyclic graphs, which may include cryptographic hash pointers. Some aspects include an untrusted decentralized database architecture that includes two constituent chains. Some aspects of a consensus layer of the untrusted decentralized computing platform alternate a proof of space with a verifiable delay function to reduce compute resource waste relative to systems reliant on compute sources for proofs of work. In some aspects of a consensus layer alternating the proof-of-space and the proof-of-time, a single difficulty factors may be determined by multiplying their difficulty factors together to generate a single variable which accounts for difficulty for both proofs.

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: Disclosed are aspects of an untrusted decentralized computing platform that includes an untrusted decentralized database which participant computing systems within the platform reach consensus on an accepted representation thereof. Some aspects of the databased include one or more directed acyclic graphs, which may include cryptographic hash pointers. Some aspects include an untrusted decentralized database architecture that includes two constituent chains. Some aspects of a consensus layer of the untrusted decentralized computing platform alternate a proof of space with a verifiable delay function to reduce compute resource waste relative to systems reliant on compute sources for proofs of work. In some aspects of a consensus layer alternating the proof-of-space and the proof-of-time, a single difficulty factors may be determined by multiplying their difficulty factors together to generate a single variable which accounts for difficulty for both proofs.