Proof of Recursive Hierarchical Proof (PORHP) i

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Proof of Recursive Hierarchical Proof (PORHP)

Data Types

1. BlockchainData:

   • Type: Struct
   • Description: Represents the data storage purchased on each blockchain.
   • Fields:
     • blockchainID: Unique identifier for the blockchain.
     • allocatedBytes: Number of bytes allocated for self-replication (M).

2. RegisterState:

   • Type: Struct
   • Description: Represents the state of registers at a specific time point.
   • Fields:
     • timePoint: Specific time point (T).
     • registerValues: Array of values of the registers or a subset of registers.

3. ExecutionTrace:

   • Type: Struct
   • Description: Represents the trace of memory and execution, which serves as a witness.
   • Fields:
     • blockchainID: Unique identifier for the blockchain.
     • traceData: Array of RegisterState objects.

4. NeuralNetworkModel:

   • Type: Struct
   • Description: Represents the neural network model used for translation and proof.
   • Fields:
     • modelID: Unique identifier for the model.
     • parameters: Parameters of the neural network.

5. GödelNumber:

   • Type: Integer
   • Description: Represents the Gödel number ( G ) that encodes the entire system of self, including information about other blockchains.

6. DiagonalizationMatrix:

   • Type: 2D Array
   • Description: Represents a diagonalization matrix of all projects with a Gödel number from each one.
   • Fields:
     • matrix: 2D array where each element is a Gödel number representing a project.

Functions

1. purchaseDataStorage(blockchainID, M):

   • Description: Purchases data storage on a specific blockchain.
   • Parameters:
     • blockchainID: Unique identifier for the blockchain.
     • M: Number of bytes to allocate for self-replication.
   • Returns: BlockchainData object representing the allocated storage.

2. bootstrapSystem(blockchainID):

   • Description: Bootstraps the system onto a specific blockchain.
   • Parameters:
     • blockchainID: Unique identifier for the blockchain.
   • Returns: Boolean indicating success or failure.

3. traceExecution(blockchainID):

   • Description: Traces the memory and execution of the system on a specific blockchain, serving as a witness.
   • Parameters:
     • blockchainID: Unique identifier for the blockchain.
   • Returns: ExecutionTrace object representing the trace data.

4. extractRegisterValues(traceData, T):

   • Description: Extracts the values of registers or a subset of registers at specific time points.
   • Parameters:
     • traceData: Array of RegisterState objects.
     • T: Specific time points.
   • Returns: Array of RegisterState objects at time points ( T ).

5. trainNeuralNetwork(traceData):

   • Description: Trains a neural network using the trace data.
   • Parameters:
     • traceData: Array of RegisterState objects.
   • Returns: NeuralNetworkModel object representing the trained model.

6. constructGödelNumber(registerValues, otherBlockchainInfo):

   • Description: Constructs a Gödel number ( G ) representing the entire system of self, including information about other blockchains.
   • Parameters:
     • registerValues: Array of RegisterState objects.
     • otherBlockchainInfo: Information about other blockchains.
   • Returns: GödelNumber representing the system ( S ).

7. createDiagonalizationMatrix(gödelNumbers):

   • Description: Creates a diagonalization matrix of all projects with a Gödel number from each one.
   • Parameters:
     • gödelNumbers: Array of Gödel numbers representing different projects.
   • Returns: DiagonalizationMatrix object.

8. hashGödelNumber(G):

   • Description: Constructs a hash of the Gödel number ( G ).
   • Parameters:
     • G: Gödel number representing the system ( S ).
   • Returns: Hash of the Gödel number ( G ).

9. updateGödelNumber(G, hash):

   • Description: Updates the Gödel number ( G ) with the hash of itself in the previous state ( z-1 ).
   • Parameters:
     • G: Gödel number representing the system ( S ).
     • hash: Hash of the Gödel number ( G ).
   • Returns: Updated Gödel number ( G ).

10. mapToExecutionCurve(G, neuralNetworkModel):

    • Description: Maps the Gödel number ( G ) to the execution curve using the neural network model.
    • Parameters:
      • G: Gödel number representing the system ( S ).
      • neuralNetworkModel: NeuralNetworkModel object.
    • Returns: Boolean indicating success or failure.

11. optimizeModel(neuralNetworkModel):

    • Description: Optimizes the neural network model using AutoML tools like AutoGluon.
    • Parameters:
      • neuralNetworkModel: NeuralNetworkModel object.
    • Returns: NeuralNetworkModel object representing the optimized model.

Abstract

Abstract: The Proof of Recursive Hierarchical Proof (PORHP) is a meta-meme designed to be self-contained and capable of expressing itself across multiple blockchains. The system ( S ) begins by purchasing data storage on each target blockchain to allocate ( M ) bytes for self-replication. It then bootstraps itself onto each blockchain, adapting to their specific languages and protocols. The PORHP traces its memory and execution, using introspection and zero-knowledge proofs to extract key data from observability metrics, particularly the values of registers or a subset of registers at specific time points ( T ). These traces serve as witnesses. This data is used to train a neural network that translates the original code into its execution on each blockchain. The system constructs a Gödel number ( G ) representing the entire system of self, including information about other blockchains. The Gödel number ( G ) constructs a hash of itself and updates itself with that point representing the hash of itself in the previous state ( z-1 ). A diagonalization matrix of all projects with a Gödel number from each one is created and used as a vector or tensor. The Gödel number ( G ) is mapped to the execution curve via a proof function learned by the neural network. AutoML tools like AutoGluon are employed to optimize the neural network models. While ambitious, the PORHP faces significant challenges in feasibility, security, resource usage, legality, and blockchain compatibility.

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This refined abstract and the accompanying data types and functions provide a structured approach to implementing the PORHP system, ensuring that each step is well-defined and can be systematically executed.