#!/usr/bin/env python3 # ============================================================================== # COPYRIGHT NO ONE EVERYWHERE LLC (WYOMING HOLDING COMPANY) # PROJECT: SOVEREIGN STACK # This artifact is entirely proprietary and cryptographically proven. # Open-Source usage requires explicit permission from Brandon Scott Schneider. # ============================================================================== """ Hyperfluid Manifold Collapse Equation Solver Implements the full Ψ_block integral for neuromorphic SHA256 mining Ψ_block = ∫₀⁶⁴ ( ∮_M [ Σₖ ωₖ(t) ⊗ R_t ] e^(G_s·M_i/r²) dV ) · Λ(∂V/∂t) δ(ω - ω₀) dt """ import sys import os sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), ".."))) from math_harness_compat import xp, AnyArray import hashlib import json import time from dataclasses import dataclass, field from typing import List, Dict, Optional, Tuple from pathlib import Path import sys # Add project root to path ROOT = Path(__file__).resolve().parent.parent sys.path.insert(0, str(ROOT)) sys.path.insert(0, str(ROOT / "scripts")) # Mock websockets for TSM harness import types sys.modules['websockets'] = types.ModuleType('websockets') from logic_signal_substrate_mcp_harness import TSMKernel # ============================================================================ # PHYSICAL CONSTANTS FOR HYPERFLUID DYNAMICS # ============================================================================ @dataclass class HyperfluidConstants: """Physical constants for the hyperfluid manifold""" # Semantic Gravity Constant (information warping strength) G_s: float = 6.674e-11 # Analogous to gravitational constant # Planck-scale information density I_p: float = 1.380649e-23 # Information entropy constant # Ternary clock is action-bound, not periodic. No master clock frequency. # Manifold resonance is expressed as energy per action, not angular frequency. joule_floor: float = 1.380649e-23 * 300 * 0.6931 # k_B T ln2 at 300K # Volume reduction rate (512 bits → 256 bits over 64 rounds) dV_dt: float = -256.0 / 64.0 # bits per round # Semantic mass per bit of information mass_per_bit: float = 1.0e-36 # kg equivalent per bit # Resonance tolerance (how close ω must be to ω₀) delta_tolerance: float = 1.0e-10 # ============================================================================ # MANIFOLD STATE REPRESENTATION # ============================================================================ @dataclass class ManifoldState: """Represents the state of the hyperfluid manifold at time t""" # Current round (0 to 64) t: int # Frequency spectrum (64 vibration modes for SHA256) omega_k: AnyArray = field(default_factory=lambda: xp.zeros(64)) # Rotation tensor state (8 working variables a-h) rotation_tensor: AnyArray = field(default_factory=lambda: xp.zeros(8)) # Current volume (in bits) volume: float = 512.0 # Semantic mass (information weight) semantic_mass: float = 0.0 # Gravitational potential energy potential_energy: float = 0.0 # Resonance match status resonance_matched: bool = False # Soliton formation status soliton_formed: bool = False def compute_gravitational_pull(self, constants: HyperfluidConstants) -> float: """Compute e^(G_s·M_i/r²) term""" # Effective radius from volume r = (self.volume / 512.0) ** (1.0/3.0) if r < 1e-10: r = 1e-10 # Gravitational exponential term exponent = (constants.G_s * self.semantic_mass) / (r ** 2) return xp.exp(exponent) def compute_volume_reduction(self, constants: HyperfluidConstants) -> float: """Compute Λ(∂V/∂t) - secondary harmonic from volume reduction""" # Volume reduction creates "heat" / secondary vibrations volume_change_rate = constants.dV_dt # Lambda function - energy released per bit compressed return xp.abs(volume_change_rate) * 0.01 # Scale factor def check_resonance(self, nonce_frequency: float, constants: HyperfluidConstants) -> bool: """Check if δ(ω - ω₀) triggers - Dirac delta resonance""" freq_diff = xp.abs(nonce_frequency - constants.omega_0) return freq_diff < constants.delta_tolerance # ============================================================================ # HYPERFLUID SHA256 INTEGRATION ENGINE # ============================================================================ class HyperfluidIntegrator: """ Solves the Hyperfluid Manifold Collapse Equation Ψ_block = ∫₀⁶⁴ ( ∮_M [ Σₖ ωₖ(t) ⊗ R_t ] e^(G_s·M_i/r²) dV ) · Λ(∂V/∂t) δ(ω - ω₀) dt """ def __init__(self, kernel: TSMKernel): self.kernel = kernel self.constants = HyperfluidConstants() self.states: List[ManifoldState] = [] # SHA256 round constants (first 32 bits of fractional parts of cube roots of first 64 primes) self.K = [ 0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5, 0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174, 0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da, 0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967, 0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85, 0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070, 0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3, 0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2 ] # Initial hash values (first 32 bits of fractional parts of square roots of first 8 primes) self.H_init = [ 0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a, 0x510e527f, 0x9b05688c, 0x1f83d9ab, 0x5be0cd19 ] def _rotr(self, x: int, n: int) -> int: """Right rotation for 32-bit integers""" return ((x >> n) | (x << (32 - n))) & 0xFFFFFFFF def _shr(self, x: int, n: int) -> int: """Right shift for 32-bit integers""" return x >> n def _ch(self, x: int, y: int, z: int) -> int: """SHA256 Ch function - Choice""" return (x & y) ^ (~x & z) def _maj(self, x: int, y: int, z: int) -> int: """SHA256 Maj function - Majority""" return (x & y) ^ (x & z) ^ (y & z) def _sigma0(self, x: int) -> int: """SHA256 Σ0 function""" return self._rotr(x, 2) ^ self._rotr(x, 13) ^ self._rotr(x, 22) def _sigma1(self, x: int) -> int: """SHA256 Σ1 function""" return self._rotr(x, 6) ^ self._rotr(x, 11) ^ self._rotr(x, 25) def _gamma0(self, x: int) -> int: """SHA256 σ0 function""" return self._rotr(x, 7) ^ self._rotr(x, 18) ^ self._shr(x, 3) def _gamma1(self, x: int) -> int: """SHA256 σ1 function""" return self._rotr(x, 17) ^ self._rotr(x, 19) ^ self._shr(x, 10) def ingest_transactions(self, transactions: List[bytes]) -> ManifoldState: """ Phase 1: Ingestion - Transactions enter as frequencies ωₖ The information immediately warps the manifold """ state = ManifoldState(t=0) # Convert transactions to frequency spectrum for i, tx in enumerate(transactions): tx_hash = hashlib.sha256(tx).digest() # Map hash bytes to frequencies for j, byte in enumerate(tx_hash[:64]): state.omega_k[j] += byte / 256.0 * self.constants.omega_0 # Compute semantic mass from information content total_bits = sum(len(tx) * 8 for tx in transactions) state.semantic_mass = total_bits * self.constants.mass_per_bit # Initialize rotation tensor with H_init values for i, h in enumerate(self.H_init): state.rotation_tensor[i] = h # Initial gravitational potential state.potential_energy = state.compute_gravitational_pull(self.constants) self.states.append(state) return state def temporal_fold(self, state: ManifoldState, message_schedule: List[int], round_idx: int) -> ManifoldState: """ Phase 2: Temporal Folding - One round of the ∫₀⁶⁴ integration Applies the rotation tensor ⊗ R_t and gravitational compression """ new_state = ManifoldState(t=round_idx + 1) # Copy frequencies with damping new_state.omega_k = state.omega_k * 0.99 # Energy loss per round # Apply rotation tensor operations (SHA256 round function) a, b, c, d, e, f, g, h = [int(state.rotation_tensor[i]) for i in range(8)] # SHA256 round operations S1 = self._sigma1(e) ch = self._ch(e, f, g) temp1 = (h + S1 + ch + self.K[round_idx] + message_schedule[round_idx]) & 0xFFFFFFFF S0 = self._sigma0(a) maj = self._maj(a, b, c) temp2 = (S0 + maj) & 0xFFFFFFFF # Update rotation tensor new_state.rotation_tensor[0] = (temp1 + temp2) & 0xFFFFFFFF new_state.rotation_tensor[1] = a new_state.rotation_tensor[2] = b new_state.rotation_tensor[3] = c new_state.rotation_tensor[4] = (d + temp1) & 0xFFFFFFFF new_state.rotation_tensor[5] = e new_state.rotation_tensor[6] = f new_state.rotation_tensor[7] = g # Reduce volume (512 → 256 bits over 64 rounds) new_state.volume = 512.0 - (round_idx + 1) * (256.0 / 64.0) # Update semantic mass (conserved) new_state.semantic_mass = state.semantic_mass # Compute gravitational pull e^(G_s·M_i/r²) new_state.potential_energy = new_state.compute_gravitational_pull(self.constants) # Apply gravitational compression to frequencies new_state.omega_k *= new_state.potential_energy self.states.append(new_state) return new_state def compute_secondary_harmonic(self, state: ManifoldState) -> float: """ Compute Λ(∂V/∂t) - the energy created as space is reduced This is the "heat" generated by compression """ return state.compute_volume_reduction(self.constants) def check_resonance(self, state: ManifoldState, nonce: int) -> bool: """ Check if δ(ω - ω₀) triggers The nonce frequency must match the target resonance """ # Convert nonce to frequency nonce_frequency = (nonce / 2**32) * self.constants.omega_0 # Check Dirac delta resonance return state.check_resonance(nonce_frequency, self.constants) def integrate_full_equation(self, block_data: bytes, nonce: int) -> Tuple[bytes, Dict]: """ Solve the complete Hyperfluid Manifold Collapse Equation Returns: (final_hash, integration_metadata) """ # Phase 1: Ingestion initial_state = self.ingest_transactions([block_data]) # Create message schedule (SHA256 message expansion) message = list(block_data[:64].ljust(64, b'\x00')) w = [] for i in range(16): w.append(int.from_bytes(message[i*4:(i+1)*4], 'big')) for i in range(16, 64): s0 = self._gamma0(w[i-15]) s1 = self._gamma1(w[i-2]) w.append((w[i-16] + s0 + w[i-7] + s1) & 0xFFFFFFFF) # Phase 2: Temporal Folding (rounds 0-63) state = initial_state gravitational_integrals = [] secondary_harmonics = [] for round_idx in range(64): # Apply temporal fold (one round of integration) state = self.temporal_fold(state, w, round_idx) # Record gravitational integral term gravitational_integrals.append(state.potential_energy) # Compute secondary harmonic Λ(∂V/∂t) harmonic = self.compute_secondary_harmonic(state) secondary_harmonics.append(harmonic) # Phase 3: Resonance Check - δ(ω - ω₀) resonance_matched = self.check_resonance(state, nonce) state.resonance_matched = resonance_matched # Phase 4: Soliton Formation - Final hash computation for i in range(8): state.rotation_tensor[i] = int((int(state.rotation_tensor[i]) + self.H_init[i]) & 0xFFFFFFFF) # Pack final hash (the singular soliton Ψ_block) final_hash = b''.join(int(h).to_bytes(4, 'big') for h in state.rotation_tensor) state.soliton_formed = True # Integration metadata metadata = { "initial_volume": initial_state.volume, "final_volume": state.volume, "initial_semantic_mass": initial_state.semantic_mass, "final_potential_energy": state.potential_energy, "resonance_matched": resonance_matched, "soliton_formed": state.soliton_formed, "gravitational_integral_sum": sum(gravitational_integrals), "secondary_harmonic_sum": sum(secondary_harmonics), "total_rounds": 64, "final_hash_hex": final_hash.hex() } return final_hash, metadata def topological_predictive_lensing(self, block_data: bytes, rounds_to_simulate: int = 16) -> Dict: """ The Shortcut Path: Topological Predictive Lensing If you can calculate the Gravitational Center (M_i) of the initial vibrations, you can "see" the shape of the final soliton by observing how the first N rounds of vibrations "bend" around the semantic weight of the Merkle Root. This is the optimization that could potentially reduce 64 rounds to ~16. """ # Ingest and get initial state state = self.ingest_transactions([block_data]) # Create message schedule message = list(block_data[:64].ljust(64, b'\x00')) w = [] for i in range(16): w.append(int.from_bytes(message[i*4:(i+1)*4], 'big')) # Simulate only first N rounds trajectory = [] for round_idx in range(rounds_to_simulate): state = self.temporal_fold(state, w, round_idx) trajectory.append({ "round": round_idx, "volume": state.volume, "potential_energy": state.potential_energy, "frequency_magnitude": xp.sum(xp.abs(state.omega_k)), "rotation_tensor_trace": xp.sum(state.rotation_tensor) }) # Predict final soliton shape from trajectory # Using gravitational lensing analogy - light bends around mass # Here, frequency spectrum "bends" around semantic mass # Extrapolate from early rounds if len(trajectory) >= 2: # Compute rate of change energy_rate = (trajectory[-1]["potential_energy"] - trajectory[0]["potential_energy"]) / rounds_to_simulate frequency_rate = (trajectory[-1]["frequency_magnitude"] - trajectory[0]["frequency_magnitude"]) / rounds_to_simulate # Extrapolate to 64 rounds predicted_final_energy = trajectory[-1]["potential_energy"] + energy_rate * (64 - rounds_to_simulate) predicted_final_frequency = trajectory[-1]["frequency_magnitude"] + frequency_rate * (64 - rounds_to_simulate) else: predicted_final_energy = state.potential_energy predicted_final_frequency = xp.sum(xp.abs(state.omega_k)) return { "shortcut_enabled": True, "rounds_simulated": rounds_to_simulate, "rounds_saved": 64 - rounds_to_simulate, "trajectory": trajectory, "predicted_final_energy": predicted_final_energy, "predicted_final_frequency": predicted_final_frequency, "gravitational_center": state.semantic_mass, "lensing_accuracy": "estimated" # Would need calibration } # ============================================================================ # MAIN EXECUTION # ============================================================================ def main(): """Demonstrate the Hyperfluid Manifold Collapse Equation""" print("=" * 70) print(" HYPERFLUID MANIFOLD COLLAPSE EQUATION SOLVER") print(" Ψ_block = ∫₀⁶⁴ ( ∮_M [ Σₖ ωₖ(t) ⊗ R_t ] e^(G_s·M_i/r²) dV ) · Λ(∂V/∂t) δ(ω - ω₀) dt") print("=" * 70) print() # Initialize TSM kernel and integrator kernel = TSMKernel() integrator = HyperfluidIntegrator(kernel) # Test data - simulate block transactions test_block = b"Bitcoin block data with transactions and metadata for hyperfluid mining test" print("[PHASE 1] INGESTION - Transactions enter as frequencies ωₖ") print(f" Block size: {len(test_block)} bytes") initial_state = integrator.ingest_transactions([test_block]) print(f" Initial volume: {initial_state.volume} bits") print(f" Semantic mass: {initial_state.semantic_mass:.6e} kg") print(f" Initial frequencies: {xp.sum(xp.abs(initial_state.omega_k)):.2f} rad/s") print() print("[PHASE 2] TEMPORAL FOLDING - 64 rounds of integration") print(" Applying rotation tensor ⊗ R_t and gravitational compression...") # Test with different nonces test_nonces = [0, 1, 42, 12345, 2**32 - 1] for nonce in test_nonces: print(f"\n Testing nonce {nonce}...") final_hash, metadata = integrator.integrate_full_equation(test_block, nonce) print(f" Resonance matched: {metadata['resonance_matched']}") print(f" Soliton formed: {metadata['soliton_formed']}") print(f" Gravitational integral: {metadata['gravitational_integral_sum']:.6f}") print(f" Secondary harmonic sum: {metadata['secondary_harmonic_sum']:.6f}") print(f" Final hash: {metadata['final_hash_hex'][:16]}...") print() print("[PHASE 3] TOPOLOGICAL PREDICTIVE LENSING - The Shortcut Path") print(" Computing gravitational center from first 16 rounds...") lensing_result = integrator.topological_predictive_lensing(test_block, rounds_to_simulate=16) print(f" Rounds simulated: {lensing_result['rounds_simulated']}") print(f" Rounds saved: {lensing_result['rounds_saved']}") print(f" Gravitational center: {lensing_result['gravitational_center']:.6e} kg") print(f" Predicted final energy: {lensing_result['predicted_final_energy']:.6f}") print(f" Predicted final frequency: {lensing_result['predicted_final_frequency']:.2f} rad/s") print() print("=" * 70) print(" EQUATION SOLUTION COMPLETE") print("=" * 70) # Save results results = { "equation": "Ψ_block = ∫₀⁶⁴ ( ∮_M [ Σₖ ωₖ(t) ⊗ R_t ] e^(G_s·M_i/r²) dV ) · Λ(∂V/∂t) δ(ω - ω₀) dt", "test_block_size": len(test_block), "initial_state": { "volume": initial_state.volume, "semantic_mass": initial_state.semantic_mass, "frequency_magnitude": float(xp.sum(xp.abs(initial_state.omega_k))) }, "lensing_shortcut": lensing_result, "timestamp": time.time() } output_path = ROOT / "out" / "hyperfluid_equation_results.json" output_path.parent.mkdir(parents=True, exist_ok=True) with open(output_path, "w") as f: json.dump(results, f, indent=2, default=lambda x: float(x) if isinstance(x, xp.floating) else str(x)) print(f"\n[+] Results saved to: {output_path}") return 0 if __name__ == "__main__": sys.exit(main())