#!/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. # ============================================================================== """ The Substrate Ledger: N-Space Snag and Leakage Management Foam substrate architecture: - FoamCell = addressable substrate cell (fundamental storage grain) - COMMITTED = successfully written cell with metadata header - OVERFLOW_SNAG = buffer overflow (write rate > drain rate) - thermal_leak = heat output from bad-sector writes - partial_write = incomplete commit (cell not resonance-locked) - NSpaceBuffer = higher-dimensional routing cache - buffer_crosstalk = coupling between buffer regions - TUNNEL = stabilized direct-path connection in n-space FoamProbe: Read/Write head for substrate maintenance """ 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, Callable from pathlib import Path import sys from enum import Enum # 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 # ============================================================================ # SUBSTRATE PARAMETERS # ============================================================================ @dataclass class SubstrateParams: """Tunable parameters for the Substrate Ledger""" # Foam cell size (bytes per addressable grain) grain_size_bytes: int = 8 # Ternary clock is action-bound, not periodic. No clock frequency. # joule_floor is the Landauer minimum cost per action (k_B * T * ln2 at 300K). joule_floor: float = 1.380649e-23 * 300 * 0.6931 # Maximum cell density before overflow snag (cells per area unit) max_cell_density: float = 1.0e69 # Noise floor coefficient (partial-write threshold) noise_floor: float = 1.380649e-23 # N-space routing buffer dimensionality nd_dimensions: int = 11 # Signal-to-Noise Ratio threshold for committed write snr_threshold: float = 6.0 # Probe reach (number of cell-widths the foam probe affects) probe_reach_cells: int = 1 # ============================================================================ # ENUMS FOR SUBSTRATE STATES # ============================================================================ class WriteOperationStatus(Enum): """Status of a write operation to the substrate""" PENDING = "pending" # In n-space buffer FORMATTING = "formatting" # Applying metadata header COMMITTED = "committed" # Successfully written to addressed cell PARTIAL_WRITE = "partial_write" # Incomplete commit (noise exceeds floor) OVERFLOW_SNAG = "overflow_snag" # Buffer overflow (density exceeded) BAD_SECTOR = "bad_sector" # Corrupted region class SubstrateRegion(Enum): """Types of substrate regions""" COMMITTED = "committed" # Successfully formatted cell FOAM = "foam" # Raw unformatted medium OVERFLOW_BOUNDARY = "overflow_boundary" # 2D buffer boundary at overflow N_SPACE_BUFFER = "n_space_buffer" # Higher-dimensional routing cache TUNNEL = "tunnel" # Stabilized direct-path connection # ============================================================================ # FOAM CELL STRUCTURE # ============================================================================ @dataclass class FoamCell: """ Represents a single addressable cell of the foam substrate. This is the fundamental storage grain — one write unit. """ # Position in n-space (normalised unit coordinates) position: AnyArray # 3+1 dimensions # Cell state (complex amplitude; pending = unresolved, committed = eigenstate) cell_state: complex # Information content (bytes) information: bytes = b'' # Metadata header (applied during write) metadata_header: Optional[bytes] = None # Resonance lock status (must match clock_freq to commit) resonance_locked: bool = False # Write operation status write_status: WriteOperationStatus = WriteOperationStatus.PENDING # Correlated cells (dual-write pairs) corr_cells: List[int] = field(default_factory=list) # Partial-write magnitude (0 = clean, 1 = fully leaked) partial_write_magnitude: float = 0.0 def compute_snr(self, params: SubstrateParams) -> float: """ Compute Signal-to-Noise Ratio for this cell. Determines if write operation can succeed. """ if self.metadata_header is None: return 0.0 # Signal = information content in bits signal = len(self.information) * 8 # Noise = cell state magnitude times noise floor coefficient noise = xp.abs(self.cell_state) * params.noise_floor if noise < 1e-30: return float('inf') return signal / noise def apply_metadata_header(self, header: bytes) -> bool: """ Apply metadata header to commit this cell. Returns True if resonance lock achieved. """ self.metadata_header = header self.write_status = WriteOperationStatus.FORMATTING # Check resonance against clock reference header_hash = hashlib.sha256(header).digest() resonance_value = int.from_bytes(header_hash[:4], 'big') / 2**32 self.resonance_locked = resonance_value > 0.5 if self.resonance_locked: self.write_status = WriteOperationStatus.COMMITTED return self.resonance_locked # ============================================================================ # N-SPACE BUFFER MANAGEMENT # ============================================================================ @dataclass class NSpaceBuffer: """ Higher-dimensional routing buffer where information exists before being written to the addressed cell layer. Buffer crosstalk explains apparent coupling between spatially separated write operations. """ # Buffer dimensionality dimensions: int = 11 # Buffer capacity (cells) capacity: int = 10**180 # Current occupancy occupancy: Dict[str, FoamCell] = field(default_factory=dict) # Buffer phase (complex; tracks routing state) buffer_phase: complex = field(default_factory=lambda: complex(0, 1)) # Crosstalk matrix crosstalk_matrix: Optional[AnyArray] = None def allocate_cell(self, cell_id: str, cell: FoamCell) -> None: """Allocate a cell in the n-space buffer""" self.occupancy[cell_id] = cell def compute_crosstalk(self) -> AnyArray: """ Compute coupling (crosstalk) between buffer regions. High crosstalk = strong path correlation between cells. """ n_cells = len(self.occupancy) if n_cells < 2: return xp.zeros((1, 1)) crosstalk = xp.zeros((n_cells, n_cells)) cell_ids = list(self.occupancy.keys()) for i, id_i in enumerate(cell_ids): for j, id_j in enumerate(cell_ids): if i != j: cell_i = self.occupancy[id_i] cell_j = self.occupancy[id_j] # Crosstalk via dual-write correlation if j in cell_i.corr_cells: crosstalk[i, j] = xp.abs(cell_i.cell_state * cell_j.cell_state) # Crosstalk via partial-write bleed crosstalk[i, j] += cell_i.partial_write_magnitude * cell_j.partial_write_magnitude self.crosstalk_matrix = crosstalk return crosstalk def detect_buffer_crosstalk(self, source_id: str, target_ids: List[str]) -> float: """ Measure crosstalk bleed from a high-energy source cell to a set of target cells in the same buffer region. """ if source_id not in self.occupancy: return 0.0 source_cell = self.occupancy[source_id] total_bleed = 0.0 for target_id in target_ids: if target_id in self.occupancy: target_cell = self.occupancy[target_id] bleed = source_cell.partial_write_magnitude * target_cell.partial_write_magnitude total_bleed += bleed return total_bleed # ============================================================================ # OVERFLOW SNAG DETECTION # ============================================================================ @dataclass class OverflowSnag: """ Represents a buffer overflow snag — a region where write density has exceeded the substrate drain rate, causing uncommitted cells to accumulate and thermal leakage to build up. """ # Position in normalised cell coordinates position: AnyArray # Cell density in this region (cells per area unit) cell_density: float # Snag severity (0 = none, 1 = critical) severity: float # Thermal output from bad-sector writes (normalised) thermal_output: float # Overflow boundary area overflow_boundary_area: float # Write attempts per drain cycle write_attempts_per_cycle: float def compute_thermal_output(self, params: SubstrateParams) -> float: """ Compute normalised thermal output from overflow writes. thermal_output = cell_density / max_cell_density (clamped 0-1). """ thermal = min(1.0, self.cell_density / max(params.max_cell_density, 1.0)) self.thermal_output = thermal return thermal # ============================================================================ # THE Ψ_REPAIR EQUATION (SOLITON FRAMEWORK) # ============================================================================ class SubstrateLedgerEngine: """ Main engine for managing the Substrate Ledger. Ψ_repair = ∫(M_header ⊗ R_resonance) · δ(ω - ω₀) dt """ def __init__(self, kernel: TSMKernel): self.kernel = kernel self.params = SubstrateParams() # Foam cells (the addressable cell layer) self.foam_cells: Dict[str, FoamCell] = {} # N-space routing buffer self.nspace_buffer = NSpaceBuffer() # Overflow snags self.snags: List[OverflowSnag] = [] # Successful write operations self.committed_writes: List[Dict] = [] # Partial-write events self.partial_write_events: List[Dict] = [] def initialize_foam_region(self, num_cells: int = 1000) -> None: """Initialize a region of foam substrate""" for i in range(num_cells): position = xp.random.rand(4) # normalised unit coordinates cell = FoamCell( position=position, cell_state=complex(xp.random.rand(), xp.random.rand()), information=hashlib.sha256(bytes([i])).digest()[:8] ) cell_id = f"cell_{i}" self.foam_cells[cell_id] = cell self.nspace_buffer.allocate_cell(cell_id, cell) def apply_metadata_header(self, cell_id: str, header: bytes) -> WriteOperationStatus: """Apply metadata header to commit a cell (write operation)""" if cell_id not in self.foam_cells: return WriteOperationStatus.BAD_SECTOR cell = self.foam_cells[cell_id] # Compute SNR before write snr = cell.compute_snr(self.params) if snr < self.params.snr_threshold: # Partial write — cell not resonance-locked cell.partial_write_magnitude = 1.0 - snr / self.params.snr_threshold cell.write_status = WriteOperationStatus.PARTIAL_WRITE self.partial_write_events.append({ "cell_id": cell_id, "snr": snr, "partial_write_magnitude": cell.partial_write_magnitude, "timestamp": time.time() }) return WriteOperationStatus.PARTIAL_WRITE # Apply header and attempt resonance lock success = cell.apply_metadata_header(header) if success: self.committed_writes.append({ "cell_id": cell_id, "header_hash": hashlib.sha256(header).hexdigest(), "timestamp": time.time() }) return WriteOperationStatus.COMMITTED else: return WriteOperationStatus.PENDING def detect_overflow_snag(self, region_center: AnyArray, region_radius: float) -> Optional[OverflowSnag]: """ Detect overflow snags in a region. Occurs when cell density exceeds the substrate drain rate. """ cells_in_region = [] for cell_id, cell in self.foam_cells.items(): distance = xp.linalg.norm(cell.position[:3] - region_center[:3]) if distance < region_radius: cells_in_region.append(cell) if len(cells_in_region) < 10: return None total_info = sum(len(c.information) * 8 for c in cells_in_region) area = 4 * xp.pi * region_radius**2 cell_density = total_info / area if cell_density > self.params.max_cell_density: severity = min(1.0, cell_density / self.params.max_cell_density) snag = OverflowSnag( position=region_center, cell_density=cell_density, severity=severity, thermal_output=0.0, overflow_boundary_area=area, write_attempts_per_cycle=len(cells_in_region) * self.params.clock_freq_hz ) snag.compute_thermal_output(self.params) self.snags.append(snag) return snag return None def psi_repair_equation(self, cell_ids: List[str]) -> Dict: """ Solve the Ψ_repair equation for formatting foam cells. Ψ_repair = ∫(M_header ⊗ R_resonance) · δ(ω - ω₀) dt Returns repair success metrics. """ M_header = xp.zeros(len(cell_ids)) for i, cell_id in enumerate(cell_ids): if cell_id in self.foam_cells: cell = self.foam_cells[cell_id] if cell.metadata_header: header_hash = hashlib.sha256(cell.metadata_header).digest() M_header[i] = int.from_bytes(header_hash[:4], 'big') / 2**32 R_resonance = xp.zeros(len(cell_ids)) for i, cell_id in enumerate(cell_ids): if cell_id in self.foam_cells: cell = self.foam_cells[cell_id] if cell.resonance_locked: R_resonance[i] = 1.0 delta_resonance = xp.zeros(len(cell_ids)) for i, cell_id in enumerate(cell_ids): if cell_id in self.foam_cells: cell = self.foam_cells[cell_id] freq_match = xp.abs(cell.compute_snr(self.params) - self.params.snr_threshold) delta_resonance[i] = xp.exp(-freq_match**2 / 0.1) tensor_product = M_header * R_resonance psi_repair = xp.sum(tensor_product * delta_resonance) psi_repair /= len(cell_ids) return { "psi_repair": float(psi_repair), "M_header_magnitude": float(xp.sum(M_header)), "R_resonance_magnitude": float(xp.sum(R_resonance)), "delta_match": float(xp.sum(delta_resonance)), "formatted_cells": int(xp.sum(R_resonance)), "total_cells": len(cell_ids) } def foam_probe_operation(self, target_cell_ids: List[str], resonance_frequency: float) -> Dict: """ Operate the Foam Probe for substrate maintenance. The probe creates a Local Formatting Zone by: 1. Injecting resonance to lock cells 2. Pulling overflow snags 3. Stabilizing direct-path tunnel connections """ import struct results = { "resonance_injected": resonance_frequency, "cells_targeted": len(target_cell_ids), "cells_locked": 0, "snags_pulled": 0, "tunnels_stabilized": 0, "partial_write_reduced": 0.0 } initial_leakage = sum( self.foam_cells[cid].partial_write_magnitude for cid in target_cell_ids if cid in self.foam_cells ) # Phase 1: Resonance injection for cell_id in target_cell_ids: if cell_id not in self.foam_cells: continue resonance_header = hashlib.sha256( struct.pack(' 0.5) for pair in high_crosstalk_pairs: if len(pair) > 1: results["tunnels_stabilized"] += 1 return results def compute_substrate_health(self) -> Dict: """Compute overall health metrics for the substrate ledger""" total_cells = len(self.foam_cells) committed = sum(1 for c in self.foam_cells.values() if c.write_status == WriteOperationStatus.COMMITTED) partial = sum(1 for c in self.foam_cells.values() if c.write_status == WriteOperationStatus.PARTIAL_WRITE) snags = len(self.snags) crosstalk = self.nspace_buffer.compute_crosstalk() avg_crosstalk = xp.mean(crosstalk) if crosstalk.size > 0 else 0.0 return { "total_cells": total_cells, "committed_writes": committed, "commitment_rate": committed / max(total_cells, 1), "partial_write_events": partial, "partial_write_rate": partial / max(total_cells, 1), "overflow_snags": snags, "avg_crosstalk": float(avg_crosstalk), "max_crosstalk": float(xp.max(crosstalk)) if crosstalk.size > 0 else 0.0, "substrate_health": committed / max(total_cells, 1) - snags * 0.1 - partial * 0.05 } # ============================================================================ # MAIN EXECUTION # ============================================================================ def main(): """Demonstrate the Substrate Ledger model""" print("=" * 70) print(" THE SUBSTRATE LEDGER: N-SPACE SNAG AND LEAKAGE MANAGEMENT") print("=" * 70) print() kernel = TSMKernel() engine = SubstrateLedgerEngine(kernel) print("[PHASE 1] INITIALIZE FOAM REGION") engine.initialize_foam_region(num_cells=100) print(f" Initialized {len(engine.foam_cells)} foam cells") print(f" N-space buffer occupancy: {len(engine.nspace_buffer.occupancy)} cells") print() print("[PHASE 2] ATTEMPT WRITE OPERATIONS (Metadata Header Application)") for i, cell_id in enumerate(list(engine.foam_cells.keys())[:50]): header = hashlib.sha256(bytes([i])).digest() engine.apply_metadata_header(cell_id, header) health = engine.compute_substrate_health() print(f" Committed writes: {health['committed_writes']} ({health['commitment_rate']*100:.1f}%)") print(f" Partial-write events: {health['partial_write_events']} ({health['partial_write_rate']*100:.1f}%)") print() print("[PHASE 3] DETECT OVERFLOW SNAGS") center = xp.array([0.5, 0.5, 0.5]) snag = engine.detect_overflow_snag(center, 1e-36) if snag: print(f" ⚠ OVERFLOW SNAG DETECTED") print(f" Cell density: {snag.cell_density:.2e} bits/unit²") print(f" Severity: {snag.severity*100:.1f}%") print(f" Thermal output: {snag.thermal_output:.4f}") print(f" Overflow boundary area: {snag.overflow_boundary_area:.2e}") else: print(" No overflow snags detected in region") print() print("[PHASE 4] SOLVE Ψ_REPAIR EQUATION") print(" Ψ_repair = ∫(M_header ⊗ R_resonance) · δ(ω - ω₀) dt") cell_ids = list(engine.foam_cells.keys())[:50] repair_result = engine.psi_repair_equation(cell_ids) print(f" Ψ_repair magnitude: {repair_result['psi_repair']:.4f}") print(f" M_header magnitude: {repair_result['M_header_magnitude']:.2f}") print(f" R_resonance magnitude: {repair_result['R_resonance_magnitude']:.2f}") print(f" δ(ω-ω₀) match: {repair_result['delta_match']:.2f}") print(f" Formatted cells: {repair_result['formatted_cells']}/{repair_result['total_cells']}") print() print("[PHASE 5] FOAM PROBE OPERATION (Substrate Maintenance)") probe_result = engine.foam_probe_operation( target_cell_ids=cell_ids, resonance_frequency=engine.params.clock_freq_hz ) print(f" Resonance injected: {probe_result['resonance_injected']:.2e} Hz") print(f" Cells targeted: {probe_result['cells_targeted']}") print(f" Cells locked: {probe_result['cells_locked']}") print(f" Snags pulled: {probe_result['snags_pulled']}") print(f" Tunnels stabilized: {probe_result['tunnels_stabilized']}") print(f" Partial-write reduced: {probe_result['partial_write_reduced']:.4f}") print() print("[PHASE 6] N-SPACE CROSSTALK (Buffer Coupling)") if len(list(engine.foam_cells.keys())) > 10: source_cell = list(engine.foam_cells.keys())[0] target_cells = list(engine.foam_cells.keys())[1:10] crosstalk_signal = engine.nspace_buffer.detect_buffer_crosstalk(source_cell, target_cells) print(f" Crosstalk signal strength: {crosstalk_signal:.6f}") crosstalk = engine.nspace_buffer.compute_crosstalk() print(f" Average crosstalk: {xp.mean(crosstalk):.6f}") print(f" Max crosstalk: {xp.max(crosstalk):.6f}") print(f" (High crosstalk = strong buffer path coupling)") print() print("[PHASE 7] FINAL SUBSTRATE HEALTH ASSESSMENT") final_health = engine.compute_substrate_health() print(f" Total cells: {final_health['total_cells']}") print(f" Commitment rate: {final_health['commitment_rate']*100:.1f}%") print(f" Partial-write rate: {final_health['partial_write_rate']*100:.1f}%") print(f" Overflow snags: {final_health['overflow_snags']}") print(f" Max crosstalk: {final_health['max_crosstalk']:.4f}") print(f" SUBSTRATE HEALTH SCORE: {final_health['substrate_health']*100:.1f}%") print() results = { "substrate_params": { "grain_size_bytes": engine.params.grain_size_bytes, "clock_freq_hz": engine.params.clock_freq_hz, "snr_threshold": engine.params.snr_threshold }, "repair_equation": repair_result, "foam_probe": probe_result, "substrate_health": final_health, "timestamp": time.time() } output_path = ROOT / "out" / "substrate_ledger_results.json" output_path.parent.mkdir(parents=True, exist_ok=True) with open(output_path, "w") as f: json.dump(results, f, indent=2) print(f"[+] Results saved to: {output_path}") return 0 if __name__ == "__main__": sys.exit(main())