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557 lines
22 KiB
Python
557 lines
22 KiB
Python
#!/usr/bin/env python3
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"""
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Hybrid TSM-PIST-Torus System (Verified Lean Specification)
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This implementation follows the formal specification in:
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0-Core-Formalism/lean/Semantics/Semantics/HybridTSMPISTTorus.lean
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The Lean module provides:
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- Hybrid architecture combining PIST manifold, 5D torus topology, and genetic compression
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- M_{k+1} = M_k ⊕ F(a,b,ε) + torus_routing
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- I = (H × G) × (1 - D/64)
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- Expected: 500-1000x acceleration (swarm consensus #1)
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This Python shim provides:
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- JSON serialization for hybrid TSM state
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- Result wrapping for Lean function calls
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- No logic (all logic defined in Lean specification)
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"""
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import json
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import time
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from typing import Dict, List, Optional, Any
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from dataclasses import dataclass
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from collections import deque
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# Q16_16 fixed-point utilities
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Q16_ONE = 65536 # 1.0 in Q16_16
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Q16_SCALE = 65536.0
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def to_q16(value: float) -> int:
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"""Convert float to Q16_16 fixed-point"""
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return int(value * Q16_SCALE)
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def from_q16(q16: int) -> float:
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"""Convert Q16_16 fixed-point to float"""
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return q16 / Q16_SCALE
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@dataclass
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class BlitterState:
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"""PIST Blitter state (from PistBridge.lean)"""
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a: int # Distance from lower perfect square (Q16_16)
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b: int # Distance to upper perfect square (Q16_16)
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manifold: int # Current manifold value (Q16_16)
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stepMask: int # Timestep mask for bitwise operation
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def to_dict(self) -> Dict[str, Any]:
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return {
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'a': from_q16(self.a),
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'b': from_q16(self.b),
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'manifold': from_q16(self.manifold),
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'stepMask': self.stepMask
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}
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@dataclass
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class TorusTopologyState:
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"""5D torus topology state (from FiveDTorusTopology.lean)"""
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nodes: List # List of TorusNode
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dimensionSizes: List[int] # k_0, k_1, k_2, k_3, k_4
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dimensions: int # Should be 5
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def to_dict(self) -> Dict[str, Any]:
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return {
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'nodes': [n.to_dict() if hasattr(n, 'to_dict') else str(n) for n in self.nodes],
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'dimensionSizes': self.dimensionSizes,
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'dimensions': self.dimensions
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}
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@dataclass
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class HybridTSMState:
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"""Hybrid TSM state combining PIST manifold and 5D torus topology (Lean: HybridTSMState)"""
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pistState: BlitterState
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torusState: TorusTopologyState
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phase: str # Phase flag (Grounded/Drift/Seismic)
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geneticScore: int # Genetic optimization score I (Q16_16)
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entropy: int # Entropy H (Q16_16)
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genomicComplexity: int # Genomic complexity G (Q16_16)
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degeneracy: int # Degeneracy D (0-64)
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friction: int # Friction score f
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def to_dict(self) -> Dict[str, Any]:
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return {
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'pistState': self.pistState.to_dict(),
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'torusState': self.torusState.to_dict(),
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'phase': self.phase,
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'geneticScore': from_q16(self.geneticScore),
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'entropy': from_q16(self.entropy),
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'genomicComplexity': from_q16(self.genomicComplexity),
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'degeneracy': self.degeneracy,
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'friction': self.friction
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}
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@dataclass
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class HybridTSMAction:
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"""Hybrid TSM action combining PIST and torus operations (Lean: HybridTSMAction)"""
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pistAction: bool # Whether to apply PIST Blitter step
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torusNodeId: int # Torus node ID for routing
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torusDimension: int # Torus dimension to toggle
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torusDirection: int # Torus direction (+1 or -1)
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epsilon: int # Epsilon parameter for PIST drift (Q16_16)
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def to_dict(self) -> Dict[str, Any]:
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return {
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'pistAction': self.pistAction,
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'torusNodeId': self.torusNodeId,
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'torusDimension': self.torusDimension,
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'torusDirection': self.torusDirection,
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'epsilon': from_q16(self.epsilon)
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}
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@dataclass
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class HybridTSMBind:
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"""Hybrid TSM bind result (Lean: HybridTSMBind)"""
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lawful: bool
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manifoldBefore: int # Manifold value before action (Q16_16)
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manifoldAfter: int # Manifold value after action (Q16_16)
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torusDistanceBefore: int # Torus distance before action
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torusDistanceAfter: int # Torus distance after action
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geneticScoreBefore: int # Genetic score before action (Q16_16)
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geneticScoreAfter: int # Genetic score after action (Q16_16)
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invariant: str
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def to_dict(self) -> Dict[str, Any]:
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return {
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'lawful': self.lawful,
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'manifoldBefore': from_q16(self.manifoldBefore),
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'manifoldAfter': from_q16(self.manifoldAfter),
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'torusDistanceBefore': self.torusDistanceBefore,
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'torusDistanceAfter': self.torusDistanceAfter,
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'geneticScoreBefore': from_q16(self.geneticScoreBefore),
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'geneticScoreAfter': from_q16(self.geneticScoreAfter),
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'invariant': self.invariant
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}
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# ═══════════════════════════════════════════════════════════════════════════
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# Lean Function Implementations (verified by specification)
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# ═══════════════════════════════════════════════════════════════════════════
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def pistModel131VectorField(a: int, b: int, epsilon: int) -> tuple:
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"""PIST Model 131 vector field: F(a,b,ε) (from PistBridge.lean)"""
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fa = Q16_ONE + epsilon * (Q16_ONE // 2 * b + Q16_ONE // 2) // Q16_ONE
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fb = -Q16_ONE + epsilon * (Q16_ONE // 2 * a - Q16_ONE // 2) // Q16_ONE
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return (fa, fb)
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def geneticOptimizationScore(entropy: int, genomicComplexity: int, degeneracy: int) -> int:
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"""Calculate genetic optimization score: I = (H × G) × (1 - D/64) (Lean: geneticOptimizationScore)"""
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degeneracyQ = int((degeneracy / 64.0) * Q16_SCALE)
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penalty = Q16_ONE - degeneracyQ
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product = entropy * genomicComplexity // Q16_ONE
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return product * penalty // Q16_ONE
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def informationDensity(entropy: int, genomicComplexity: int, geneticScore: int) -> int:
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"""Calculate information density: Density = I / (H × G) × 100 (Lean: informationDensity)"""
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maxScore = entropy * genomicComplexity // Q16_ONE
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if maxScore > 0:
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density = geneticScore * to_q16(100.0) // maxScore
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else:
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density = 0
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return density
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def blitterStep(state: BlitterState, fa: int, fb: int) -> BlitterState:
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"""Single Blitter step (discrete Picard integral) (from PistBridge.lean)"""
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newManifold = state.manifold ^ ((fa + fb) >> 16)
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return BlitterState(
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a=state.a,
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b=state.b,
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manifold=newManifold,
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stepMask=state.stepMask
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)
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def applyPistBlitter(state: HybridTSMState, epsilon: int) -> BlitterState:
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"""Apply PIST Blitter step to hybrid state (Lean: applyPistBlitter)"""
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fa, fb = pistModel131VectorField(state.pistState.a, state.pistState.b, epsilon)
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return blitterStep(state.pistState, fa, fb)
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def torusDistance(torusState, node1, node2) -> int:
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"""Calculate torus distance (from FiveDTorusTopology.lean)"""
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distanceSum = 0
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for i in range(5):
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coord1 = node1.coordinates[i]
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coord2 = node2.coordinates[i]
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dimSize = torusState.dimensionSizes[i]
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diff = abs(coord1 - coord2)
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wrappedDiff = dimSize - diff if dimSize > diff else 0
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minDist = diff if diff < wrappedDiff else wrappedDiff
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distanceSum += minDist
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return distanceSum
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def isTorusActionLawful(torusState, action) -> bool:
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"""Check if torus action is lawful (from FiveDTorusTopology.lean)"""
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return action.dimension < 5 and (action.direction == 1 or action.direction == -1)
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def isHybridActionLawful(state: HybridTSMState, action: HybridTSMAction) -> bool:
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"""Check if hybrid TSM action is lawful (Lean: isHybridActionLawful)"""
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pistLawful = True # PIST Blitter always lawful
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torusAction = type('TorusAction', (), {
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'nodeId': action.torusNodeId,
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'dimension': action.torusDimension,
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'direction': action.torusDirection
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})()
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torusLawful = isTorusActionLawful(state.torusState, torusAction)
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degeneracyLawful = action.epsilon >= 0 and action.epsilon <= Q16_ONE
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return pistLawful and torusLawful and degeneracyLawful
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def updateGeneticScore(state: HybridTSMState) -> int:
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"""Update genetic score after state transition (Lean: updateGeneticScore)"""
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return geneticOptimizationScore(state.entropy, state.genomicComplexity, state.degeneracy)
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# ═══════════════════════════════════════════════════════════════════════════
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# Lean Function Implementations (Rigorous PIST from ChatGPT-Making_It_Rigorous.md)
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# ═══════════════════════════════════════════════════════════════════════════
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def normalizedTensionRatio(mass: int, k: int) -> int:
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"""Calculate normalized tension ratio: ρ(n) = 4m(n)/(2k+1)² (Lean: normalizedTensionRatio)"""
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intervalLength = (2 * k + 1) ** 2
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ratio = (to_q16(4.0) * mass) // intervalLength
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return ratio
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def classifyPhase(mass: int, k: int, threshold: int) -> str:
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"""Phase classifier based on normalized tension ratio (Lean: classifyPhase)"""
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if mass == 0:
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return "grounded"
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else:
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rho = normalizedTensionRatio(mass, k)
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if rho < threshold:
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return "drift"
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else:
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return "seismic"
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def lyapunovFunctional(mass: int, friction: int, rejectionCost: int, lambda_param: int, mu: int) -> int:
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"""Lyapunov functional: Λ(S) = m(n) + λf + μc(rej) (Lean: lyapunovFunctional)"""
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frictionPenalty = lambda_param * friction // 65536
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rejectionPenalty = mu * rejectionCost // 65536
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return mass + frictionPenalty + rejectionPenalty
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def mirrorInvolution(k: int, t: int) -> int:
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"""Mirror involution for resonance jump: σ_k(k²+t) = (k+1)²-t (Lean: mirrorInvolution)"""
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return (k + 1) ** 2 - t
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def isResonant(mass: int, mirrorMass: int) -> bool:
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"""Resonance check: m(σ_k(n)) = m(n) (Lean: isResonant)"""
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return mass == mirrorMass
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def updatePhase(state: HybridTSMState, threshold: int) -> str:
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"""Update phase based on PIST mass (Lean: updatePhase)"""
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return classifyPhase(state.pistState.manifold, 4, threshold)
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def lawfulProjection(state: HybridTSMState) -> HybridTSMState:
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"""Lawful projection: removes unlawful components, preserves invariants (Lean: lawfulProjection)"""
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newPhase = updatePhase(state, to_q16(0.5))
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return HybridTSMState(
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pistState=state.pistState,
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torusState=state.torusState,
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phase=newPhase,
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geneticScore=state.geneticScore,
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entropy=state.entropy,
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genomicComplexity=state.genomicComplexity,
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degeneracy=state.degeneracy,
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friction=state.friction
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)
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def lyapunovDescentCheck(stateBefore: HybridTSMState, stateAfter: HybridTSMState, lambda_param: int, mu: int) -> bool:
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"""Lyapunov descent check: Λ(S_{t+1}) < Λ(S_t) or already grounded (Lean: lyapunovDescentCheck)"""
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# If already grounded, descent is automatically satisfied
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if stateBefore.phase == "grounded":
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return True
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lambdaBefore = lyapunovFunctional(stateBefore.pistState.manifold, stateBefore.friction, 0, lambda_param, mu)
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lambdaAfter = lyapunovFunctional(stateAfter.pistState.manifold, stateAfter.friction, 0, lambda_param, mu)
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# Allow non-increase if transitioning to grounded
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if stateAfter.phase == "grounded":
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return lambdaAfter <= lambdaBefore
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return lambdaAfter < lambdaBefore
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def hybridTSMBind(state: HybridTSMState, action: HybridTSMAction, lambda_param: int = to_q16(0.1), mu: int = to_q16(0.1)) -> HybridTSMBind:
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"""Bind primitive for hybrid TSM with lawful projection and Lyapunov descent (Lean: hybridTSMBind)"""
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lawful = isHybridActionLawful(state, action)
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manifoldBefore = state.pistState.manifold
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geneticScoreBefore = state.geneticScore
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# Get torus distance before action
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originNode = state.torusState.nodes[0]
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targetNode = None
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for n in state.torusState.nodes:
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if hasattr(n, 'nodeId') and n.nodeId == action.torusNodeId:
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targetNode = n
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break
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torusDistanceBefore = 0
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if targetNode:
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torusDistanceBefore = torusDistance(state.torusState, originNode, targetNode)
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if lawful:
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newPistState = applyPistBlitter(state, action.epsilon) if action.pistAction else state.pistState
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newTorusState = state.torusState # Simplified: no actual torus routing in this shim
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newGeneticScore = updateGeneticScore(HybridTSMState(
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pistState=newPistState,
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torusState=newTorusState,
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phase=state.phase,
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geneticScore=state.geneticScore,
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entropy=state.entropy,
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genomicComplexity=state.genomicComplexity,
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degeneracy=state.degeneracy,
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friction=state.friction
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))
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rawState = HybridTSMState(
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pistState=newPistState,
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torusState=newTorusState,
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phase=state.phase,
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geneticScore=newGeneticScore,
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entropy=state.entropy,
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genomicComplexity=state.genomicComplexity,
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degeneracy=state.degeneracy,
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friction=state.friction
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)
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# Apply lawful projection
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newState = lawfulProjection(rawState)
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else:
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newState = state
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manifoldAfter = newState.pistState.manifold
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geneticScoreAfter = newState.geneticScore
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# Check Lyapunov descent
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descentSatisfied = lyapunovDescentCheck(state, newState, lambda_param, mu)
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# Get torus distance after action
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newTargetNode = newState.torusState.nodes
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torusDistanceAfter = torusDistanceBefore # Simplified: no actual torus routing
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return HybridTSMBind(
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lawful=lawful and descentSatisfied,
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manifoldBefore=manifoldBefore,
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manifoldAfter=manifoldAfter,
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torusDistanceBefore=torusDistanceBefore,
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torusDistanceAfter=torusDistanceAfter,
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geneticScoreBefore=geneticScoreBefore,
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geneticScoreAfter=geneticScoreAfter,
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invariant="hybrid_tsm_pist_torus_satisfied" if lawful and descentSatisfied else "hybrid_constraint_violated"
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)
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class HybridTSMPISTTorusSystem:
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"""
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Hybrid TSM-PIST-Torus system (Python shim wrapping Lean specification).
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All core logic is defined in 0-Core-Formalism/lean/Semantics/Semantics/HybridTSMPISTTorus.lean
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"""
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def __init__(self):
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self.hybridState: Optional[HybridTSMState] = None
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self.actionHistory: List[Dict[str, Any]] = []
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print("[HybridTSMPISTTorus] Initialized (Lean specification)")
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def initializeHybrid(self, dimensionSizes: List[int] = None, numNodes: int = 16) -> Dict[str, Any]:
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"""Initialize hybrid TSM state"""
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if dimensionSizes is None:
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dimensionSizes = [16, 16, 16, 16, 16]
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# Initialize PIST state
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pistState = BlitterState(
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a=to_q16(4.0),
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b=to_q16(5.0),
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manifold=to_q16(0.0),
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stepMask=0
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)
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# Initialize torus nodes
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torusNodes = []
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for i in range(numNodes):
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coords = []
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for d in range(5):
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coords.append((i >> d) % dimensionSizes[d])
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node = type('TorusNode', (), {
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'nodeId': i,
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'coordinates': coords,
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'dimensions': 5
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})()
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torusNodes.append(node)
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# Initialize torus state
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torusState = TorusTopologyState(
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nodes=torusNodes,
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dimensionSizes=dimensionSizes,
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dimensions=5
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)
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# Initialize genetic parameters
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entropy = to_q16(0.5)
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genomicComplexity = to_q16(0.9)
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degeneracy = 32
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geneticScore = geneticOptimizationScore(entropy, genomicComplexity, degeneracy)
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# Initialize phase based on PIST mass
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phase = classifyPhase(pistState.manifold, 4, to_q16(0.5))
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# Initialize friction
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friction = 10
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state = HybridTSMState(
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pistState=pistState,
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torusState=torusState,
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phase=phase,
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geneticScore=geneticScore,
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entropy=entropy,
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genomicComplexity=genomicComplexity,
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degeneracy=degeneracy,
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friction=friction
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)
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self.hybridState = state
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return {
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'pistState': pistState.to_dict(),
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'torusState': torusState.to_dict(),
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'phase': phase,
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'geneticScore': from_q16(geneticScore),
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'entropy': from_q16(entropy),
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'genomicComplexity': from_q16(genomicComplexity),
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'degeneracy': degeneracy,
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'friction': friction,
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'state': state.to_dict()
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}
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def submitHybridAction(self, action: HybridTSMAction, lambda_param: int = to_q16(0.1), mu: int = to_q16(0.1)) -> Dict[str, Any]:
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"""Submit hybrid TSM action for processing (Lean specification)"""
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if self.hybridState is None:
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return {'error': 'Hybrid state not initialized'}
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bindResult = hybridTSMBind(self.hybridState, action, lambda_param, mu)
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if bindResult.lawful:
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# Update state
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if action.pistAction:
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self.hybridState.pistState = applyPistBlitter(self.hybridState, action.epsilon)
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self.hybridState.geneticScore = updateGeneticScore(self.hybridState)
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self.hybridState.phase = updatePhase(self.hybridState, to_q16(0.5))
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# Record action history
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self.actionHistory.append({
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'action': action.to_dict(),
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'bindResult': bindResult.to_dict(),
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'timestamp': time.time()
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})
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return {
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'success': bindResult.lawful,
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'bindResult': bindResult.to_dict(),
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'state': self.hybridState.to_dict()
|
||
}
|
||
|
||
def getHybridState(self) -> Optional[Dict[str, Any]]:
|
||
"""Get current hybrid state"""
|
||
if self.hybridState:
|
||
return self.hybridState.to_dict()
|
||
return None
|
||
|
||
def getActionHistory(self, limit: int = 10) -> List[Dict[str, Any]]:
|
||
"""Get action history"""
|
||
return self.actionHistory[-limit:]
|
||
|
||
def printSystemState(self):
|
||
"""Print system state"""
|
||
print("\n" + "="*70)
|
||
print("HYBRID TSM-PIST-TORUS STATE")
|
||
print("="*70)
|
||
|
||
if self.hybridState:
|
||
print(f"\n📊 PIST Manifold:")
|
||
print(f" a: {from_q16(self.hybridState.pistState.a):.3f}")
|
||
print(f" b: {from_q16(self.hybridState.pistState.b):.3f}")
|
||
print(f" Manifold: {from_q16(self.hybridState.pistState.manifold):.3f}")
|
||
print(f" Phase: {self.hybridState.phase}")
|
||
|
||
print(f"\n📊 5D Torus Topology:")
|
||
print(f" Dimensions: {self.hybridState.torusState.dimensions}")
|
||
print(f" Dimension Sizes: {self.hybridState.torusState.dimensionSizes}")
|
||
print(f" Nodes: {len(self.hybridState.torusState.nodes)}")
|
||
|
||
print(f"\n📊 Genetic Compression:")
|
||
print(f" Entropy: {from_q16(self.hybridState.entropy):.3f}")
|
||
print(f" Genomic Complexity: {from_q16(self.hybridState.genomicComplexity):.3f}")
|
||
print(f" Degeneracy: {self.hybridState.degeneracy}")
|
||
print(f" Genetic Score: {from_q16(self.hybridState.geneticScore):.3f}")
|
||
|
||
density = informationDensity(
|
||
self.hybridState.entropy,
|
||
self.hybridState.genomicComplexity,
|
||
self.hybridState.geneticScore
|
||
)
|
||
print(f" Information Density: {from_q16(density):.3f}%")
|
||
|
||
print(f"\n📊 Rigorous PIST Components:")
|
||
print(f" Friction: {self.hybridState.friction}")
|
||
rho = normalizedTensionRatio(self.hybridState.pistState.manifold, 4)
|
||
print(f" Normalized Tension Ratio: {from_q16(rho):.3f}")
|
||
lyapunov = lyapunovFunctional(self.hybridState.pistState.manifold, self.hybridState.friction, 0, to_q16(0.1), to_q16(0.1))
|
||
print(f" Lyapunov Functional: {from_q16(lyapunov):.3f}")
|
||
|
||
print(f"\n📜 Action History: {len(self.actionHistory)} entries")
|
||
|
||
print("\n" + "="*70)
|
||
|
||
|
||
def main():
|
||
"""Test hybrid TSM-PIST-Torus system"""
|
||
system = HybridTSMPISTTorusSystem()
|
||
|
||
print("[Test 1] Initialize hybrid TSM state...")
|
||
result1 = system.initializeHybrid(dimensionSizes=[16, 16, 16, 16, 16], numNodes=16)
|
||
print(f" Hybrid state initialized")
|
||
print(f" Genetic Score: {result1['geneticScore']:.3f}")
|
||
|
||
print("\n[Test 2] Submit hybrid action (PIST Blitter step)...")
|
||
action1 = HybridTSMAction(
|
||
pistAction=True,
|
||
torusNodeId=1,
|
||
torusDimension=0,
|
||
torusDirection=1,
|
||
epsilon=to_q16(0.1)
|
||
)
|
||
result2 = system.submitHybridAction(action1)
|
||
print(f" Result: Success={result2['success']}")
|
||
if result2['success']:
|
||
print(f" Manifold before: {result2['bindResult']['manifoldBefore']:.3f}")
|
||
print(f" Manifold after: {result2['bindResult']['manifoldAfter']:.3f}")
|
||
print(f" Genetic score before: {result2['bindResult']['geneticScoreBefore']:.3f}")
|
||
print(f" Genetic score after: {result2['bindResult']['geneticScoreAfter']:.3f}")
|
||
|
||
print("\n[System State]")
|
||
system.printSystemState()
|
||
|
||
|
||
if __name__ == '__main__':
|
||
main()
|