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441 lines
16 KiB
Python
441 lines
16 KiB
Python
#!/usr/bin/env python3
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"""
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Hypercube Topology 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/HypercubeTopology.lean
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The Lean module provides:
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- 12-dimensional hypercube topology for unified topology
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- d_hc = Σ_{i=0}^{n-1} |x_i - y_i| (hypercube distance)
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- neighbor_count = 2n (2n neighbors per node)
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- connectivity = 2^n nodes (4,096 nodes for 12 dimensions)
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- Direct neighbor communication avoids Von Neumann bottleneck
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This Python shim provides:
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- JSON serialization for hypercube state
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- Result wrapping for Lean function calls
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- History deque for topology operations
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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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try:
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from holographic_projection import HolographicProjectionSystem, HolographicSurfacePoint, HolographicAction
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_HAS_HOLOGRAPHIC = True
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except ImportError:
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_HAS_HOLOGRAPHIC = False
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print("[!] Holographic projection system not available")
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# Q16_16 fixed-point utilities (from Lean FixedPoint module)
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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 HypercubeNode:
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"""Hypercube node position (Lean: HypercubeNode)"""
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nodeId: int # UInt64
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coordinates: List[int] # n-dimensional coordinates (n = 12 for CM)
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dimensions: int # Number of dimensions (typically 12)
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def to_dict(self) -> Dict[str, Any]:
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return {
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'nodeId': self.nodeId,
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'coordinates': self.coordinates,
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'dimensions': self.dimensions
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}
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@dataclass
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class HypercubeTopologyState:
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"""Hypercube topology state (Lean: HypercubeTopologyState)"""
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nodes: List[HypercubeNode]
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dimensions: int # Number of dimensions
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maxNodeId: int # Maximum node ID
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def to_dict(self) -> Dict[str, Any]:
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return {
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'nodes': [n.to_dict() for n in self.nodes],
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'dimensions': self.dimensions,
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'maxNodeId': self.maxNodeId
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}
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@dataclass
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class HypercubeAction:
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"""Hypercube topology action (Lean: HypercubeAction)"""
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nodeId: int # UInt64
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dimension: int # Dimension to toggle (0 to n-1)
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def to_dict(self) -> Dict[str, Any]:
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return {
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'nodeId': self.nodeId,
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'dimension': self.dimension
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}
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@dataclass
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class HypercubeBind:
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"""Hypercube bind result (Lean: HypercubeBind)"""
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lawful: bool
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distanceBefore: int # Distance before action
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distanceAfter: int # Distance after action
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neighborCount: int # Number of neighbors
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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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'distanceBefore': self.distanceBefore,
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'distanceAfter': self.distanceAfter,
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'neighborCount': self.neighborCount,
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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 hypercubeDistance(node1: HypercubeNode, node2: HypercubeNode) -> int:
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"""Calculate hypercube distance: d_hc = Σ_{i=0}^{n-1} |x_i - y_i| (Lean: hypercubeDistance)"""
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minDim = min(node1.dimensions, node2.dimensions)
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dist = 0
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for i in range(minDim):
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x = node1.coordinates[i] if i < len(node1.coordinates) else 0
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y = node2.coordinates[i] if i < len(node2.coordinates) else 0
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dist += abs(x - y)
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return dist
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def areNeighbors(node1: HypercubeNode, node2: HypercubeNode) -> bool:
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"""Check if two nodes are neighbors (distance = 1) (Lean: areNeighbors)"""
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return hypercubeDistance(node1, node2) == 1
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def getNeighbors(state: HypercubeTopologyState, node: HypercubeNode) -> List[HypercubeNode]:
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"""Get neighbors of a node (Lean: getNeighbors)"""
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dim = node.dimensions
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neighbors = []
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for i in range(dim):
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newCoords = list(node.coordinates)
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newCoords[i] = (newCoords[i] + 1) % (2 ** dim)
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for n in state.nodes:
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if n.coordinates == newCoords:
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neighbors.append(n)
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break
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return neighbors
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def neighborCount(dimensions: int) -> int:
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"""Calculate neighbor count: neighbor_count = 2n (Lean: neighborCount)"""
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return 2 * dimensions
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def connectivity(dimensions: int) -> int:
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"""Calculate connectivity: connectivity = 2^n nodes (Lean: connectivity)"""
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return 2 ** dimensions
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def hypercubeDiameter(dimensions: int) -> int:
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"""Calculate hypercube diameter: max distance = n (Lean: hypercubeDiameter)"""
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return dimensions
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def bisectionBandwidth(dimensions: int) -> int:
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"""Calculate bisection bandwidth: 2^(n-1) edges cut (Lean: bisectionBandwidth)"""
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return 2 ** (dimensions - 1)
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def isHypercubeActionLawful(state: HypercubeTopologyState, action: HypercubeAction) -> bool:
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"""Check if hypercube action is lawful (Lean: isHypercubeActionLawful)"""
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return action.dimension < state.dimensions and action.nodeId < state.maxNodeId
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def toggleCoordinate(node: HypercubeNode, dimension: int) -> HypercubeNode:
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"""Toggle coordinate in specified dimension (Lean: toggleCoordinate)"""
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newCoords = list(node.coordinates)
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newCoords[dimension] = (newCoords[dimension] + 1) % (2 ** node.dimensions)
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return HypercubeNode(
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nodeId=node.nodeId,
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coordinates=newCoords,
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dimensions=node.dimensions
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)
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def hypercubeBind(state: HypercubeTopologyState, action: HypercubeAction, currentTime: float = 0.0) -> HypercubeBind:
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"""Bind primitive for hypercube topology (Lean: hypercubeBind)"""
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lawful = isHypercubeActionLawful(state, action)
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oldNode = None
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for n in state.nodes:
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if n.nodeId == action.nodeId:
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oldNode = n
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break
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referenceNode = state.nodes[0] if state.nodes else None
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distanceBefore = hypercubeDistance(oldNode, referenceNode) if oldNode and referenceNode else 0
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newNode = None
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if lawful and oldNode:
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newNode = toggleCoordinate(oldNode, action.dimension)
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elif oldNode:
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newNode = oldNode
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else:
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newNode = HypercubeNode(
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nodeId=action.nodeId,
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coordinates=[0] * state.dimensions,
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dimensions=state.dimensions
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)
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distanceAfter = hypercubeDistance(newNode, referenceNode) if referenceNode else distanceBefore
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nCount = neighborCount(state.dimensions)
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return HypercubeBind(
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lawful=lawful,
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distanceBefore=distanceBefore,
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distanceAfter=distanceAfter,
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neighborCount=nCount,
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invariant="hypercube_topology_satisfied" if lawful else "hypercube_constraint_violated"
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)
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class HypercubeTopologySystem:
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"""
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Hypercube topology system (Python shim wrapping Lean specification).
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All core logic is defined in 0-Core-Formalism/lean/Semantics/Semantics/HypercubeTopology.lean
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"""
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def __init__(self):
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self.topologyState: Optional[HypercubeTopologyState] = None
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self.actionHistory: List[Dict[str, Any]] = []
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self.holographicProjectionSystem: Optional[HolographicProjectionSystem] = None
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if _HAS_HOLOGRAPHIC:
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self.holographicProjectionSystem = HolographicProjectionSystem()
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print("[HypercubeTopology] Initialized (Lean specification)")
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def initializeTopology(self, dimensions: int = 16, numNodes: int = 16) -> Dict[str, Any]:
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"""Initialize hypercube topology state"""
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maxNodeId = connectivity(dimensions)
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nodes = []
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for i in range(numNodes):
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# Generate coordinates for node i
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coords = []
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for d in range(dimensions):
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coords.append((i >> d) & 1)
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node = HypercubeNode(
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nodeId=i,
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coordinates=coords,
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dimensions=dimensions
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)
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nodes.append(node)
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state = HypercubeTopologyState(
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nodes=nodes,
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dimensions=dimensions,
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maxNodeId=maxNodeId
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)
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self.topologyState = state
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# Initialize holographic projection if available
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if self.holographicProjectionSystem:
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self.holographicProjectionSystem.initializeProjection(temperature=300.0, numPoints=numNodes)
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return {
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'dimensions': dimensions,
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'connectivity': connectivity(dimensions),
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'neighborCount': neighborCount(dimensions),
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'diameter': hypercubeDiameter(dimensions),
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'bisectionBandwidth': bisectionBandwidth(dimensions),
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'state': state.to_dict()
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}
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def registerNode(self, nodeId: int, coordinates: List[int], dimensions: int = 12) -> Dict[str, Any]:
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"""Register a node in the hypercube topology"""
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if self.topologyState is None:
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self.initializeTopology(dimensions)
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node = HypercubeNode(
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nodeId=nodeId,
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coordinates=coordinates,
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dimensions=dimensions
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)
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# Add node if not exists, update if exists
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existing = False
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newNodes = []
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for n in self.topologyState.nodes:
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if n.nodeId == nodeId:
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newNodes.append(node)
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existing = True
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else:
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newNodes.append(n)
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if not existing:
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newNodes.append(node)
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self.topologyState.nodes = newNodes
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# Register node as holographic surface point if available
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if self.holographicProjectionSystem:
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# Use hypercube distance as proxy for amplitude (closer to origin = higher amplitude)
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distance = sum(abs(c) for c in coordinates)
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amplitude = 1.0 / (1.0 + distance) if distance > 0 else 1.0
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phase = 0.0 # Phase based on node ID
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coherence = 0.8 # Default coherence
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self.holographicProjectionSystem.registerSurfacePoint(
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pointId=nodeId,
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amplitude=amplitude,
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phase=phase,
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coherence=coherence
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)
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return {
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'nodeId': nodeId,
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'node': node.to_dict(),
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'state': self.topologyState.to_dict()
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}
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def submitHypercubeAction(self, action: HypercubeAction, currentTime: float = 0.0) -> Dict[str, Any]:
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"""Submit hypercube action for processing (Lean specification)"""
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if self.topologyState is None:
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return {'error': 'Topology not initialized'}
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bindResult = hypercubeBind(self.topologyState, action, currentTime)
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if bindResult.lawful:
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# Update node in state
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for i, n in enumerate(self.topologyState.nodes):
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if n.nodeId == action.nodeId:
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self.topologyState.nodes[i] = toggleCoordinate(n, action.dimension)
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break
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# Record action history
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self.actionHistory.append({
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'nodeId': action.nodeId,
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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.topologyState.to_dict()
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}
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def getTopologyState(self) -> Optional[Dict[str, Any]]:
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"""Get current topology state"""
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if self.topologyState:
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return self.topologyState.to_dict()
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return None
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def getNeighbors(self, nodeId: int) -> List[Dict[str, Any]]:
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"""Get neighbors of a node"""
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if self.topologyState is None:
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return []
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for n in self.topologyState.nodes:
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if n.nodeId == nodeId:
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neighbors = getNeighbors(self.topologyState, n)
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return [neighbor.to_dict() for neighbor in neighbors]
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return []
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def getActionHistory(self, limit: int = 10) -> List[Dict[str, Any]]:
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"""Get action history"""
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return self.actionHistory[-limit:]
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def printSystemState(self):
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"""Print system state"""
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print("\n" + "="*60)
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print("HYPERCUBE TOPOLOGY STATE")
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print("="*60)
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if self.topologyState:
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print(f"\n📊 Topology Properties:")
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print(f" Dimensions: {self.topologyState.dimensions}")
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print(f" Connectivity: {connectivity(self.topologyState.dimensions)} nodes")
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print(f" Neighbor Count: {neighborCount(self.topologyState.dimensions)}")
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print(f" Diameter: {hypercubeDiameter(self.topologyState.dimensions)}")
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print(f" Bisection Bandwidth: {bisectionBandwidth(self.topologyState.dimensions)}")
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print(f"\n📍 Registered Nodes: {len(self.topologyState.nodes)}")
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for node in self.topologyState.nodes:
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print(f" Node {node.nodeId}:")
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print(f" Coordinates: {node.coordinates}")
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print(f" Neighbors: {len(getNeighbors(self.topologyState, node))}")
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print(f"\n📜 Action History: {len(self.actionHistory)} entries")
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# Add holographic projection information if available
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if self.holographicProjectionSystem:
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holoState = self.holographicProjectionSystem.getProjectionState()
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if holoState:
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print(f"\n🌌 Holographic Projection:")
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print(f" Temperature: {holoState['temperature']:.3f} K")
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print(f" Stabilization Probability: {holoState['stabilizationProbability']:.3f}")
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print(f" Entropy Reduction: {holoState['entropyReduction']:.3f}")
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print(f" Surface Points: {len(holoState['surfacePoints'])}")
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print("\n" + "="*60)
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def main():
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"""Test hypercube topology system"""
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system = HypercubeTopologySystem()
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print("[Test 1] Initialize 16-dimensional hypercube topology (65,536 nodes)...")
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result1 = system.initializeTopology(dimensions=16, numNodes=16)
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print(f" Topology initialized: {result1['connectivity']} nodes, {result1['neighborCount']} neighbors per node")
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print("\n[Test 2] Register node at origin...")
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result2 = system.registerNode(nodeId=1, coordinates=[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], dimensions=16)
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print(f" Node 1 registered")
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print("\n[Test 3] Register node at distance 1...")
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result3 = system.registerNode(nodeId=2, coordinates=[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], dimensions=16)
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print(f" Node 2 registered")
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print("\n[Test 4] Register node at distance 2...")
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result4 = system.registerNode(nodeId=3, coordinates=[1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], dimensions=16)
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print(f" Node 3 registered")
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print("\n[Test 5] Submit hypercube action (toggle dimension 0 for node 1)...")
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action1 = HypercubeAction(nodeId=1, dimension=0)
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result5 = system.submitHypercubeAction(action1)
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print(f" Result: Success={result5['success']}")
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if result5['success']:
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print(f" Distance before: {result5['bindResult']['distanceBefore']}")
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print(f" Distance after: {result5['bindResult']['distanceAfter']}")
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print("\n[System State]")
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system.printSystemState()
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if __name__ == '__main__':
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main()
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