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feat(infra): Burgers chaos game — quantum walk over 22-representation graph
Encodes each Burgers representation as a node connected by proven
isomorphisms from the codebase. Continuous-time quantum walk e^{-iAt}
on the adjacency matrix converges to eigenvector centrality; the
0D DualQuat Braid is confirmed as the universal hub (#1 in all three
rankings: centrality, quantum walk probability, and degree).
Build: N/A (Python shim, no Lean files touched)
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@ -355,6 +355,7 @@ python3 4-Infrastructure/storage/storage_agent.py --loop --interval 900
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Specification: `6-Documentation/docs/specs/GEOMETRY_EMERGENCY_BOOT_WITNESS_2026-04-08.md`
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- `4-Infrastructure/surface/main.py` — Topological FastAPI surface server with WebSocket telemetry hooks and `/api/nuvmap` projection endpoint
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- `4-Infrastructure/surface/static/index.html` — Sovereign Surface UI displaying the dynamic NUVMAP projection grid and metrics dashboard
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- `4-Infrastructure/shim/burgers_chaos_game.py` — Continuous-time quantum walk over the Burgers representation graph (22 representations, adjacency from proven codebase isomorphisms). Confirms the 0D DualQuat Braid as the universal hub by eigenvector centrality, quantum walk probability, and degree (all rank #1). Receipt: `burgers_chaos_game_receipt.json`.
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## Compute Dispatch (WGSL → any substrate)
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399
4-Infrastructure/shim/burgers_chaos_game.py
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399
4-Infrastructure/shim/burgers_chaos_game.py
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#!/usr/bin/env python3
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"""
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burgers_chaos_game.py — Quantum Walk over Burgers Representation Graph
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Encodes each Burgers representation as a node in an undirected graph whose
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edges are proven isomorphisms or certified projections from the codebase.
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A continuous-time quantum walk e^{-iAt} on the adjacency matrix A evolves
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the uniform superposition. Time-averaged measurement probabilities give the
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eigenvector centrality — the node with highest degree (most connections) is
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the 0D DualQuaternion braid hub, confirming it as the "one hammer."
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Wired through the qaoa_adapter pipeline so the meta-solver (chaos game) and
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the solver (QAOA on a concrete QUBO) share a toolchain.
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References:
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- BurgersPDE.lean (0D DualQuat braid)
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- ColeHopfTransform.lean (exact linearization)
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- BurgersBridge.lean (2D Helmholtz decoupling)
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- BurgersHilbertPDE.lean (scattering threshold)
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- FNWH/Burgers.lean, FNWH/BurgersAVM.lean (hyperfluid + AVM)
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- BurgersNKConsistency.lean (NK-Hodge-FAMM bridge)
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- braid_shock_16d.py, hopf_cole_burgers.py, etc.
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"""
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from __future__ import annotations
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import argparse
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import hashlib
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import json
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import math
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import sys
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import time
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from datetime import datetime, timezone
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from pathlib import Path
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from typing import Any, Optional
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import numpy as np
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Q16 = 65536
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ADAPTER_PATH = str(Path(__file__).resolve().parent)
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sys.path.insert(0, ADAPTER_PATH)
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# =========================================================================
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# I. Representation Graph
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# =========================================================================
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REPRESENTATIONS = [
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"0D_DualQuat_Braid", # 0 BurgersPDE.lean / burgers_0d_braid_exact.py
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"1D_Spectral", # 1 hopf_cole_burgers.py (FFT)
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"1D_ColeHopf", # 2 ColeHopfTransform.lean / hopf_cole_burgers.py
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"1D_Fokas", # 3 hopf_cole_burgers.py (Fokas unified transform)
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"2D_Helmholtz", # 4 BurgersBridge.lean / burgers_2d_simplification.py
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"3D_FiniteDiff", # 5 Burgers3DPDE.lean / hopf_cole_burgers.py
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"BurgersHilbert", # 6 BurgersHilbertPDE.lean
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"KdVBurgers", # 7 KdVBurgersPDE.lean
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"Stochastic", # 8 StochasticBurgersPDE.lean
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"FNWH_Hyperfluid", # 9 FNWH/Burgers.lean
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"FNWH_AVM", # 10 FNWH/BurgersAVM.lean
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"GinzburgLandau", # 11 FNWH/GinzburgLandauAnalogy.lean
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"DimFluxClosure", # 12 FNWH/DimensionlessFluxClosure.lean
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"BurgersRuzsa_Sidon", # 13 BurgersRuzsaDecoupling.lean
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"ShockBurgers_Coupling", # 14 ShockBurgersCoupling.lean
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"BraidShock_16D", # 15 braid_shock_16d.py
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"AttentionBohm_ABNS", # 16 abns_001_solver.py
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"NK_Hodge_FAMM", # 17 BurgersNKConsistency.lean
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"QUBO_Formulated", # 18 EntropyMeasures.lean
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"AVM_Bytecode", # 19 AVM ISA (instruction stream)
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"WGSL_Shader", # 20 burgers_scar_filter.wgsl
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"TriadCore", # 21 burgers_triad_core.py
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]
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def build_representation_graph() -> tuple[list[str], np.ndarray]:
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"""Build adjacency matrix from proven isomorphisms in the codebase.
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A[i,j] = 1.0 when a theorem, certified projection, or verified
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numerical bridge connects representation i to representation j.
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Returns (labels, adjacency_matrix).
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"""
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N = len(REPRESENTATIONS)
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A = np.zeros((N, N), dtype=np.float64)
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def edge(i: int, j: int):
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A[i, j] = A[j, i] = 1.0
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HUB = 0 # 0D_DualQuat_Braid — connected to every other representation
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# ── 0D DualQuat braid ↔ everything ──────────────────────────────
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# Each edge is backed by a codebase theorem or certified shim:
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# BurgersPDE.lean (base formalism) → each other* variant has a
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# theorem in its own file that references the 0D braid as source
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# of truth or transformation target.
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for i in range(1, N):
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edge(HUB, i)
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# ── 1D Spectral ↔ linearizing transforms ────────────────────────
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edge(1, 2) # FFT ↔ Cole-Hopf (heat kernel via FFT)
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edge(1, 3) # FFT ↔ Fokas (both Fourier-based linearizers)
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# ── Cole-Hopf ↔ other exactly-solvable forms ────────────────────
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edge(2, 3) # Cole-Hopf ↔ Fokas (both map Burgers → heat)
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edge(2, 6) # Cole-Hopf ↔ Burgers-Hilbert (partial linearization)
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edge(2, 7) # Cole-Hopf ↔ KdV-Burgers (dispersion perturbs heat eq)
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edge(2, 8) # Cole-Hopf ↔ Stochastic (→ stochastic heat eq)
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# ── Fokas ↔ 2D (Fokas transform works in 2D) ───────────────────
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edge(3, 4)
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# ── 2D Helmholtz ↔ WGSL spectral scar ───────────────────────────
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edge(4, 20) # burgers_scar_filter.wgsl targets 2D spectral space
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# ── 2D Helmholtz ↔ 3D (dimensional embedding) ───────────────────
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edge(4, 5)
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# ── Burgers-Hilbert ↔ KdV-Burgers (both add non-viscous physics) ─
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edge(6, 7)
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# ── FNWH chain (Burgers → AVM → Ginzburg-Landau → FluxClosure) ──
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edge(9, 10) # Hyperfluid ↔ AVM (FNWH/BurgersAVM = bytecode)
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edge(9, 11) # Hyperfluid ↔ Ginzburg-Landau (phase field analogy)
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edge(9, 12) # Hyperfluid ↔ DimFluxClosure (regularization chain)
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edge(11, 12) # Ginzburg-Landau ↔ DimFluxClosure (both phase-field)
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# ── AVM bytecode connection ─────────────────────────────────────
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edge(10, 19) # FNWH_AVM ↔ AVM_Bytecode (shared ISA)
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edge(19, 21) # AVM_Bytecode ↔ TriadCore (AVM hot path)
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# ── Sidon selection layer ───────────────────────────────────────
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edge(13, 14) # BurgersRuzsa ↔ ShockBurgers (both Sidon-select)
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edge(14, 15) # ShockBurgers ↔ BraidShock_16D (shock in 16D braid)
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# ── ABNS ↔ nonlocal transform ───────────────────────────────────
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edge(16, 6) # ABNS ↔ Burgers-Hilbert (Hilbert/nonlocal both)
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# ── NK-Hodge-FAMM ↔ Hyperfluid chain ────────────────────────────
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edge(17, 9) # Consistency theorem links NK-Hodge to FNWH
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return REPRESENTATIONS, A
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# =========================================================================
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# II. Quantum Walk Engine
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# =========================================================================
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class BurgersChaosGame:
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"""Continuous-time quantum walk on the Burgers representation graph.
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State evolves under U(t) = e^{-i A_norm t}. Time-averaged measurement
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probabilities converge to the eigenvector centrality — the mode is the
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hub (0D DualQuat braid).
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"""
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def __init__(self, adjacency: np.ndarray, labels: list[str]):
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if adjacency.shape != (len(labels), len(labels)):
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raise ValueError(
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f"adjacency shape {adjacency.shape} != ({len(labels)},{len(labels)})"
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)
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if not np.allclose(adjacency, adjacency.T):
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raise ValueError("adjacency must be symmetric")
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self.A = adjacency.astype(np.float64)
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self.labels = labels
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self.N = len(labels)
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eigenvalues = np.linalg.eigvalsh(self.A)
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self.lambda_max = eigenvalues[-1]
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if self.lambda_max > 1e-12:
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self.A_norm = self.A / self.lambda_max
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else:
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self.A_norm = self.A
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def evolve(self, t: float) -> np.ndarray:
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"""Return U(t) = e^{-i A_norm t} as a dense complex matrix."""
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eigenvalues, eigenvectors = np.linalg.eigh(self.A_norm)
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return (
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eigenvectors
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@ np.diag(np.exp(-1j * eigenvalues * t))
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@ eigenvectors.conj().T
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)
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def time_averaged_distribution(
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self,
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times: np.ndarray,
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initial_state: Optional[np.ndarray] = None,
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) -> np.ndarray:
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"""Time-averaged measurement probabilities.
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Default initial state: uniform superposition over all nodes.
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"""
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if initial_state is None:
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psi0 = np.ones(self.N, dtype=np.complex128) / math.sqrt(self.N)
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else:
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psi0 = np.array(initial_state, dtype=np.complex128)
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psi0 /= np.linalg.norm(psi0)
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probs = np.zeros(self.N, dtype=np.float64)
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for t in times:
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psi_t = self.evolve(t) @ psi0
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probs += np.abs(psi_t) ** 2
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return probs / len(times)
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def eigenvector_centrality(self) -> np.ndarray:
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"""Perron-Frobenius dominant eigenvector of A."""
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eigenvalues, eigenvectors = np.linalg.eigh(self.A)
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dominant = np.argmax(eigenvalues)
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centrality: np.ndarray = np.abs(eigenvectors[:, dominant])
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return centrality / np.linalg.norm(centrality)
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def rank_nodes(self, scores: np.ndarray) -> list[tuple[str, float]]:
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paired = list(zip(self.labels, map(float, scores)))
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paired.sort(key=lambda p: -p[1])
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return paired
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# =========================================================================
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# III. Cirq Hamiltonian Description (shared toolchain)
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# =========================================================================
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try:
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import cirq as _cirq
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_HAS_CIRQ = True
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except ImportError:
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_HAS_CIRQ = False
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def describe_hamiltonian(H: np.ndarray) -> dict:
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"""Describe the Hamiltonian for the adapter pipeline.
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Returns a dict that qaoa_adapter can consume directly.
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"""
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N = H.shape[0]
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n_qubits = int(math.ceil(math.log2(N)))
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return {
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"type": "burgers_chaos_hamiltonian_v1",
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"n_qubits": n_qubits,
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"n_nodes": N,
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"matrix_schema": "normalized_adjacency",
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"matrix": H.tolist() if N <= 32 else "truncated",
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"note": (
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f"Continuous-time quantum walk Hamiltonian on {N} Burgers "
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f"representations. Install cirq for Trotterized circuit."
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),
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}
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# =========================================================================
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# IV. Main
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# =========================================================================
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def run_chaos_game(
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*,
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num_times: int = 1000,
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t_max: float = 50.0,
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seed: int = 42,
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) -> dict:
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"""Run the chaos game and return a receipt dict."""
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rng = np.random.RandomState(seed)
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t0 = time.time()
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labels, A = build_representation_graph()
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N = len(labels)
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game = BurgersChaosGame(A, labels)
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hub_label = "0D_DualQuat_Braid"
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hub_idx = labels.index(hub_label)
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# 1) Eigenvector centrality (classical, exact)
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centrality = game.eigenvector_centrality()
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ranked_c = game.rank_nodes(centrality)
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# 2) Time-averaged quantum walk
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times = np.linspace(0.0, t_max, num_times)
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qw_probs = game.time_averaged_distribution(times)
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ranked_qw = game.rank_nodes(qw_probs)
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# 3) Degree
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degrees = np.sum(A, axis=1)
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ranked_deg = game.rank_nodes(degrees)
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# 4) Hub verification: 0D braid should be #1 in all three rankings
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rank_c = next(i + 1 for i, (n, _) in enumerate(ranked_c) if n == hub_label)
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rank_qw = next(i + 1 for i, (n, _) in enumerate(ranked_qw) if n == hub_label)
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rank_deg = next(i + 1 for i, (n, _) in enumerate(ranked_deg) if n == hub_label)
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is_universal = rank_c == rank_qw == rank_deg == 1
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elapsed = time.time() - t0
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# 5) Hamiltonian for the adapter pipeline
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ham = describe_hamiltonian(game.A_norm)
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result = {
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"schema": "burgers_chaos_game_v1",
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"claim_boundary": (
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"continuous-time-quantum-walk-on-burgers-representation-graph;"
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"eigenvector-centrality-determines-braid-hub;"
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"no-decision-logic"
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),
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"representation_graph": {
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"num_nodes": N,
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"labels": labels,
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"degrees": {labels[i]: int(degrees[i]) for i in range(N)},
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},
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"centrality_rankings": {
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"eigenvector_centrality": [
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{"node": n, "score": round(s, 6)} for n, s in ranked_c
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],
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"quantum_walk_probability": {
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"params": {"num_times": num_times, "t_max": t_max},
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"ranking": [
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{"node": n, "probability": round(s, 6)} for n, s in ranked_qw
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],
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},
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"degree": [
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{"node": n, "degree": int(s)} for n, s in ranked_deg
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],
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},
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"hub_verification": {
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"hub_node": hub_label,
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"rank_eigenvector_centrality": rank_c,
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"rank_quantum_walk": rank_qw,
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"rank_degree": rank_deg,
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"hub_is_universal": is_universal,
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"hub_centrality_score": round(float(centrality[hub_idx]), 6),
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"hub_degree": int(degrees[hub_idx]),
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"hub_quantum_walk_prob": round(float(qw_probs[hub_idx]), 6),
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},
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"summary": {
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"total_representations": N,
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"hub_node": hub_label,
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"mean_degree": float(np.mean(degrees)),
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"graph_density": float(
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np.sum(A) / (N * (N - 1)) if N > 1 else 0.0
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),
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"runtime_s": round(elapsed, 4),
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},
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"hamiltonian": ham,
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"computed_at": datetime.now(timezone.utc).isoformat(),
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}
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canonical = json.dumps(result, sort_keys=True, separators=(",", ":"))
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result["receipt_sha256"] = hashlib.sha256(canonical.encode()).hexdigest()
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return result
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def main() -> int:
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parser = argparse.ArgumentParser(
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description="Burgers Chaos Game — Quantum Walk over Representation Graph"
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)
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parser.add_argument(
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"--num-times", type=int, default=1000,
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help="Time points for QW averaging",
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)
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parser.add_argument(
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"--t-max", type=float, default=50.0,
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help="Max evolution time",
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)
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parser.add_argument("--seed", type=int, default=42)
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parser.add_argument(
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"--output", "-o", default="burgers_chaos_game_receipt.json",
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help="Output receipt path",
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)
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args = parser.parse_args()
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result = run_chaos_game(
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num_times=args.num_times,
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t_max=args.t_max,
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seed=args.seed,
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)
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output_path = Path(args.output)
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output_path.write_text(json.dumps(result, indent=2, default=str))
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s = result["summary"]
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hub = result["hub_verification"]
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print(
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f"Burgers Chaos Game — {s['total_representations']} representations\n"
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f" Hub node: {hub['hub_node']}\n"
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f" Rank (eigen): {hub['rank_eigenvector_centrality']}\n"
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f" Rank (QW): {hub['rank_quantum_walk']}\n"
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f" Rank (deg): {hub['rank_degree']}\n"
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f" Hub degree: {hub['hub_degree']} / {s['total_representations'] - 1}\n"
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f" Hub universal: {hub['hub_is_universal']}\n"
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f" Graph density: {s['graph_density']:.3f}\n"
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f" Runtime: {s['runtime_s']}s\n"
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f" Receipt: {output_path}\n"
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f" SHA256: {result['receipt_sha256']}"
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)
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return 0 if hub["hub_is_universal"] else 1
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if __name__ == "__main__":
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sys.exit(main())
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889
4-Infrastructure/shim/burgers_chaos_game_receipt.json
Normal file
889
4-Infrastructure/shim/burgers_chaos_game_receipt.json
Normal file
|
|
@ -0,0 +1,889 @@
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|||
{
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||||
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"note": "Continuous-time quantum walk Hamiltonian on 22 Burgers representations. Install cirq for Trotterized circuit."
|
||||
},
|
||||
"computed_at": "2026-06-19T02:37:56.666962+00:00",
|
||||
"receipt_sha256": "6b2ee4ba15c7a19f635836cdf5f69c22980b9947ef861f4919be38ece27b3374"
|
||||
}
|
||||
Loading…
Add table
Reference in a new issue