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allaun
558431fc45
- Renamed Corpus278/Matrices278 to Corpus250/Matrices250 across all Lean modules, Python shims, JSON schemas, and documentation - Applied SLOS-calibrated defaults to braid_search.py: bracket_cost base=8x/16x, crossing_penalty gap_reward=0.01 - Synced same defaults to research-compute-fabric submodule - Updated Burgers 0D defaults: nu=0.9995, advection=0.075 - Fixed 278→250 refs in pist_predictions JSON (claim_boundary, total) - Fixed stale schema refs in .devin/skills/lean-proof/SKILL.md - Updated AGENTS.md build baselines to post-clean counts (3314 jobs) - Updated lake-manifest.json sparkle rev to match lakefile.toml - Fixed Q16_16 signed conversion bug in qaoa_adapter tunable costs - NBody.lean: pre-existing dirty changes (introN failures, NOT our work) Build: 3314 jobs, 0 errors (lake build Compiler)
581 lines
21 KiB
Python
581 lines
21 KiB
Python
#!/usr/bin/env python3
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"""
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geometric_entropy_explorer.py — Exploration-phase candidate generator
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for the Rainbow Raccoon Compiler (RRC).
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Places 8 points (braid strands) on a torus and maximizes Shannon entropy
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of the pairwise-distance distribution via gradient descent (TF.js-compatible).
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Exports candidate BraidReceipt JSON for downstream Lean certification.
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Usage:
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python3 geometric_entropy_explorer.py # run with defaults
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python3 geometric_entropy_explorer.py --manifold sphere # try different manifold
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python3 geometric_entropy_explorer.py --export candidates.json
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Architecture (per the DP-RRC spec):
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┌─ Exploration phase ──────────────────────────────────┐
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│ torus → entropy maximization → candidate point cloud │
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│ → export candidate receipt JSON │
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└──────────────────────────┬───────────────────────────┘
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│ candidate (JSON)
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▼
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┌─ Certification phase (Lean) ────────────────────────┐
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│ crossStep verification → eigensolid_convergence │
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│ → receipt_invertible theorem → AVM stamp │
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└──────────────────────────────────────────────────────┘
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This script is pure I/O + feature extraction (Python-owned per AGENTS.md).
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No gating, alignment, or promotion decisions are made here.
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"""
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import numpy as np
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import json
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import os
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import sys
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import argparse
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from dataclasses import dataclass, field
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from typing import List, Optional, Tuple
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# ---------------------------------------------------------------------------
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# Q16_16 helpers (fixed-point matching the Lean representation)
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# ---------------------------------------------------------------------------
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def to_q16(x: float) -> int:
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"""Float → Q16_16 signed 32-bit integer."""
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return int(round(x * 65536.0))
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def from_q16(q: int) -> float:
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"""Q16_16 → float."""
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return q / 65536.0
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Q16_ONE = to_q16(1.0)
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Q16_PI = to_q16(np.pi)
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Q16_PI_4 = to_q16(np.pi / 4)
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# ---------------------------------------------------------------------------
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# Manifold parameterizations
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# ---------------------------------------------------------------------------
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class Manifold:
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"""Base class for constraint manifolds (torus, sphere, cube, etc.)."""
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def sample(self, n: int, rng: np.random.Generator) -> np.ndarray:
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"""Sample n random points on the manifold. Returns (n, 3)."""
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raise NotImplementedError
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def project(self, points: np.ndarray) -> np.ndarray:
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"""Project points onto the manifold surface."""
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raise NotImplementedError
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def __str__(self) -> str:
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return self.__class__.__name__
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class Torus(Manifold):
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"""Torus of revolution: major radius R, minor radius r."""
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def __init__(self, R: float = 2.0, r: float = 1.0):
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self.R = R
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self.r = r
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def _uv_to_xyz(self, u: np.ndarray, v: np.ndarray) -> np.ndarray:
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"""(u, v) in [0, 2π)² → (x, y, z) on torus."""
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x = (self.R + self.r * np.cos(v)) * np.cos(u)
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y = (self.R + self.r * np.cos(v)) * np.sin(u)
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z = self.r * np.sin(v)
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return np.stack([x, y, z], axis=-1)
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def sample(self, n: int, rng: np.random.Generator) -> np.ndarray:
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u = rng.uniform(0, 2 * np.pi, size=n)
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v = rng.uniform(0, 2 * np.pi, size=n)
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return self._uv_to_xyz(u, v)
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def project(self, points: np.ndarray) -> np.ndarray:
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"""Project (x, y, z) onto nearest point on torus surface."""
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x, y, z = points[..., 0], points[..., 1], points[..., 2]
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phi = np.arctan2(y, x)
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# distance from central circle axis
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d_xy = np.sqrt(x**2 + y**2)
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theta = np.arctan2(z, d_xy - self.R)
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return self._uv_to_xyz(phi, theta)
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class Sphere(Manifold):
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"""Unit sphere S²."""
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def __init__(self, radius: float = 1.0):
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self.radius = radius
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def sample(self, n: int, rng: np.random.Generator) -> np.ndarray:
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# Normal distribution → normalize to sphere surface
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pts = rng.normal(size=(n, 3))
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norms = np.linalg.norm(pts, axis=-1, keepdims=True)
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return self.radius * pts / norms
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def project(self, points: np.ndarray) -> np.ndarray:
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norms = np.linalg.norm(points, axis=-1, keepdims=True)
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return self.radius * points / norms
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class CubeShell(Manifold):
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"""Cube surface (6 faces)."""
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def __init__(self, side: float = 2.0):
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self.side = side
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self.half = side / 2
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def sample(self, n: int, rng: np.random.Generator) -> np.ndarray:
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# Pick a random face, then random 2D coordinates on it
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pts = np.zeros((n, 3))
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faces = rng.integers(0, 6, size=n)
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for i, f in enumerate(faces):
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coord = rng.uniform(-self.half, self.half, size=2)
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if f == 0: pts[i] = [self.half, coord[0], coord[1]]
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if f == 1: pts[i] = [-self.half, coord[0], coord[1]]
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if f == 2: pts[i] = [coord[0], self.half, coord[1]]
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if f == 3: pts[i] = [coord[0], -self.half, coord[1]]
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if f == 4: pts[i] = [coord[0], coord[1], self.half]
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if f == 5: pts[i] = [coord[0], coord[1], -self.half]
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return pts
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def project(self, points: np.ndarray) -> np.ndarray:
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# Clamp to cube surface (closest face)
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return np.clip(points, -self.half, self.half)
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# ---------------------------------------------------------------------------
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# Entropy computation (matching the geometric-entropy-lab approach)
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# ---------------------------------------------------------------------------
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def pairwise_distances(points: np.ndarray) -> np.ndarray:
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"""(n, 3) → (n, n) Euclidean distance matrix."""
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diff = points[:, np.newaxis, :] - points[np.newaxis, :, :]
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return np.sqrt(np.sum(diff**2, axis=-1))
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def gaussian_kde_entropy(
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distances: np.ndarray,
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bandwidth: float = 0.3,
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temperature: float = 1.0,
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) -> float:
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"""
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Shannon entropy of the pairwise-distance distribution using Gaussian KDE,
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matching the geometric-entropy-lab approach:
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G = D² (Gram matrix of squared distances)
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ρ = softmax(G / τ) (density via softmax)
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H = -Σ p·log(p) (Shannon entropy)
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The lab uses dot products; we use squared distances, which is equivalent
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for centered point clouds.
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"""
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n = distances.shape[0]
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# Gaussian kernel over squared distances
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D2 = distances**2
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K = np.exp(-D2 / (2 * bandwidth**2))
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# Density via softmax over kernel matrix
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K_scaled = K / temperature
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K_max = np.max(K_scaled, axis=-1, keepdims=True)
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K_stable = K_scaled - K_max
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exp_K = np.exp(K_stable)
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rho = exp_K / np.sum(exp_K, axis=-1, keepdims=True)
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# Shannon entropy: H = -Σ p·log(p)
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p = np.mean(rho, axis=0)
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p = p / np.sum(p)
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H = -np.sum(p * np.log(p + 1e-30))
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return float(H)
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def entropy_gradient(
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points: np.ndarray,
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bandwidth: float = 0.3,
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temperature: float = 1.0,
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eps: float = 1e-6,
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) -> np.ndarray:
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"""
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Numerical gradient of entropy w.r.t. point positions via central differences.
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Returns (n, 3) gradient: dH/dx_i.
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"""
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grad = np.zeros_like(points)
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D = pairwise_distances(points)
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H0 = gaussian_kde_entropy(D, bandwidth, temperature)
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for i in range(points.shape[0]):
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for j in range(3):
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points[i, j] += eps
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Dp = pairwise_distances(points)
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Hp = gaussian_kde_entropy(Dp, bandwidth, temperature)
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points[i, j] -= 2 * eps
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Dm = pairwise_distances(points)
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Hm = gaussian_kde_entropy(Dm, bandwidth, temperature)
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points[i, j] += eps
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grad[i, j] = (Hp - Hm) / (2 * eps)
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return grad
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# ---------------------------------------------------------------------------
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# BraidStrand mapping: point on manifold → BraidStrand parameters
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# ---------------------------------------------------------------------------
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def points_to_braid_state(
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points: np.ndarray,
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slots: Optional[List[int]] = None,
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) -> dict:
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"""
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Map (n, 3) point cloud on torus to BraidState-compatible dict.
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Encoding (per DP-RRC spec):
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- point spherical angles → PhaseVec (x, y)
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- Sidon labels from toroidal coordinate quanta
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- kappa from pairwise distance entropy gradient
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- bracket from PhaseVec via fromPhaseVec equivalent
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"""
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n = points.shape[0]
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assert n == 8, f"BraidStorm requires exactly 8 strands, got {n}"
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if slots is None:
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slots = [1, 2, 4, 8, 16, 32, 64, 128]
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# Normalize to unit sphere for phase angles
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norms = np.linalg.norm(points, axis=-1, keepdims=True)
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unit = points / (norms + 1e-30)
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# Theta (polar) and phi (azimuthal) as PhaseVec (x, y) in Q16_16
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theta = np.arccos(np.clip(unit[:, 2], -1.0, 1.0))
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phi = np.arctan2(unit[:, 1], unit[:, 0])
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# Pairwise distances for kappa computation (octagonal norm analog)
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D = pairwise_distances(points)
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# kappa = normalized mean distance to nearest neighbor (like octagonal norm)
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diag_mask = np.eye(n, dtype=bool)
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D_masked = D.copy()
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D_masked[diag_mask] = np.inf
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min_d = np.min(D_masked, axis=1)
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kappa_vals = min_d / np.max(min_d + 1e-30)
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# Compute bracket kappa as octagonal norm equivalent
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bracket_kappa = float(np.mean(D[~diag_mask]))
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strands = []
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for i in range(n):
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phase_vec = {
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"x": to_q16(float(np.sin(theta[i]) * np.cos(phi[i]))),
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"y": to_q16(float(np.sin(theta[i]) * np.sin(phi[i]))),
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}
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mu = slots[i]
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kappa_q = to_q16(float(kappa_vals[i]))
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# BraidBracket: lower = κ - μ, upper = κ + μ, gap = 2μ
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lower_q = to_q16(float(kappa_vals[i] - 0.1 * mu / 128.0))
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upper_q = to_q16(float(kappa_vals[i] + 0.1 * mu / 128.0))
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gap_q = to_q16(float(0.2 * mu / 128.0))
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admissible = lower_q <= upper_q
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strands.append({
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"phaseAcc": phase_vec,
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"parity": bool(i % 2),
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"slot": slots[i],
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"residue": 0,
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"jitter": 0,
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"bracket": {
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"lower": lower_q,
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"upper": upper_q,
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"gap": gap_q,
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"kappa": kappa_q,
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"phi": Q16_PI_4 if kappa_q != 0 else 0,
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"admissible": admissible,
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}
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})
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# Sidon slack: budget - max label used
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sidon_slack = 128 - max(slots)
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return {
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"strands": strands,
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"bracket_kappa": to_q16(float(bracket_kappa)),
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"sidon_slack": sidon_slack,
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}
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# ---------------------------------------------------------------------------
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# Gradient descent optimizer (entropy maximization)
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# ---------------------------------------------------------------------------
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def optimize_entropy(
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manifold: Manifold,
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n_points: int = 8,
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n_steps: int = 200,
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lr: float = 0.1,
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bandwidth: float = 0.3,
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temperature: float = 1.0,
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seed: Optional[int] = None,
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verbose: bool = True,
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cluster_init: bool = True,
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) -> Tuple[np.ndarray, List[float]]:
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"""
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Run gradient descent to maximize Shannon entropy of pairwise distances
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on the given manifold.
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Strategy: start with a clustered initialization (low entropy), then
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maximize entropy to spread points out. This gives a clear gradient signal.
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Returns:
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points: (n, 3) optimized point cloud
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history: [H_0, H_1, ..., H_n_steps] entropy trace
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"""
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rng = np.random.default_rng(seed)
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if cluster_init:
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# Start all points in a tight cluster → low entropy → strong gradient
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center = manifold.sample(1, rng)[0]
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points = center + rng.normal(0, 0.05, size=(n_points, 3))
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points = manifold.project(points)
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else:
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points = manifold.sample(n_points, rng)
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history = []
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for step in range(n_steps):
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D = pairwise_distances(points)
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H = gaussian_kde_entropy(D, bandwidth, temperature)
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history.append(H)
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if step % 20 == 0 and verbose:
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print(f" step {step:4d}: H = {H:.6f} (spread: {float(np.mean(D[~np.eye(n_points, dtype=bool)])):.4f})")
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if step == n_steps - 1:
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break
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grad = entropy_gradient(points, bandwidth, temperature)
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# Gradient ascent (maximize entropy)
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points = points + lr * grad
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# Project back onto manifold
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points = manifold.project(points)
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# Repulsion regularizer: prevent collapse
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D_self = pairwise_distances(points)
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np.fill_diagonal(D_self, np.inf)
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min_sep = np.min(D_self)
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if min_sep < 0.05:
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for i in range(n_points):
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for j in range(n_points):
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if i != j:
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diff = points[i] - points[j]
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dist = np.linalg.norm(diff)
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if 0 < dist < 0.2:
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repel = 0.02 * diff / (dist + 1e-30)
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points[i] += repel
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points[j] -= repel
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points = manifold.project(points)
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return points, history
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# ---------------------------------------------------------------------------
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# Candidate export (bridge to Lean certification pipeline)
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# ---------------------------------------------------------------------------
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def export_candidate(
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points: np.ndarray,
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manifold: Manifold,
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entropy_history: List[float],
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equation_id: str = "rrc_eq_entropy_explorer",
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output_path: Optional[str] = None,
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bandwidth: float = 0.3,
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temperature: float = 1.0,
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) -> dict:
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"""
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Export a candidate receipt JSON that the Lean pipeline can consume.
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Format matches the BraidReceipt structure from BraidEigensolid.lean
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plus provenance metadata for the exploration phase.
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"""
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braid_state = points_to_braid_state(points)
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final_entropy = entropy_history[-1] if entropy_history else 0.0
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# Serialize manifold params safely
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if isinstance(manifold, Torus):
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mparams = {"R": manifold.R, "r": manifold.r}
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elif isinstance(manifold, Sphere):
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mparams = {"radius": manifold.radius}
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elif isinstance(manifold, CubeShell):
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mparams = {"side": manifold.side}
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else:
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mparams = {}
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candidate = {
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"schema": "rrc_candidate_entropy_v1",
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"claim_boundary": "exploration-phase-only;not-certified",
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"genesis": {
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"method": "entropy_maximization",
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"manifold": str(manifold),
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"manifold_params": mparams,
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"entropy_final": round(final_entropy, 6),
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"entropy_history": [round(h, 6) for h in entropy_history],
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"bandwidth": bandwidth,
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"temperature": temperature,
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},
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"braid_state": braid_state,
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"equation_id": equation_id,
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"sidon_slack": braid_state["sidon_slack"],
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}
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if output_path:
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os.makedirs(os.path.dirname(output_path) or ".", exist_ok=True)
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with open(output_path, "w") as f:
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json.dump(candidate, f, indent=2)
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print(f"Exported candidate to {output_path}")
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return candidate
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||
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# ---------------------------------------------------------------------------
|
||
# Main
|
||
# ---------------------------------------------------------------------------
|
||
|
||
def main():
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||
parser = argparse.ArgumentParser(
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||
description="Geometric Entropy Explorer — RRC candidate generator"
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)
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parser.add_argument(
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"--manifold", choices=["torus", "sphere", "cube"],
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default="torus", help="Constraint manifold"
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)
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parser.add_argument("--n-strands", type=int, default=8)
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parser.add_argument("--steps", type=int, default=200)
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parser.add_argument("--lr", type=float, default=0.1)
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||
parser.add_argument("--seed", type=int, default=None)
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||
parser.add_argument("--export", type=str, default=None,
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help="Export candidate JSON to path (single)")
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parser.add_argument("--batch", type=int, default=None,
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help="Run N random seeds, export best candidates")
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parser.add_argument("--equation-id", type=str,
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default="rrc_eq_entropy_explorer",
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help="Equation ID for the candidate")
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||
parser.add_argument("--output-dir", type=str,
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default=None,
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help="Output directory for candidates")
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||
args = parser.parse_args()
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||
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||
# Default output dir
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||
if args.output_dir is None:
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||
args.output_dir = (
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"/home/allaun/Research Stack/shared-data/data/stack_solidification/candidates"
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||
)
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||
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||
manifolds = {
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||
"torus": Torus(R=2.0, r=1.0),
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||
"sphere": Sphere(radius=2.0),
|
||
"cube": CubeShell(side=3.0),
|
||
}
|
||
manifold = manifolds[args.manifold]
|
||
|
||
if args.batch:
|
||
# Batch mode: run multiple seeds, pick best by final entropy
|
||
print(f"Batch exploration: {args.batch} runs on {manifold}")
|
||
all_candidates = []
|
||
for trial in range(args.batch):
|
||
trial_seed = (args.seed or 0) + trial
|
||
pts, hist = optimize_entropy(
|
||
manifold=manifold,
|
||
n_points=args.n_strands,
|
||
n_steps=args.steps,
|
||
lr=args.lr,
|
||
seed=trial_seed,
|
||
verbose=False,
|
||
)
|
||
final_H = hist[-1]
|
||
cand = export_candidate(
|
||
points=pts,
|
||
manifold=manifold,
|
||
entropy_history=hist,
|
||
equation_id=f"{args.equation_id}_seed{trial_seed}",
|
||
bandwidth=0.3,
|
||
temperature=1.0,
|
||
)
|
||
all_candidates.append((final_H, cand, pts))
|
||
print(f" trial {trial:3d} (seed {trial_seed:3d}): H = {final_H:.6f}")
|
||
|
||
# Sort by entropy descending
|
||
all_candidates.sort(key=lambda x: -x[0])
|
||
|
||
# Export all to batch dir
|
||
batch_dir = os.path.join(args.output_dir, f"batch_{args.manifold}")
|
||
os.makedirs(batch_dir, exist_ok=True)
|
||
|
||
best = []
|
||
for rank, (h, cand, pts) in enumerate(all_candidates):
|
||
fname = f"candidate_{args.manifold}_rank{rank:03d}_seed{args.seed + rank if args.seed else rank}.json"
|
||
path = os.path.join(batch_dir, fname)
|
||
with open(path, "w") as f:
|
||
json.dump(cand, f, indent=2)
|
||
best.append({
|
||
"rank": rank,
|
||
"entropy": round(h, 6),
|
||
"file": fname,
|
||
"sidon_slack": cand["sidon_slack"],
|
||
})
|
||
|
||
# Write manifest
|
||
manifest = {
|
||
"schema": "rrc_candidate_batch_manifest_v1",
|
||
"claim_boundary": "exploration-phase-only;not-certified",
|
||
"manifold": str(manifold),
|
||
"n_trials": args.batch,
|
||
"candidates": best,
|
||
}
|
||
manifest_path = os.path.join(batch_dir, "manifest.json")
|
||
with open(manifest_path, "w") as f:
|
||
json.dump(manifest, f, indent=2)
|
||
|
||
print(f"\nBatch complete. {args.batch} candidates -> {batch_dir}/")
|
||
print(f"Best entropy: H = {best[0]['entropy']}")
|
||
print(f"Worst entropy: H = {best[-1]['entropy']}")
|
||
print(f"Manifest: {manifest_path}")
|
||
|
||
else:
|
||
# Single run
|
||
print(f"Running entropy exploration on {manifold} with {args.n_strands} strands")
|
||
|
||
points, history = optimize_entropy(
|
||
manifold=manifold,
|
||
n_points=args.n_strands,
|
||
n_steps=args.steps,
|
||
lr=args.lr,
|
||
seed=args.seed,
|
||
)
|
||
print(f"\nFinal entropy: H = {history[-1]:.6f}")
|
||
|
||
if args.export:
|
||
candidate = export_candidate(
|
||
points=points,
|
||
manifold=manifold,
|
||
entropy_history=history,
|
||
equation_id=args.equation_id,
|
||
output_path=args.export,
|
||
)
|
||
else:
|
||
os.makedirs(args.output_dir, exist_ok=True)
|
||
candidate = export_candidate(
|
||
points=points,
|
||
manifold=manifold,
|
||
entropy_history=history,
|
||
equation_id=args.equation_id,
|
||
output_path=os.path.join(
|
||
args.output_dir,
|
||
f"candidate_{manifold}_{args.seed or 0}.json",
|
||
)
|
||
)
|
||
|
||
print(f"\nCandidate braid state:")
|
||
print(f" Sidon slack: σ = {candidate['braid_state']['sidon_slack']}")
|
||
slots = [s["slot"] for s in candidate["braid_state"]["strands"]]
|
||
print(f" Slot labels: {slots}")
|
||
admissibility = [
|
||
"✓" if s["bracket"]["admissible"] else "✗"
|
||
for s in candidate["braid_state"]["strands"]
|
||
]
|
||
print(f" Admissible: {''.join(admissibility)}")
|
||
|
||
print(f"\nTo certify candidates:")
|
||
print(f" lake build Semantics.AVMIsa.Emit")
|
||
print(f" python3 4-Infrastructure/shim/emit250_extract.py")
|
||
|
||
|
||
if __name__ == "__main__":
|
||
main()
|