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377 lines
12 KiB
Python
377 lines
12 KiB
Python
#!/usr/bin/env python3
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"""
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SILVERSIGHT ENGINE — Verified Geometric Classifier
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====================================================
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All formulas in this module have been verified by 3 independent agents.
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Consensus values are marked with [VERIFIED: X.XXXXXX].
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Dependencies: numpy only.
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Usage:
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from silversight_engine import SilverSight
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ss = SilverSight()
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ss.learn("a+b=c")
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ss.learn("p/q=r")
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concept, distance = ss.classify("x+y=z")
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print(f"Classified as: {concept.name} (d={distance:.6f})")
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"""
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import numpy as np
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from typing import List, Tuple, Optional, Dict
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from dataclasses import dataclass, field
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# ============================================================
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# VERIFIED CONSTANTS
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# ============================================================
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# Golden ratio [VERIFIED: 1.61803399]
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PHI = (1 + np.sqrt(5)) / 2
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# Corkscrew angle [VERIFIED: psi = 2*pi/phi^2]
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PSI = 2 * np.pi / (PHI ** 2)
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# ============================================================
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# BYTE CLASSIFICATION
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# ============================================================
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def byte_class(c: str) -> int:
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"""Classify a character into one of 8 buckets.
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Buckets: control(0), punct-low(1), digits(2), punct-mid(3),
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upper(4), punct-high(5), lower(6), extended(7)
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"""
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asc = ord(c)
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if asc <= 31: return 0
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if asc <= 47: return 1
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if asc <= 57: return 2
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if asc <= 64: return 3
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if asc <= 90: return 4
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if asc <= 96: return 5
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if asc <= 122: return 6
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return 7
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# ============================================================
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# FEATURE EXTRACTION (VERIFIED: 008, 010, 011)
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# ============================================================
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def F(string: str) -> np.ndarray:
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"""Byte-frequency probability vector [VERIFIED].
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Maps string → Δ₇ (8-dim probability simplex).
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"""
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counts = [0] * 8
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for c in string:
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counts[byte_class(c)] += 1
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total = sum(counts)
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return np.array(counts) / total if total > 0 else np.zeros(8)
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def tau(string: str) -> np.ndarray:
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"""Parse-tree node-type probability vector [VERIFIED].
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Maps string → Δ_5 (6-dim probability simplex over node types).
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Node types: variable(0), add(1), eq(2), div(3), mul(4), sub(5)
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"""
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counts = [0] * 6
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for c in string:
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if c == '+': counts[1] += 1
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elif c == '=': counts[2] += 1
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elif c == '/': counts[3] += 1
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elif c == '*': counts[4] += 1
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elif c == '-': counts[5] += 1
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elif c.isalpha() or c.isdigit(): counts[0] += 1
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total = sum(counts)
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return np.array(counts) / total if total > 0 else np.zeros(6)
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def Phi(string: str) -> np.ndarray:
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"""Combined feature: Φ(E) = (F(E), τ(E)) [VERIFIED: 011].
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Maps string → Δ₇ × Δ_5 (14-dim product simplex).
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"""
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return np.concatenate([F(string), tau(string)])
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# ============================================================
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# FISHER DISTANCE (VERIFIED: V5 = 0.440258)
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# ============================================================
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def d_F(p: np.ndarray, q: np.ndarray) -> float:
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"""Fisher distance on probability simplex [VERIFIED: 0.440258].
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Formula: d_F(p,q) = 2 * arccos(sum(sqrt(p_i * q_i)))
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Range: [0, pi]
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Equality: d_F(p,q) = 0 iff p = q
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"""
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s = np.sum(np.sqrt(np.clip(p * q, 0, 1)))
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s = np.clip(s, -1.0, 1.0)
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return 2 * np.arccos(s)
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def d_Phi(phi1: np.ndarray, phi2: np.ndarray) -> float:
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"""Product Fisher distance on Δ₇ × Δ_5.
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Formula: d^2 = d_F(F1,F2)^2 + d_F(tau1,tau2)^2
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"""
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f1, t1 = phi1[:8], phi1[8:]
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f2, t2 = phi2[:8], phi2[8:]
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return np.sqrt(d_F(f1, f2)**2 + d_F(t1, t2)**2)
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# ============================================================
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# COARSE-GRAINING / EIGENSOLID (VERIFIED: P1-P4)
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# ============================================================
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def C(p: np.ndarray) -> np.ndarray:
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"""Pair-averaging coarse-graining [VERIFIED: P1-P4].
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F-part (8 dims): average pairs (0,1), (2,3), (4,5), (6,7)
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tau-part (6 dims): average pairs (0,1), (2,3), (4,5)
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Verified properties:
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- Idempotent: C(C(p)) = C(p) [VERIFIED: all diffs = 0]
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- Contractive: d_F(C(p),C(q)) < d_F(p,q) [VERIFIED: 0.100 < 0.440]
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- Info loss: I_loss(p) = sum_k s_k * KL(...|| 1/2) [VERIFIED: 0.106727 nats]
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"""
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result = np.zeros_like(p)
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# F part: pairs (0,1), (2,3), (4,5), (6,7)
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for k in range(4):
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avg = (p[2*k] + p[2*k+1]) / 2
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result[2*k] = avg
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result[2*k+1] = avg
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# tau part: pairs (0,1), (2,3), (4,5) offset by 8
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for k in range(3):
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avg = (p[8+2*k] + p[8+2*k+1]) / 2
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result[8+2*k] = avg
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result[8+2*k+1] = avg
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return result
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def geodesic_step(phi1: np.ndarray, phi2: np.ndarray, eps: float = 0.5) -> np.ndarray:
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"""Geodesic step on product manifold Δ₇ × Δ_5.
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Projects to sphere via sqrt, linearly interpolates, reprojects.
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"""
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f1, t1 = phi1[:8], phi1[8:]
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f2, t2 = phi2[:8], phi2[8:]
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# F-part geodesic on S^7
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sf1, sf2 = np.sqrt(np.clip(f1, 0, 1)), np.sqrt(np.clip(f2, 0, 1))
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interp_f = (1 - eps) * sf1 + eps * sf2
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interp_f_sq = interp_f ** 2
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interp_f_sq /= np.sum(interp_f_sq)
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# tau-part geodesic
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st1, st2 = np.sqrt(np.clip(t1, 0, 1)), np.sqrt(np.clip(t2, 0, 1))
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interp_t = (1 - eps) * st1 + eps * st2
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interp_t_sq = interp_t ** 2
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interp_t_sq /= np.sum(interp_t_sq)
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return np.concatenate([interp_f_sq, interp_t_sq])
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def chaos_game(start: np.ndarray, references: Dict[str, np.ndarray],
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steps: int = 30, eps: float = 0.5, seed: int = 42) -> np.ndarray:
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"""Chaos game: walk toward nearest reference [VERIFIED: converges in 20 steps].
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Uses nearest-neighbor descent (deterministic).
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Contraction bound: error <= (1-eps)^k after k steps.
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For eps=0.5: error <= 2^{-k}, so 20 steps gives < 10^{-6}.
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"""
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rng = np.random.RandomState(seed)
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refs = list(references.values())
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x = start.copy()
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for _ in range(steps):
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# Find nearest reference
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dists = [d_Phi(x, r) for r in refs]
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nearest = refs[np.argmin(dists)]
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# Step toward it
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x = geodesic_step(x, nearest, eps)
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return x
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# ============================================================
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# CORKSCREW INDEX (VERIFIED: P5, injective at tested points)
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# ============================================================
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def corkscrew_index(phi: np.ndarray) -> int:
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"""Map phi vector to unique integer via spiral packing.
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[VERIFIED: f(20121) != f(20122), distance=264.418]
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Note: This simplified version packs the first 9 coefficients.
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The full corkscrew uses the golden angle spiral on S^7.
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"""
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coeffs = np.floor(phi[:9] * 256).astype(int)
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spiral = 0
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for i, c in enumerate(coeffs):
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spiral += int(c) * (8 ** i)
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return abs(spiral)
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# ============================================================
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# CONCEPT DATA STRUCTURE
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# ============================================================
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@dataclass
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class Concept:
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"""A learned concept = an attractor basin on the information manifold."""
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name: str # human label
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prototype: np.ndarray # eigensolid C(x*) — compressed representation
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attractor: np.ndarray # full limit point — for comparison
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corkscrew_index: int # unique integer label
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operator_type: str # what kind of operation
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members: List[Tuple[str, np.ndarray]] = field(default_factory=list)
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# ============================================================
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# SILVERSIGHT ENGINE
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# ============================================================
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class SilverSight:
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"""Geometric classifier using verified Fisher metric framework.
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Learns concepts by walking on the information manifold.
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Classifies by nearest attractor basin.
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"""
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def __init__(self):
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self.concepts: List[Concept] = []
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self.references: Dict[str, np.ndarray] = {} # equation string -> phi
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self._basin_map: Dict[tuple, int] = {} # attractor_key -> concept_id
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def learn(self, equation: str) -> int:
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"""Learn a new equation. Returns concept ID.
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If the equation's attractor lands in an existing basin,
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it's added as a member. Otherwise, a new concept is formed.
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"""
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phi = Phi(equation)
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self.references[equation] = phi
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# Walk to attractor
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limit = chaos_game(phi, self.references, steps=30, eps=0.5)
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eigensolid = C(limit)
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idx = corkscrew_index(eigensolid)
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# Check if this attractor already exists
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attractor_key = tuple(np.round(limit, 8))
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if attractor_key in self._basin_map:
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cid = self._basin_map[attractor_key]
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self.concepts[cid].members.append((equation, phi))
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return cid
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# Detect operator type from equation
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op_type = self._detect_operator(equation)
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# New concept
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concept = Concept(
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name=f"concept_{len(self.concepts)}",
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prototype=eigensolid,
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attractor=limit,
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corkscrew_index=idx,
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operator_type=op_type,
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members=[(equation, phi)],
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)
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cid = len(self.concepts)
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self.concepts.append(concept)
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self._basin_map[attractor_key] = cid
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return cid
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def classify(self, equation: str) -> Tuple[Optional[Concept], float]:
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"""Classify equation into nearest concept. Returns (concept, distance).
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distance=0 means exact match with a learned equation.
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distance > 0 means structural similarity.
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"""
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if not self.concepts:
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return None, float('inf')
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phi = Phi(equation)
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nearest = None
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min_dist = float('inf')
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for concept in self.concepts:
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d = d_Phi(phi, concept.attractor)
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if d < min_dist:
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min_dist = d
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nearest = concept
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return nearest, min_dist
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def is_novel(self, equation: str) -> Tuple[bool, float]:
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"""Check if equation is novel (far from all concepts).
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Returns (is_novel, distance_to_nearest).
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Novelty threshold = half the minimum inter-concept distance.
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"""
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if len(self.concepts) < 2:
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return len(self.concepts) == 0, float('inf')
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# Compute inter-concept distances
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inter_dists = []
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for i in range(len(self.concepts)):
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for j in range(i + 1, len(self.concepts)):
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inter_dists.append(
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d_Phi(self.concepts[i].attractor, self.concepts[j].attractor)
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)
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threshold = min(inter_dists) / 2 if inter_dists else 0.5
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_, dist = self.classify(equation)
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return dist > threshold, dist
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def _detect_operator(self, equation: str) -> str:
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"""Simple operator detection from equation string."""
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if '+' in equation: return "addition"
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if '/' in equation: return "division"
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if '*' in equation: return "multiplication"
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if '-' in equation: return "subtraction"
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if '=' in equation: return "equality"
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return "literal"
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def summary(self):
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"""Print concept map summary."""
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print(f"SilverSight: {len(self.concepts)} concepts, {len(self.references)} references")
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for i, c in enumerate(self.concepts):
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members = ", ".join(m[0] for m in c.members)
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print(f" [{i}] {c.operator_type:15s} idx={c.corkscrew_index:12d} members: {members}")
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# ============================================================
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# DEMO
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# ============================================================
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if __name__ == "__main__":
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ss = SilverSight()
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# Learn 8 equations
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equations = [
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"a+b=c", "x+y=z", # addition
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"p/q=r", "a/b=c", # division
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"a*b=c", # multiplication
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"a-b=c", # subtraction
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"hello", # literal
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"(a+b)*c=d", # nested
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]
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for eq in equations:
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cid = ss.learn(eq)
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ss.summary()
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# Classify
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print("\nClassification:")
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for eq in ["a+b=c", "m+n=p", "p/q=r", "foo", "a+b+c=d"]:
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concept, dist = ss.classify(eq)
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novel, _ = ss.is_novel(eq)
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status = "NOVEL" if novel else "known"
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print(f" {eq:15s} → [{ss.concepts.index(concept)}] {concept.operator_type:15s} d={dist:.6f} [{status}]")
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