independent_formula_checks.py

1#!/usr/bin/env python3 2"""Independent formula counterexamples for the 2026-09-15 GitHub review. 3 4These are small Python reproductions of inspected formulas, NOT execution of 5any repository's source files, build, deployment, or original test suite. 6Uses Python 3 standard library only; no network, credentials, or host changes. 7Run: python3 independent_formula_checks.py 8""" 9from __future__ import annotations 10import json 11import math 12 13PHI = (1 + math.sqrt(5)) / 2 14DELTA = 0.013618 15 16 17def softsign(x: float) -> float: 18 return x / (1 + abs(x)) 19 20 21def normalizer(values: list[float]) -> float: 22 return 1 / (1 + sum(x * x for x in values) / PHI) 23 24 25def gate_first_tick() -> dict: 26 """Compare zero-state first ticks, not compression or measured throughput.""" 27 phase_dna = DELTA % 1 28 phase_fib = (1 / PHI) % 1 29 threshold = ((phase_dna + phase_fib) / 2) * 1000 30 repo_output = [int(i % 1000 < threshold) for i in range(5000)] 31 plan_flip = int((phase_dna + phase_fib) % 1 > 0.5) 32 plan_output = [plan_flip] * 5000 33 assert sum(repo_output) == 1580 34 assert sum(plan_output) == 5000 35 return { 36 "initial_conditions": "5,000 zero gates, zero phases, zero input", 37 "repository_rule_ones": sum(repo_output), 38 "rebuild_plan_rule_ones": sum(plan_output), 39 "differing_gate_positions": sum(a != b for a, b in zip(repo_output, plan_output)), 40 "interpretation": "Different transition rules; neither is chosen as canonical by this check.", 41 } 42 43 44def consciousness_output() -> float: 45 """Reproduce ConsciousnessEngine.evaluate(), which has no state input.""" 46 previous = 0.5 47 core: list[float] = [] 48 for i in range(174): 49 value = 0.5 + 0.5 * math.sin(2 * math.pi * (i / 174) * PHI) * previous 50 core.append(value) 51 previous = value 52 supplemental = [core[i % 174] * math.cos((i / 200) * math.pi) for i in range(200)] 53 return sum(core + supplemental) / 374 54 55 56def meta_state_order() -> dict: 57 """Compare operation order with explicitly equal, controlled parameters. 58 59 The parameters below are a diagnostic setup, NOT a claim that every C++ 60 deployment uses these values. Formula definitions are taken from inspected 61 C++ build_families/update_meta_state and JS families/MetaState.step. 62 """ 63 cur = [0.1] * 16 64 prev = [0.1] * 16 65 dx, err, utility, stability = 0.3, 0.1, 0.6, 0.8 66 gamma_min = 0.1 67 gamma = gamma_min + (1 - gamma_min) * stability 68 rho = 1 / (1 + PHI) 69 x = 0.1 70 family_outputs = [ 71 x + 0.1 * (dx - x), 72 0.9 * x + 0.1 * utility, 73 x + 0.05 * (softsign(dx) - x), 74 x + 0.2 * softsign(utility - x), 75 max(0, min(1, (x + utility) / (1 + abs(utility)))), 76 x + 0.1 * dx, 77 0.5 * (x + 1 / (1 + math.exp(-dx))), 78 x - 0.05 * err + 0.05 * utility, 79 0.95 * x + 0.05 * dx, 80 x + 0.05 * softsign(dx - x), 81 (1 - rho) * x + rho * dx, 82 x - 0.05 * abs(dx) + 0.05 * utility, 83 x - 0.05 * abs(dx), 84 x + 0.02 * (dx + utility), 85 x + 0.15 * softsign(utility) - 0.05 * err, 86 x + (PHI - 1) * 0.01 * (stability - x), 87 ] 88 blended = [0.5 * raw + 0.5 * (old + (PHI - 1) * (now - old)) 89 for raw, now, old in zip(family_outputs, cur, prev)] 90 gated = [now + gamma * (new - now) for now, new in zip(cur, blended)] 91 cpp_b = normalizer(family_outputs) 92 js_b = normalizer(gated) 93 cpp_next = [v * cpp_b for v in gated] 94 js_next = [v * js_b for v in gated] 95 maximum_difference = max(abs(a - b) for a, b in zip(cpp_next, js_next)) 96 assert maximum_difference > 1e-6 97 return { 98 "controlled_parameters": { 99 "current_and_previous_components": 0.1, "weights": "all 1", 100 "dx_norm": dx, "ed_error": err, "utility": utility, 101 "stability": stability, "gamma_min": gamma_min, "phi_override": None, 102 }, 103 "cpp_normalizer_before_blend_and_gate": cpp_b, 104 "js_normalizer_after_blend_and_gate": js_b, 105 "max_absolute_next_component_difference": maximum_difference, 106 "interpretation": "Different operation orders change outputs even with equal parameters.", 107 } 108 109 110def main() -> None: 111 repeat_a = consciousness_output() 112 repeat_b = consciousness_output() 113 assert repeat_a == repeat_b 114 synchrony = sum(math.cos(2 * math.pi * i / 88) for i in range(88)) / 88 115 assert abs(synchrony) < 1e-14 116 result = { 117 "audit_date": "2026-09-15", 118 "execution_scope": "Independent Python formula reproductions only; NOT original repository test execution.", 119 "source_refs": { 120 "seferim-core": "1f05cd5640edf0a5fe93dc276a12a48db84fc702", 121 "seferim-agi-g16": "25f281b08b2f786f5a235b5abebfc39bf44d1044", 122 "gate_rebuild_plan": "Library Pasted text(1).txt: Gate5000 section, eq80-89 reference", 123 }, 124 "gate5000": gate_first_tick(), 125 "neural_synchrony": { 126 "agent_count": 88, "value_from_fixed_km": synchrony, 127 "interpretation": "The inspected step() does not update km; this statistic stays fixed regardless of evolving x/y/P/c.", 128 }, 129 "consciousness_engine": { 130 "value": repeat_a, "repeat_equal": repeat_a == repeat_b, 131 "interpretation": "Reinitializing the same input-free recurrence produces a constant, not a measurement of external runtime state.", 132 }, 133 "meta_state_normalization_order": meta_state_order(), 134 } 135 print(json.dumps(result, indent=2, ensure_ascii=False)) 136 137 138if __name__ == "__main__": 139 main() 140