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76 lines
2.8 KiB
Python
76 lines
2.8 KiB
Python
#!/usr/bin/env python3
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"""Numerical audit for the Φ-scaling transfold equations."""
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from __future__ import annotations
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import hashlib
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import json
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import math
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from pathlib import Path
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from typing import Any
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def stable_hash(payload: dict[str, Any]) -> str:
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stable = {k: v for k, v in payload.items() if k != "receipt_hash"}
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encoded = json.dumps(stable, sort_keys=True, separators=(",", ":")).encode()
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return hashlib.sha256(encoded).hexdigest()
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def main() -> None:
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phi = (1.0 + math.sqrt(5.0)) / 2.0
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lambda_phi = phi**2
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fractal_dimension = math.log(2.0) / math.log(phi)
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k_b_ev_per_k = 8.617333262e-5
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temperatures = {
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"room_298K": 298.0,
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"ltee_310K": 310.0,
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}
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barriers_ev = [0.05, 0.1, 0.5, 1.0, 10.0]
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boltzmann = {}
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for label, temp in temperatures.items():
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kT = k_b_ev_per_k * temp
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boltzmann[label] = {
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"kT_eV": kT,
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"suppression_by_barrier_eV": {
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str(barrier): math.exp(-barrier / kT) for barrier in barriers_ev
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},
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}
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receipt: dict[str, Any] = {
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"runner": "phi_scaling_math_audit.py",
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"constants": {
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"phi": phi,
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"lambda_phi_phi_squared": lambda_phi,
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"fractal_dimension_log2_over_logphi": fractal_dimension,
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"phi_to_fractal_dimension": phi**fractal_dimension,
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"phi_squared_to_fractal_dimension": lambda_phi**fractal_dimension,
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"phi_to_6": phi**6,
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"thirty_phi_to_6": 30.0 * phi**6,
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},
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"boltzmann_gate_audit": boltzmann,
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"corrections": [
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"Phi^1.44 is approximately 2 when Phi means the golden ratio.",
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"(Phi^2)^1.44 is approximately 4 when Phi^2 is the hierarchy scale factor.",
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"The previous approximate 3.5 constant mixed notation and is not retained.",
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"Raw exp(-E_bind/kT) with chemical-scale binding energies suppresses too strongly for direct phenotype amplitude.",
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"Use exp(-gamma * DeltaE_eff/kT) as a route barrier or prune gate.",
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"Drake-rule mutation scaling should preserve inverse genome-size direction for per-site mutation rates.",
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"500 generations is near 30 * phi^6 but is not derived as a Nyquist rate.",
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],
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"claim_boundary": (
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"This is a numerical audit of local equations. It does not validate "
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"the biological, physical, compression, or FPGA claims."
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),
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}
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receipt["receipt_hash"] = stable_hash(receipt)
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out = Path(__file__).with_name("phi_scaling_math_audit_receipt.json")
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out.write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n", encoding="utf-8")
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print(json.dumps(receipt["constants"], indent=2, sort_keys=True))
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print(f"receipt: {out}")
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print(f"receipt_hash: {receipt['receipt_hash']}")
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if __name__ == "__main__":
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main()
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