#!/usr/bin/env python """ emergence_audit — four controls for any claim of the form "X (a geometry, a law, a metric, a symmetry, a world model) EMERGES from a network trained on D". The audit does not know what X is. It asks the user's pipeline to fit data from several GENERATORS under several PRIORS, summarises each output with the user's FEATURE function, and reports four differentials: C1 STATELESS generator — data with the claimed physics removed (a closed-form curve, a shuffled/random process). If feature(stateless) ≈ feature(real), X is a property of the pipeline or of low-order data shape. C2 NON-SOLUTION generator— data that VIOLATE the law claimed to emerge. If it fits as well and the violation is reproduced, the pipeline does not forbid the alternative — it cannot have "found" the law. C3 PRIOR SWAP at fixed fit— among outputs with (near-)equal fit, swap the regulariser. The part of X that moves is the prior's, not the data's. C4 FAMILY DISTANCE + conditioning — distance of the output to the nearest member of the claimed solution family vs to the generator; and the condition number of the parametrisation (function-space MSE hides parameter error when it is large). Plugin interface (a Python module or object with these attributes): generators : dict name -> callable(seed) -> data (must include 'real'; optional 'stateless', 'nonsolution') priors : dict name -> prior spec (opaque; passed to fit) (first entry = the paper's) fit : callable(data, prior, seed) -> (output, fit_quality: float, lower is better) feature : callable(output) -> 1-D np.ndarray (the summary of X) family_distance : callable(output) -> float (optional) generator_distance : callable(output, data) -> float (optional) condition_number : float or callable() -> float (optional) fit_tolerance : float relative tolerance for "equal fit" in C3 (default 0.25) Usage: python emergence_audit.py --plugin path/to/plugin.py --seeds 5 --out audit.json python emergence_audit.py --demo # AdS/DL reproduction (Hashimoto et al. 2018) """ from __future__ import annotations import argparse import importlib.util import json import os import sys import numpy as np def _load_plugin(path): spec = importlib.util.spec_from_file_location("audit_plugin", path) mod = importlib.util.module_from_spec(spec) spec.loader.exec_module(mod) return mod def _stat(xs): xs = np.asarray(xs, float) return float(np.mean(xs)), float(np.std(xs)) def run_audit(plugin, seeds=5, verbose=True): gens = plugin.generators priors = plugin.priors paper_prior = next(iter(priors)) tol = getattr(plugin, "fit_tolerance", 0.25) has_fam = hasattr(plugin, "family_distance") has_gen = hasattr(plugin, "generator_distance") runs = {} # (gen, prior) -> list of dict(fit, feature, fam, gen) for g in gens: for p in priors: if g != "real" and p != paper_prior and g != "nonsolution": continue # stateless only under the paper's prior rows = [] for s in range(seeds): data = gens[g](s) out, fit = plugin.fit(data, priors[p], s) row = dict(fit=float(fit), feature=np.asarray(plugin.feature(out), float)) if has_fam: row["fam"] = float(plugin.family_distance(out)) if has_gen: row["gen"] = float(plugin.generator_distance(out, data)) rows.append(row) runs[(g, p)] = rows if verbose: f = _stat([r["fit"] for r in rows]) extra = "" if has_fam: extra += f" family {_stat([r['fam'] for r in rows])[0]:.3f}" if has_gen: extra += f" generator {_stat([r['gen'] for r in rows])[0]:.3f}" print(f" [{g:11s} | {p:12s}] fit {f[0]:.4g}±{f[1]:.2g}{extra}") def feat(g, p): F = np.array([r["feature"] for r in runs[(g, p)]]) return F.mean(0), F.std(0).mean() + 1e-12 report = {"seeds": seeds, "paper_prior": paper_prior, "controls": {}} base_f, base_sd = feat("real", paper_prior) base_fit = _stat([r["fit"] for r in runs[("real", paper_prior)]])[0] # C1 stateless if "stateless" in gens: sf, _ = feat("stateless", paper_prior) d = float(np.linalg.norm(sf - base_f) / np.sqrt(len(base_f))) z = d / base_sd report["controls"]["C1_stateless"] = dict(feature_rms_gap=d, gap_over_seed_sd=z, verdict=("SAME X from stateless data — X is not evidence of the physics" if z < 2 else "stateless data give a different X (differential exists)")) # C2 non-solution if "nonsolution" in gens: ns_fit = _stat([r["fit"] for r in runs[("nonsolution", paper_prior)]])[0] c2 = dict(fit_ratio_nonsolution_over_real=float(ns_fit / base_fit) if base_fit > 0 else float("nan")) if has_fam: fr = _stat([r["fam"] for r in runs[("real", paper_prior)]])[0] fn = _stat([r["fam"] for r in runs[("nonsolution", paper_prior)]])[0] c2.update(family_distance_real=fr, family_distance_nonsolution=fn, violation_reproduced=bool(fn > 2 * fr)) fits_as_well = c2["fit_ratio_nonsolution_over_real"] <= 1 + tol c2["verdict"] = ("non-solution data fit as well" + (" and the violation is reproduced" if c2.get("violation_reproduced") else "") + " — the pipeline does not forbid the alternative") if fits_as_well else "non-solution data fit worse (pipeline discriminates)" report["controls"]["C2_nonsolution"] = c2 # C3 prior swap at fixed fit c3 = {} for p in priors: if p == paper_prior: continue pf, _ = feat("real", p) pfit = _stat([r["fit"] for r in runs[("real", p)]])[0] equal = abs(pfit - base_fit) <= tol * base_fit d = float(np.linalg.norm(pf - base_f) / np.sqrt(len(base_f))) entry = dict(fit=pfit, equal_fit=bool(equal), feature_rms_shift=d, shift_over_seed_sd=d / base_sd) if has_fam: fam_p = _stat([r["fam"] for r in runs[("real", p)]])[0] fam_0 = _stat([r["fam"] for r in runs[("real", paper_prior)]])[0] entry["family_distance"] = fam_p entry["family_distance_ratio_vs_paper_prior"] = float(fam_p / fam_0) if fam_0 > 0 else float("nan") if has_gen: entry["generator_distance"] = _stat([r["gen"] for r in runs[("real", p)]])[0] entry["generator_distance_paper_prior"] = _stat([r["gen"] for r in runs[("real", paper_prior)]])[0] if "nonsolution" in gens and ("nonsolution", p) in runs and has_fam: entry["nonsolution_family_distance_under_this_prior"] = _stat([r["fam"] for r in runs[("nonsolution", p)]])[0] c3[p] = entry if c3: moved = [p for p, e in c3.items() if e["equal_fit"] and (e["shift_over_seed_sd"] > 2 or not (0.5 <= e.get("family_distance_ratio_vs_paper_prior", 1.0) <= 2.0))] report["controls"]["C3_prior_swap"] = dict(priors=c3, verdict=("X moves under a prior swap at equal fit — the moved part is the prior's, not the data's: " + ", ".join(moved)) if moved else "X is stable under prior swap at equal fit") # C4 family + conditioning c4 = {} if has_fam: c4["family_distance_real"] = _stat([r["fam"] for r in runs[("real", paper_prior)]]) if has_gen: c4["generator_distance_real"] = _stat([r["gen"] for r in runs[("real", paper_prior)]]) cn = getattr(plugin, "condition_number", None) if cn is not None: c4["condition_number"] = float(cn() if callable(cn) else cn) if c4: notes = [] if "family_distance_real" in c4 and "generator_distance_real" in c4 and c4["generator_distance_real"][0] > 2 * c4["family_distance_real"][0]: notes.append("output is closer to ANOTHER member of the family than to its generator") if c4.get("condition_number", 0) > 30: notes.append(f"ill-conditioned parametrisation (cond {c4['condition_number']:.0f}): function-space fit hides parameter error") c4["verdict"] = "; ".join(notes) if notes else "no family/conditioning flags" report["controls"]["C4_family_conditioning"] = c4 # overall flags = [k for k, v in report["controls"].items() if any(w in v["verdict"] for w in ("not evidence", "does not forbid", "prior's", "ANOTHER member", "ill-conditioned"))] report["overall"] = ("EMERGENCE CLAIM NOT SUPPORTED by these controls: " + ", ".join(flags)) if flags else \ "no control flagged — the differential the claim needs is present" return report, runs def print_report(report): print("\n=== emergence audit ===") for k, v in report["controls"].items(): print(f"{k:26s} {v['verdict']}") print("-" * 26) print(report["overall"]) def main(argv=None): ap = argparse.ArgumentParser(description="Four controls for 'X emerges from a network' claims.") ap.add_argument("--plugin", help="path to a plugin .py exposing generators/priors/fit/feature[/family_distance/...]") ap.add_argument("--seeds", type=int, default=5) ap.add_argument("--out", help="write JSON report here") ap.add_argument("--demo", action="store_true", help="run the AdS/DL (Hashimoto et al. 2018) plugin, 3 seeds, full recipe (~4 min)") a = ap.parse_args(argv) if a.demo: here = os.path.dirname(os.path.abspath(__file__)) plugin = _load_plugin(os.path.join(here, "plugins", "adsdl_plugin.py")) seeds = min(a.seeds, 3) # full recipe (60 epochs); reduced epochs flip verdicts elif a.plugin: plugin = _load_plugin(a.plugin); seeds = a.seeds else: ap.error("give --plugin or --demo") report, _ = run_audit(plugin, seeds=seeds) print_report(report) if a.out: json.dump(report, open(a.out, "w"), indent=1, default=float) print(f"\nwrote {a.out}") return 0 if __name__ == "__main__": sys.exit(main())