"""Reproducible adversarial checks. Run: python code/verify.py These finite tests corroborate the proofs; they are neither formal verification nor a novelty/priority audit. """ from __future__ import annotations import json, math, platform, sys from pathlib import Path from dataclasses import asdict import numpy as np import scipy import sympy as sp from scipy.integrate import quad from floquet import (fixed_period, free_period, monodromy, log_spectral_radius, cell_gain, transfer, solve_eta, defect_integrand) from exact_inverse import (layer_product, moments, recover_exponential_polynomial, peel_first_row) def lifted_angle(psi, w): n = math.floor((psi + math.pi/2)/math.pi) p = psi - n*math.pi return math.atan(w*math.tan(p)) + n*math.pi def phase_segments(us, ts, M): vals, vecs = np.linalg.eig(M) j = int(np.argmax(np.abs(vals))) x = np.real(vecs[:, j]).astype(float) theta = math.atan2(-x[1], x[0]) initial = theta out = [] for u, duration in zip(us, ts): w = math.sqrt(u) psi = math.atan2(-x[1]/w, x[0]) nxt = theta + lifted_angle(psi+w*duration, w) - lifted_angle(psi, w) out.append((theta, nxt, float(u))) x = transfer(float(u), float(duration)) @ x x /= np.linalg.norm(x) theta = nxt n = round((theta-initial)/math.pi) assert abs(theta-initial-n*math.pi) < 2e-8 return out, n def integrate_defect(segments, eta, R): value = 0.0 for left, right, u in segments: points = [] for base in [math.pi/2, -math.atan(eta)]: for j in range(math.floor((left-base)/math.pi)-1, math.ceil((right-base)/math.pi)+2): z = base+j*math.pi if left < z < right: points.append(z) value += quad(lambda th: defect_integrand(th,u,eta,R), left, right, points=sorted(set(points)), epsabs=2e-10, epsrel=2e-10, limit=250)[0] return value def main(): rng = np.random.default_rng(240925) random_count = 0 hyperbolic_count = 0 worst_excess = -math.inf defect_cases = [] for R in [1.1, 1.5, 2.0, 3.0, 5.0]: for S in np.linspace(0.3,9.0,22): optimum, candidates = fixed_period(R, float(S)) for j in range(60): r = int(rng.integers(1,17)) us = (rng.choice([1.,R*R],size=r) if j%2 == 0 else rng.uniform(1.,R*R,size=r)) ts = rng.dirichlet(np.ones(r))*S M = monodromy(us,ts) L = log_spectral_radius(M) random_count += 1 worst_excess = max(worst_excess,L-optimum) assert L <= optimum+1e-9, (R,S,us,ts,L,optimum) if L > 1e-5: hyperbolic_count += 1 if len(defect_cases) < 60: defect_cases.append((R,float(S),us,ts,M,L)) defect_error = 0.0 for R,S,us,ts,M,L in defect_cases: segments,n = phase_segments(us,ts,M) eta = solve_eta(R,S/n) exact = n*cell_gain(R,eta)-L computed = integrate_defect(segments,eta,R) defect_error = max(defect_error,abs(exact-computed)) assert abs(exact-computed) < 1e-7 canonical_count = 0 canonical_error = 0.0 for R in [1.1,1.5,2.,3.,5.]: for S in np.linspace(0.25,6,40): bound,candidates = fixed_period(R,float(S)) for c in candidates: M=monodromy([R*R,1.]*c.winding,[c.high_time,c.low_time]*c.winding) err=abs(log_spectral_radius(M)-c.log_gain) canonical_error=max(canonical_error,err) assert err<1e-9 canonical_count += 1 free = {str(R): asdict(free_period(R)) for R in [1.1,2.,3.,5.,10.]} sharp = [] R=2.; S=3*math.pi/4 for s in [0.02,0.01,0.005,0.0025]: M=monodromy([4.,1.],[math.pi/4+s,math.pi/2-s]) deficit=math.log(2)-log_spectral_radius(M) ratio=deficit/s**2 sharp.append({'s':s,'deficit':deficit,'deficit_over_s_squared':ratio}) assert abs(ratio-1.5)<0.002 # Exact signed-frequency identity for the all-discriminant counterexample. A=[(sp.Rational(4),sp.Rational(1,2)),(sp.Rational(2),sp.Rational(1,2))] B=[(sp.Rational(5,2),sp.Rational(4,5)),(sp.Rational(5),sp.Rational(1,5))] from exact_inverse import add, scaled HA,HB=layer_product(A),layer_product(B) assert scaled(add(HA[0][0],HA[1][1]),sp.Rational(1,2)) == \ scaled(add(HB[0][0],HB[1][1]),sp.Rational(1,2)) assert HA[0] != HB[0] # Includes collisions of signed optical-duration sums. datasets = [ [(sp.Rational(2),sp.Rational(3,7))], A, B, [(sp.Rational(2),sp.Rational(1,5)),(sp.Rational(3),sp.Rational(2,7)), (sp.Rational(5),sp.Rational(3,11))], [(sp.Rational(2),sp.Rational(1,2)),(sp.Rational(3),sp.Rational(1,3)), (sp.Rational(4),sp.Rational(1,4)),(sp.Rational(5),sp.Rational(1,5))] ] inverse_results=[] for layers in datasets: r=len(layers); N=2**r H=layer_product(layers) f=recover_exponential_polynomial(moments(H[0][0],2*N),N) g=recover_exponential_polynomial(moments(H[0][1],2*N),N) assert f == H[0][0] and g == H[0][1] result=peel_first_row(f,g,r) assert result == layers,(layers,result) inverse_results.append({'r':r,'first_row_terms':[len(f),len(g)], 'recovered_layers':[[str(c),str(t)] for c,t in result], 'exact':True}) report={ 'seed':240925,'random_profiles_tested':random_count, 'hyperbolic_random_profiles':hyperbolic_count, 'maximum_random_bound_violation':max(0.,worst_excess), 'canonical_profiles_tested':canonical_count, 'maximum_canonical_gain_error':canonical_error, 'defect_identities_tested':len(defect_cases), 'maximum_defect_identity_error':defect_error, 'free_period_examples':free,'sharpness_examples':sharp, 'exact_inverse_roundtrips':inverse_results, 'exact_discriminant_counterexample_passed':True, 'all_assertions_passed':True, 'python':platform.python_version(),'numpy':np.__version__, 'scipy':scipy.__version__,'sympy':sp.__version__, 'scope':'Finite computational tests; not formal verification or peer review.' } path=Path(__file__).resolve().parents[1]/'results'/'verification.json' path.parent.mkdir(parents=True,exist_ok=True) path.write_text(json.dumps(report,indent=2)+'\n') print(json.dumps(report,indent=2)) if __name__ == '__main__': main()