#!/usr/bin/env python3 """ CHIMERA / HAR-QEGT machine witness ================================== 1. Reconstruct canonical E47 FROM spin-2 SU(2) generators. 2. Verify Casimir spectrum, projector algebra, contraction, 47/125 invariant. 3. Implement the QEGT Gibbs/softmax strategy law. 4. Typed synthetic HAR->operator demonstration (NOT fitted biology). Evidence classes kept separate: - E47: exact finite-dimensional / machine reconstructed - Gibbs strategy law: mathematical statistical operator - HAR bridge: hypothesis interface awaiting fitted biological operators Requires: numpy """ from __future__ import annotations import json import platform import sys import numpy as np SEED = 470125 TOL = 1e-9 def spin2_generators(): """Hermitian spin-2 Jx, Jy, Jz in the |m=2,1,0,-1,-2> basis.""" j = 2 m = np.arange(j, -j - 1, -1, dtype=float) d = 2 * j + 1 Jp = np.zeros((d, d), dtype=complex) for col, mm in enumerate(m): mp = mm + 1 if mp <= j: rows = np.where(np.isclose(m, mp))[0] if len(rows): row = int(rows[0]) Jp[row, col] = np.sqrt(j * (j + 1) - mm * (mm + 1)) Jm = Jp.conj().T Jx = (Jp + Jm) / 2 Jy = (Jp - Jm) / (2j) Jz = np.diag(m) return Jx, Jy, Jz def kron3(a, b, c): return np.kron(np.kron(a, b), c) def build_e47(): Jx, Jy, Jz = spin2_generators() I5 = np.eye(5) Jtot = [ kron3(J, I5, I5) + kron3(I5, J, I5) + kron3(I5, I5, J) for J in (Jx, Jy, Jz) ] C = sum(J @ J for J in Jtot) I = np.eye(125, dtype=complex) K = (C - 6 * I) @ (C - 30 * I) G = K.conj().T @ K evals_C, evecs_C = np.linalg.eigh(C) mask = np.isclose(evals_C, 6, atol=1e-8) | np.isclose(evals_C, 30, atol=1e-8) P = evecs_C[:, mask] @ evecs_C[:, mask].conj().T Ppoly = C.copy() for a in (2, 12, 20, 31, 42): Ppoly = Ppoly @ (C - a * I) Ppoly /= 1814400.0 eps = 1.0 / 99144.0 R = I - eps * G return C, K, G, P, Ppoly, R, evals_C def cluster_spectrum(vals, decimals=8): u, n = np.unique(np.round(np.real(vals), decimals), return_counts=True) return {str(float(a)): int(b) for a, b in zip(u, n)} def qegt_gibbs(costs, beta=1.0): costs = np.asarray(costs, dtype=float) z = -beta * costs z -= np.max(z) w = np.exp(z) return w / w.sum() def synthetic_har_operator_demo(): """Typed HAR-distribution DEMO. Mixed signs model compensatory substitution. Values are arbitrary synthetic coefficients — not biological effect sizes.""" H0 = np.diag([0.9, 0.6, 0.8, 1.1, 0.7]).astype(float) B = [ np.diag([-0.10, +0.04, 0.00, 0.00, +0.02]), np.diag([+0.06, -0.08, +0.03, 0.00, 0.00]), np.diag([0.00, +0.03, -0.07, +0.05, 0.00]), np.diag([+0.02, 0.00, +0.04, -0.06, +0.01]), ] h = np.array([1.0, 1.0, 1.0, 1.0]) H = H0 + sum(x * b for x, b in zip(h, B)) costs = np.diag(H) p = qegt_gibbs(costs, beta=2.0) return { "status": "SYNTHETIC_BRIDGE_DEMO_ONLY", "baseline_costs": np.diag(H0).tolist(), "perturbed_costs": costs.tolist(), "strategy_probabilities": p.tolist(), "normalization_residual": float(abs(p.sum() - 1.0)), "note": ( "Replace B_i and h_i with estimates from HAR sequence swaps, " "MPRA, single-cell multiome, and 3D-contact data." ), } def validate(): C, K, G, P, Ppoly, R, evals_C = build_e47() evals_G = np.linalg.eigvalsh(G) nonzero_G = evals_G[evals_G > 1e-6] eps = 1.0 / 99144.0 rho_perp = max(abs(1.0 - eps * nonzero_G)) R250 = np.linalg.matrix_power(R, 250) out = { "run": "CHIMERA-QEGT-HAR-20260915", "status": "PASS", "seed": SEED, "evidence_classes": { "E47": "E0 exact identities + E1 deterministic NumPy reconstruction", "QEGT_Gibbs": "mathematical structural formalism", "HAR_bridge": "hypothesis / synthetic demonstrator only", }, "e47": { "dimension": 125, "casimir_spectrum_multiplicity": cluster_spectrum(evals_C), "kernel_dimension": int(round(np.real(np.trace(P)))), "transient_dimension": 125 - int(round(np.real(np.trace(P)))), "omega_c": int(round(np.real(np.trace(P)))) / 125.0, "projector_rank": int(np.linalg.matrix_rank(P, tol=1e-8)), "projector_idempotence_fro": float(np.linalg.norm(P @ P - P, "fro")), "projector_hermiticity_fro": float(np.linalg.norm(P - P.conj().T, "fro")), "K_projector_fro": float(np.linalg.norm(K @ P, "fro")), "poly_vs_spectral_projector_fro": float(np.linalg.norm(Ppoly - P, "fro")), "nonzero_G_spectrum": sorted(set(np.round(nonzero_G, 6).tolist())), "epsilon_star": eps, "rho_perp_numeric": float(rho_perp), "rho_perp_exact_target": 15 / 17, "contraction_250_operator_norm": float(np.linalg.norm(R250 - P, 2)), }, "qegt_softmax_check": { "costs": [0.2, 0.8, 1.3, -0.1], "beta": 1.7, "probabilities": qegt_gibbs([0.2, 0.8, 1.3, -0.1], beta=1.7).tolist(), }, "har_demo": synthetic_har_operator_demo(), "boundary": ( "No biological HAR effect size, cognition threshold, or physical " "quantum implementation is inferred by this script. The 47/125 " "quantity is the exact E47 invariant, not a fitted biological constant." ), "environment": { "python": sys.version, "platform": platform.platform(), "numpy": np.__version__, }, } checks = [ out["e47"]["kernel_dimension"] == 47, abs(out["e47"]["omega_c"] - 47 / 125) < 1e-15, out["e47"]["projector_idempotence_fro"] < 1e-10, out["e47"]["K_projector_fro"] < 1e-9, abs(out["e47"]["rho_perp_numeric"] - 15 / 17) < 1e-12, out["e47"]["contraction_250_operator_norm"] < 1e-10, out["har_demo"]["normalization_residual"] < 1e-15, ] out["status"] = "PASS" if all(checks) else "FAIL" return out if __name__ == "__main__": print(json.dumps(validate(), indent=2))