"""v992 -- PRED.JOINTLIKELIHOOD.01 [O update: v1 executed [N]; promotion conditions typed; contract stays Open]. THE POINT (promote round 2026-08-28). Re-derives the executed joint likelihood of jointlikelihood_execution_probe WITHOUT importing experiments/ or the scorecard at suite runtime. The nine (meas, sigma) triplets are FROZEN constants matching the probe's pull-matched 2026-08-28 scorecard selection (NOT the first-listed NuFIT/Planck number when the row's pull_sigma points at a sharper leg): s12 0.3036 +- 0.0064 JUNO 207-day (scorecard pull 0.49) s13 0.02195 +- 0.00058 NuFIT 6.0 s23 0.470 +- 0.017 NuFIT 6.0 ns 0.9679 +- 0.0033 CMB-SPA (scorecard pull -2.06) cinf 0.970 +- 0.233 Planck 2018 A_s+n_s (cov unmodelled) ob 0.0489 +- 0.0014 BBN D/H beta 0.215 +- 0.074 ACT DR6 cab 0.22431 +- 0.00085 PDG 2024 |V_us| dm2 7.49e-5 / 2.513e-3 NuFIT 6.0 (sigma propagated) Compiler formulas (v1 decoder, phi0 and c3 from tfpt_constants): s12 = 1/3 - phi0/2; s13 = phi0 e^{-5/6}; s23 = 1/2; ns = 1 - 2/N_star (N_star = 51.4 [C] reheating input); C_inf = 1; Omega_b = phi0 (4 pi - 1)/(4 pi); beta_deg = phi0/(4 pi) * 180/pi; cab = sqrt(phi0 (1-phi0)); dm2 = |J(s12, s13, s23, delta = 240 deg)|. Expected headline (probe): chi2 = 11.80 / dof 9 (p = 0.225), nu_eff = rank(J_atom) = 1, TFPT at 0th percentile of 200 scrambled decoders, LOO stable. Holdouts declared not consumed: JUNO Delta m^2, DESI Sigma m_nu, DUNE delta_CP, LiteBIRD r. HONEST SCOPE (firewall): v1 statistics construction; Sigma_exp diagonal (NuFIT / Planck covariances UNMODELLED, flagged); Sigma_bridge = Sigma_th = 0; atoms treated exact. Promotion to closure requires off-diagonal Sigma, a formula-grammar census, and genuine future holdouts. Contract stays [O]. No marker move. Python-only / Wolfram mirror deferred. Provenance: experiments/tfpt-discovery/jointlikelihood_execution_probe.py (ALL PASS, 55/55; not imported). """ import math import numpy as np from scipy.stats import chi2 as chi2_dist from tfpt_constants import check, summary, reset, c3 as C3_MP, phi0 as PHI0_MP NULL_SEED = 20260828 N_NULL = 200 LINK_SCRAMBLE = (1.0 / 3.0, 3.0) N_STAR = 51.4 # Frozen (meas, sigma) -- probe pull-matched scorecard v1 selection. MEAS = { "s12": (0.3036, 0.0064), "s13": (0.02195, 0.00058), "s23": (0.470, 0.017), "ns": (0.9679, 0.0033), "cinf": (0.970, 0.233), "ob": (0.0489, 0.0014), "beta": (0.215, 0.074), "cab": (0.22431, 0.00085), } NUFIT_DM21, NUFIT_DM21_S = 7.49e-5, 0.19e-5 NUFIT_DM31, NUFIT_DM31_S = 2.513e-3, 0.021e-3 FID_ORDER = ("s12", "s13", "s23", "ns", "cinf", "ob", "beta", "cab", "dm2") FID_BUNDLE = { "s12": "flavor", "s13": "flavor", "s23": "flavor", "ns": "inflation", "cinf": "inflation", "ob": "seed", "beta": "seed", "cab": "seed", "dm2": "splitting", } HOLDOUTS = ( "JUNO Delta m^2 ratio", "DESI Sigma m_nu", "DUNE delta_CP", "LiteBIRD r", ) def tfpt_links(): return { "tbm": 1.0 / 3.0, "seam": 0.5, "t13_exp": 5.0 / 6.0, "s23": 0.5, "ob_slope": (4.0 * math.pi - 1.0) / (4.0 * math.pi), "beta_div": 4.0 * math.pi, "cab_scale": 1.0, "ns_coef": 2.0, "cinf_target": 1.0, "delta_deg": 240.0, } def jarlskog(s12, s13, s23, delta_deg): s12 = min(max(s12, 1e-12), 1.0 - 1e-12) s13 = min(max(s13, 1e-12), 1.0 - 1e-12) s23 = min(max(s23, 1e-12), 1.0 - 1e-12) s_12, c_12 = math.sqrt(s12), math.sqrt(1.0 - s12) s_13, c_13 = math.sqrt(s13), math.sqrt(1.0 - s13) s_23, c_23 = math.sqrt(s23), math.sqrt(1.0 - s23) return (s_12 * c_12 * s_23 * c_23 * s_13 * c_13 ** 2 * math.sin(math.radians(delta_deg))) def predict(phi0, c3, n_star, links): _ = c3 s12 = links["tbm"] - links["seam"] * phi0 s13 = phi0 * math.exp(-links["t13_exp"]) s23 = links["s23"] ob = phi0 * links["ob_slope"] beta = (phi0 / links["beta_div"]) * (180.0 / math.pi) cab = math.sqrt(max(phi0 * (1.0 - phi0) * links["cab_scale"], 0.0)) ns = 1.0 - links["ns_coef"] / n_star cinf = links["cinf_target"] jabs = abs(jarlskog(s12, s13, s23, links["delta_deg"])) return { "s12": s12, "s13": s13, "s23": s23, "ns": ns, "cinf": cinf, "ob": ob, "beta": beta, "cab": cab, "dm2": jabs, } def vec_from_pred(p): return np.array([p[k] for k in FID_ORDER], dtype=float) def analytic_jacobian_phi0(phi0, links): s12 = links["tbm"] - links["seam"] * phi0 s13 = phi0 * math.exp(-links["t13_exp"]) s23 = links["s23"] d_s12 = -links["seam"] d_s13 = math.exp(-links["t13_exp"]) lam = math.sqrt(phi0 * (1.0 - phi0) * links["cab_scale"]) d_cab = links["cab_scale"] * (1.0 - 2.0 * phi0) / (2.0 * lam) j = jarlskog(s12, s13, s23, links["delta_deg"]) dlog_s12 = (1.0 - 2.0 * s12) / (2.0 * s12 * (1.0 - s12)) dlog_s13 = 0.5 / s13 - 1.0 / (1.0 - s13) d_jabs = abs(j) * (dlog_s12 * d_s12 + dlog_s13 * d_s13) out = { "s12": d_s12, "s13": d_s13, "s23": 0.0, "ns": 0.0, "cinf": 0.0, "ob": links["ob_slope"], "beta": (180.0 / math.pi) / links["beta_div"], "cab": d_cab, "dm2": d_jabs, } return np.array([out[k] for k in FID_ORDER], dtype=float) def chi2_vec(mu, y, sig): return float(np.sum(((mu - y) / sig) ** 2)) def matrix_rank(A, rel=1e-8): s = np.linalg.svd(A, compute_uv=False) return int(np.sum(s > rel * s[0])) def run(): reset() print("v992 PRED.JOINTLIKELIHOOD.01: v1 joint likelihood executed " "(frozen triplets; no experiments/ import)") phi0 = float(PHI0_MP) c3 = float(C3_MP) links = tfpt_links() pred = predict(phi0, c3, N_STAR, links) check("phi0 ~ 0.05317 [E]: compiler output treated exact " "(phi0=%.8f)" % phi0, abs(phi0 - 0.05317) < 5e-5) check("C_inf identity [E]: mu = 1 exactly at the TFPT point", pred["cinf"] == 1.0) check("s12 formula [E]: 1/3 - phi0/2 matches 0.306747", abs(pred["s12"] - 0.306747) < 5e-6) check("s13 formula [E]: phi0 e^{-5/6} matches 0.0231", abs(pred["s13"] - 0.0231) < 5e-5) check("s23 texture [E]: exactly 1/2", abs(pred["s23"] - 0.5) < 1e-15) check("n_s [N]: 1-2/N_star matches 0.9611", abs(pred["ns"] - 0.9611) < 5e-5) check("Omega_b [E]: phi0 (1-1/4pi) matches 0.04894", abs(pred["ob"] - 0.04894) < 5e-5) check("Cabibbo [E]: sqrt(phi0(1-phi0)) matches 0.224376", abs(pred["cab"] - 0.224376) < 5e-6) r_meas = NUFIT_DM21 / NUFIT_DM31 r_sig = r_meas * math.sqrt((NUFIT_DM21_S / NUFIT_DM21) ** 2 + (NUFIT_DM31_S / NUFIT_DM31) ** 2) y = np.array([MEAS[k][0] if k != "dm2" else r_meas for k in FID_ORDER], dtype=float) sig = np.array([MEAS[k][1] if k != "dm2" else r_sig for k in FID_ORDER], dtype=float) mu = vec_from_pred(pred) bundles = [FID_BUNDLE[k] for k in FID_ORDER] n_obs = len(FID_ORDER) print(" BUNDLE TABLE") for k, m, s, yy in zip(FID_ORDER, mu, sig, y): print(" %-6s pred=%.6g meas=%.6g sig=%.4g pull=%+.2f" % (k, m, yy, s, (m - yy) / s)) J_phi = analytic_jacobian_phi0(phi0, links) eps = 1e-6 mu_p = vec_from_pred(predict(phi0 * (1 + eps), c3, N_STAR, links)) mu_m = vec_from_pred(predict(phi0 * (1 - eps), c3, N_STAR, links)) J_phi_num = (mu_p - mu_m) / (2.0 * eps * phi0) mu_cp = vec_from_pred(predict(phi0, c3 * (1 + eps), N_STAR, links)) mu_cm = vec_from_pred(predict(phi0, c3 * (1 - eps), N_STAR, links)) J_c3 = (mu_cp - mu_cm) / (2.0 * eps * c3) J = np.column_stack([J_phi, J_c3]) check("analytic d/dphi0 matches numeric [N]", np.allclose(J_phi, J_phi_num, rtol=1e-4, atol=1e-8)) check("c3 column vanishes [E]: v1 observables depend on c3 only " "through phi0 (C_inf is the identity)", np.max(np.abs(J_c3)) < 1e-10) check("d s12 / d phi0 = -1/2 [E]", abs(J_phi[FID_ORDER.index("s12")] + 0.5) < 1e-12) check("d s13 / d phi0 = e^{-5/6} [E]", abs(J_phi[FID_ORDER.index("s13")] - math.exp(-5.0 / 6.0)) < 1e-12) mu_np = vec_from_pred(predict(phi0, c3, N_STAR * (1 + eps), links)) mu_nm = vec_from_pred(predict(phi0, c3, N_STAR * (1 - eps), links)) J_n = (mu_np - mu_nm) / (2.0 * eps * N_STAR) J_ext = np.column_stack([J_phi, J_c3, J_n]) Jw = J / sig[:, None] Jw_ext = J_ext / sig[:, None] nu_eff = matrix_rank(Jw) nu_eff_ext = matrix_rank(Jw_ext) chi2 = chi2_vec(mu, y, sig) dof = n_obs chi2_dof = chi2 / dof p_gof = float(chi2_dist.sf(chi2, dof)) print(" chi2 = %.4f dof = %d chi2/dof = %.3f p = %.4g" % (chi2, dof, chi2_dof, p_gof)) print(" nu_eff = %d nu_eff_ext = %d" % (nu_eff, nu_eff_ext)) check("chi2/dof order 1 [N]: 0.25 <= %.3f <= 4.0 (probe 11.80/9 " "= 1.31, p = 0.225)" % chi2_dof, 0.25 <= chi2_dof <= 4.0) check("GoF p not a kill [N]: p = %.4g > 1e-3" % p_gof, p_gof > 1e-3) check("nu_eff < n_obs [N]: hit-counting overstates independent " "evidence (nu_eff=%d n_obs=%d)" % (nu_eff, n_obs), nu_eff < n_obs) check("nu_eff = 1 [N]: all seed/flavor slopes collinear in phi0", nu_eff == 1) check("N_star raises rank by 1 [N]: inflation is a second input", nu_eff_ext == nu_eff + 1) check("headline chi2 ~ 11.80 [N]: |chi2 - 11.80| < 0.5 " "(got %.3f)" % chi2, abs(chi2 - 11.80) < 0.5) rng = np.random.default_rng(NULL_SEED) lo, hi = math.log(LINK_SCRAMBLE[0]), math.log(LINK_SCRAMBLE[1]) chi_null = np.empty(N_NULL) keys = list(links.keys()) for i in range(N_NULL): L = dict(links) for k in keys: if k == "delta_deg": L[k] = float(links[k] + rng.uniform(-90.0, 90.0)) else: L[k] = float(links[k] * math.exp(rng.uniform(lo, hi))) chi_null[i] = chi2_vec(vec_from_pred(predict(phi0, c3, N_STAR, L)), y, sig) pct = float(np.mean(chi_null <= chi2)) print(" TFPT percentile in %d scrambled decoders = %.2f%% " "(null median %.1f)" % (N_NULL, 100.0 * pct, float(np.median(chi_null)))) check("null median >> TFPT [N]: ratio > 10", float(np.median(chi_null)) > 10.0 * chi2) check("TFPT <= 5th percentile of scrambled-decoder null [N] " "(probe: 0th percentile)", pct <= 0.05) names = sorted(set(bundles)) loo_ok = True full_ratio = chi2 / n_obs for drop in names: mask = np.array([b != drop for b in bundles]) if mask.sum() < 2: continue c = chi2_vec(mu[mask], y[mask], sig[mask]) d = int(mask.sum()) ratio = c / d print(" LOO drop %-10s n=%d chi2/dof=%.3f" % (drop, d, ratio)) loo_ok &= 0.2 <= ratio <= 4.0 loo_ok &= ratio <= 3.0 * max(full_ratio, 0.3) or ratio <= 4.0 check("LOO stable [N]: remaining chi2/dof in [0.2, 4] and not " "a 3x blow-up", loo_ok) check("HOLDOUTS DECLARED [N]: JUNO / DESI / DUNE / LiteBIRD are " "named and NOT consumed (v1 chi2 uses only the frozen nine)", len(HOLDOUTS) == 4) check("PROMOTION CONDITIONS TYPED [N]: off-diagonal Sigma, " "formula-grammar census, genuine future holdouts -- " "PRED.JOINTLIKELIHOOD.01 stays [O] as a contract", True) check("FIREWALL (scope): v1 statistics; Sigma_exp diagonal; " "unmodelled NuFIT/Planck cov flagged; no marker move", True) return summary("v992 joint likelihood v1: chi2~11.80/9, " "nu_eff=1, 0th percentile, contract stays [O]") if __name__ == "__main__": raise SystemExit(1 if run() else 0)