"""v467 -- FLAV.THIRDGEN.PATTERN.01: the third-generation ladder-base pattern -- the suite's THREE ~2 sigma mixing tensions (sin^2 theta13 +2.0, sin^2 theta23 +1.8, V_cb +1.8) are ONE common ~ -phi0 suppression, quantified and pre-registered as a CANDIDATE. The frozen record (v84/REG.FREEZE.01) is NOT changed; like v328 this module names and machine-checks a pattern, it does not silently upgrade or switch a prediction. The observation. The three most-tensioned mixing readouts of the watchdog (v307) are exactly the three THIRD-GENERATION channels, and all three sit LOW by the same relative amount. In the existing vocabulary the pattern has a closed, parameter-free form: the seed enters third-generation mixing through the LADDER BASE lambda_C^2 = phi0(1-phi0) (the same base that carries the Yukawa mass ladder lambda_Y, tfpt_2) instead of bare phi0, and the 2-3 texture carries the same -phi0/2 seed shift that theta12 already has: sin^2 theta13 = lambda_C^2 e^{-5/6} = 0.021880 (record phi0 e^{-5/6}, +2.00 -> -0.12 sigma) sin^2 theta23 = (1-phi0)/2, cos 2theta23=phi0 = 0.473414 (record 1/2, +1.76 -> +0.20 sigma) V_cb = lambda_C^2/(1+lambda_C) = 0.041119 (record phi0/(1+lambda_C), +1.79 -> +0.01 sigma) Scope check that makes it a RULE, not a fit: V_ub = lambda_C^3/3 contains NO bare phi0 -- the rule leaves it untouched, and it is the one third-gen channel that is already consistent (-0.23 sigma). The 1-2 channels (theta12, lambda_C) must stay undressed and do (dressing them would give -1.4 / -24 sigma). [E] 1. VOCABULARY IDENTITIES (exact, sympy): lambda_C^2 = phi0(1-phi0) (the frozen Cabibbo, v84); sin^2 theta23=(1-phi0)/2 <=> cos 2theta23 = phi0; and the suppression magnitude phi0 = 5.32% sits INSIDE the seam-gapped first-correction band (2/3)^6 = 8.78% (v393 class) -- an allowed-size correction, no new scale. [N] 2. COMMON SUPPRESSION: the three affected channels deviate from the record by -5.0%/-6.0%/-5.4% (weighted -5.36% +- 1.67%): non-zero at 3.2 sigma, consistent with -phi0 at -0.03 sigma (repo-documented NuFIT 6.0 / PDG 2024 data, v307). [N] 3. JOINT CHI^2, ZERO PARAMETERS: over the four third-gen observables (theta13, theta23, V_cb, V_ub) the joint chi^2 drops 10.4 -> 0.11 under the pattern; the 1-2 channels stay undressed-correct (theta12 -0.02, lambda_C -0.25 sigma). [N] 4. REACTOR-ONLY DISCRIMINATOR: against Daya Bay alone (0.02175 +- 0.00065) the record is +2.09 sigma, the pattern +0.20 sigma (Delta chi^2 = 4.3) -- current reactor data already prefer the pattern form. [C] 5. LOOK-ELSEWHERE (honest): the pattern is POST-HOC. A census of 16 equally-simple multiplicative dressings finds 5 that fix the two PMNS tensions; and (1-phi0), (1-c3), (1-lambda_C^2), 1/(1+phi0) are DEGENERATE at current precision (<1.4% apart, channel errors ~2.5-3.4%). V_cb + the V_ub scope check are what single out the ladder-base form; still a candidate, not a discovery. [O] 6. NO DERIVATION -- RECORD UNCHANGED: attempted derivations (Bernoulli-variance reading lambda_Y^2 = Var[Bernoulli(phi0)] -- an exact identity but only an interpretation; resolvent transport phi0/(1+phi0), degenerate to 0.28%; 1-2 x 2-3 composition fails by 6.6x) do NOT yield the rule first-principles. The frozen record stays the prediction of record (v84); this row is [O] until a seam-transport derivation exists. [X] 7. PRE-REGISTERED DECISION: (i) sin^2 theta13 stabilising on the 0.0231 side (record) kills the pattern; stabilising at ~0.0219 with sigma_rel < 1% kills the record's bare-phi0 reading; (ii) an exclusive-|Vcb| resolution at ~0.0395 kills BOTH readings; (iii) separating the degenerate dressing forms needs sigma_rel < 0.5% on one channel (JUNO-era reactors / Belle II). HONEST SCOPE: data are the repo-documented centrals (NuFIT 6.0 NO w/ SK atm: theta13 0.02195(58), theta23 0.470(17); PDG 2024: |Vcb| 0.0411(13), |Vub| 0.00382(24), lambda_C 0.2245(5); NuFIT theta12 0.307(12); Daya Bay 0.02175(65)). A quantified pattern CANDIDATE in the v328 style -- it upgrades no prediction, changes no frozen value, and closes no gate. Python-only (floats + sympy identities; data confrontation). """ import math import sympy as sp from tfpt_constants import check, summary, reset, phi0 as phi0_mp PHI0 = float(phi0_mp) LAM = math.sqrt(PHI0 * (1.0 - PHI0)) # frozen Cabibbo lambda_C (v84) E56 = math.exp(-5.0 / 6.0) # repo-documented data (v307 watchdog + NuFIT 6.0 NO with SK-atm + Daya Bay) D_TH13 = (0.02195, 0.00058) # NuFIT 6.0 D_TH23 = (0.470, 0.017) # NuFIT 6.0 NO (SK-atm), first octant D_VCB = (0.0411, 0.0013) # PDG 2024 |Vcb| D_VUB = (0.00382, 0.00024) # PDG 2024 |Vub| D_TH12 = (0.307, 0.012) # NuFIT 6.0 D_LAMC = (0.2245, 0.0005) # PDG 2024 D_DAYABAY = (0.02175, 0.00065) # Daya Bay final (reactor-only) def _pull(pred, dat): return (pred - dat[0]) / dat[1] def run(): reset() print("v467 FLAV.THIRDGEN.PATTERN.01: the third-generation ladder-base pattern " "(candidate, record unchanged)") # ---- 1. vocabulary identities (exact) ---- p = sp.Symbol("phi0", positive=True) lam2 = p * (1 - p) cos2th23 = sp.simplify(1 - 2 * (1 - p) / 2) # 1 - 2 sin^2 theta23' seam_band = sp.Rational(2, 3) ** 6 check("VOCABULARY IDENTITIES [E]: lambda_C^2 = phi0(1-phi0) (frozen Cabibbo, " "v84); sin^2 theta23 = (1-phi0)/2 <=> cos 2theta23 = phi0 (exact); and the " "suppression phi0 = %.2f%% sits INSIDE the seam-gapped first-correction " "band (2/3)^6 = %.2f%% (v393) -- allowed size, no new scale" % (100 * PHI0, 100 * float(seam_band)), sp.simplify(lam2 - p * (1 - p)) == 0 and cos2th23 == p and abs(LAM ** 2 - PHI0 * (1 - PHI0)) < 1e-15 and PHI0 < float(seam_band)) # ---- 2. common suppression of the three affected channels ---- rec = {"th13": PHI0 * E56, "th23": 0.5, "vcb": PHI0 / (1 + LAM), "vub": LAM ** 3 / 3} pat = {"th13": LAM ** 2 * E56, "th23": (1 - PHI0) / 2, "vcb": LAM ** 2 / (1 + LAM), "vub": LAM ** 3 / 3} # V_ub: no bare phi0 dat = {"th13": D_TH13, "th23": D_TH23, "vcb": D_VCB, "vub": D_VUB} devs, sigs = [], [] for k in ("th13", "th23", "vcb"): devs.append(dat[k][0] / rec[k] - 1.0) sigs.append(dat[k][1] / rec[k]) w = [1.0 / s ** 2 for s in sigs] mean_dev = sum(wi * di for wi, di in zip(w, devs)) / sum(w) mean_sig = math.sqrt(1.0 / sum(w)) z0 = mean_dev / mean_sig zphi = (mean_dev + PHI0) / mean_sig print(f" rel. deviations vs record: th13 {100 * devs[0]:+.2f}%, " f"th23 {100 * devs[1]:+.2f}%, Vcb {100 * devs[2]:+.2f}% " f"-> weighted {100 * mean_dev:+.2f}% +- {100 * mean_sig:.2f}%") check("COMMON SUPPRESSION [N]: the three affected third-gen channels share one " "relative deviation %.2f%% +- %.2f%% -- non-zero at %.1f sigma, consistent " "with -phi0 (= -%.2f%%) at %.2f sigma" % (100 * mean_dev, 100 * mean_sig, abs(z0), 100 * PHI0, zphi), abs(z0) > 2.5 and abs(zphi) < 1.0) # ---- 3. joint chi^2, zero parameters; 1-2 channels stay undressed ---- chi_rec = sum(_pull(rec[k], dat[k]) ** 2 for k in rec) chi_pat = sum(_pull(pat[k], dat[k]) ** 2 for k in pat) th12_pull = _pull(1 / 3 - PHI0 / 2, D_TH12) lamc_pull = _pull(LAM, D_LAMC) lamc_dressed_pull = _pull(LAM * (1 - PHI0), D_LAMC) print(f" joint chi^2 (th13, th23, Vcb, Vub): record {chi_rec:.2f} -> " f"pattern {chi_pat:.2f}") check("JOINT CHI^2 [N]: over the four third-gen observables the pattern drops " "chi^2 from %.2f to %.2f with ZERO new parameters (V_ub = lambda_C^3/3 has " "no bare phi0 and stays untouched at %+.2f sigma); the 1-2 channels stay " "undressed-correct (theta12 %+.2f, lambda_C %+.2f sigma; dressing lambda_C " "would give %+.1f sigma -- the scope is checked, not chosen)" % (chi_rec, chi_pat, _pull(pat["vub"], D_VUB), th12_pull, lamc_pull, lamc_dressed_pull), chi_rec > 9.0 and chi_pat < 1.0 and abs(th12_pull) < 0.5 and abs(lamc_pull) < 0.5 and lamc_dressed_pull < -5.0) # ---- 4. reactor-only discriminator (Daya Bay) ---- p_rec_db = _pull(rec["th13"], D_DAYABAY) p_pat_db = _pull(pat["th13"], D_DAYABAY) dchi_db = p_rec_db ** 2 - p_pat_db ** 2 check("REACTOR-ONLY DISCRIMINATOR [N]: against Daya Bay alone (0.02175 +- " "0.00065) the record is %+.2f sigma, the pattern %+.2f sigma (Delta chi^2 " "= %.1f) -- current reactor data already prefer the pattern form" % (p_rec_db, p_pat_db, dchi_db), p_rec_db > 1.8 and abs(p_pat_db) < 0.6 and dchi_db > 3.0) # ---- 5. look-elsewhere honesty: dressing census + degeneracy ---- c3f = 1.0 / (8.0 * math.pi) cands = [("phi0", PHI0), ("phi0/2", PHI0 / 2), ("lambda_C", LAM), ("c3", c3f), ("lambda_C^2", LAM * LAM), ("(2/3)^6", (2 / 3) ** 6), ("dtop", 48 * c3f ** 4), ("phibase", 1 / (6 * math.pi))] winners = [] for name, x in cands: for sgn in (+1, -1): ok13 = abs(_pull(rec["th13"] * (1 + sgn * x), D_TH13)) <= 1.0 ok23 = abs(_pull(rec["th23"] * (1 + sgn * x), D_TH23)) <= 1.0 if ok13 and ok23: winners.append(("+" if sgn > 0 else "-") + name) resolvent = PHI0 / (1 + PHI0) degen = abs(resolvent / (PHI0 * (1 - PHI0)) - 1) check("LOOK-ELSEWHERE (honest) [C]: POST-HOC pattern; %d of 16 equally-simple " "dressings fix the two PMNS tensions (%s); and (1-phi0) vs (1-c3) vs " "1/(1+phi0) are degenerate at current precision (resolvent differs by " "%.2f%% << channel errors ~2.5-3.4%%) -- V_cb + the V_ub scope check single " "out the ladder-base form; a candidate, NOT a discovery" % (len(winners), ", ".join(winners), 100 * degen), 3 <= len(winners) <= 7 and degen < 0.01) # ---- 6. no derivation -- record unchanged ---- var_id = sp.simplify(p * (1 - p) - (p - p ** 2)) # Var[Bernoulli(phi0)] s12s23_sq = (1 / 3 - PHI0 / 2) * 0.5 # 1-2 x 2-3 composition comp_off = s12s23_sq / rec["th13"] check("NO DERIVATION -- RECORD UNCHANGED [O]: the Bernoulli-variance reading " "lambda_Y^2 = Var[Bernoulli(phi0)] = phi0(1-phi0) is an exact identity but " "only an INTERPRETATION; the 1-2 x 2-3 composition misses by %.1fx; no " "seam-transport derivation exists, so the frozen record (v84/REG.FREEZE.01) " "stays the prediction of record and this row is a named [O] candidate" % comp_off, var_id == 0 and comp_off > 5.0) # ---- 7. pre-registered decision ---- kill = ("theta13 stable at 0.0231 kills the pattern; theta13 at ~0.0219 with " "sigma_rel<1% kills the record's bare-phi0 reading; exclusive |Vcb| " "~0.0395 kills both; separating (1-phi0)/(1-c3)/resolvent needs " "sigma_rel<0.5%") check("PRE-REGISTERED DECISION [X]: %s -- JUNO-era reactors and Belle II " "|Vcb| decide; symmetric kill conditions on BOTH readings, no knob" % kill, "0.0231" in kill and "0.0395" in kill) return summary("v467 FLAV.THIRDGEN.PATTERN.01: the three ~2 sigma mixing tensions " "(theta13, theta23, Vcb) are ONE common -phi0 suppression (-5.36% " "+- 1.67%, 3.2 sigma non-zero, -0.03 sigma from -phi0); ladder-base " "forms lambda_C^2 e^{-5/6} / (1-phi0)/2 / lambda_C^2/(1+lambda_C) " "drop joint chi^2 10.4 -> 0.11 with zero parameters; POST-HOC " "candidate [O], record unchanged, JUNO/Belle II decide") if __name__ == "__main__": raise SystemExit(1 if run() else 0)