"""v482 -- FLAV.NUSCALE.03: the decision computation NAMED by v481, EXECUTED in bracketed (assumption-robust) form -- the integer rung M_R = c3^3 Mbar is EXCLUDED as an unstructured exact pin, conditional on the carrier premise y_nu = y_t; the required rescue factor is quantified, its post-hoc proximity to the atom rational g_car/N_fam = 5/3 is recorded and DECLINED (v354/v355); the one-parameter window candidate of v481 is UNAFFECTED. No gate closes. Background. v481 (FLAV.NUSCALE.02) collapsed the seesaw to one parameter under y_nu = y_t and found the integer rung M_R = c3^3 Mbar predicts m_3 = 0.030 eV -- 40% below the observed 0.0503 eV at 1-loop -- and NAMED the decision computation (higher loops + thresholds). Instead of trusting any single set of higher-loop coefficients, this module executes the decision ROBUSTLY: every input is bracketed with a band far wider than its real uncertainty, and the question is whether ANY of them (or all combined) can bridge the gap. [E-num] 1. THE GAP: central m_3(rung) = 0.0301 eV vs 0.0503 observed -- rescue factor F_req = 1.670 (+67%), i.e. 0.154 c3-rungs. [E-num] 2. BRACKETED EXCLUSION: with m_t(MSbar) +- 3 GeV (>3 sigma), alpha_3^-1 -+ 0.10 (>3 sigma), a +-10% band on the ADKLR kappa run-down, and the PS-leg Yukawa beta scaled x[0.5, 1.5] between M_PS and M_R (a >50% envelope on the PS-vs-SM running difference), the largest single shift is x1.10 and the ALL-favourable combination reaches only x1.165 -- far below the required x1.670. The unstructured rung is EXCLUDED conditional on [P] y_nu = y_t: the 1-loop miss of v481 is NOT an RG artifact. [C] 3. THE NAMED ESCAPE, RECORDED AND DECLINED: only a third-generation Majorana STRUCTURE factor r = M_R/M_{R,3} ~ 1.67 can revive the rung. Post-hoc: r_needed = 1.6696 sits 0.18% from g_car/N_fam = 5/3. NO mechanism forces a 3/5 Clebsch on M_{R,3} today, so per the anti-numerology discipline (v354/v355) this is a NAMED coincidence with a NAMED missing mechanism (a PS Majorana-sector Clebsch), not a claim -- exactly the t0 ~ 30 pattern of v478. [O] 4. CANDIDATE UNAFFECTED: v481's one-parameter statement (M_R free in the PS window, required M_R = 9.3e13 GeV at rung 3.15, NO floor Sigma m_nu = 0.059 eV) never used the integer rung and stands. NET EFFECT: the v481 candidate is now CLEANLY TYPED -- the exact-pin reading is dead (robustly), the window reading lives; the frozen record (v84) untouched. Numerical (explicit 1-loop RG + bracketed envelopes), Python-only by nature. """ import math from tfpt_constants import check, summary, reset, c3, Mbar, g_car, N_fam MZ = 91.1876 V_EW = 246.22 LAM_MZ = 0.130 M3_OBS = 0.0503 M_PS = 4.2e13 C3 = float(c3) MR_RUNG = C3 ** 3 * float(Mbar) def m3_rung(mt_msbar=162.5, a3_inv=8.44, kappa_band=1.0, ps_beta_scale=1.0, n=20000) -> float: """m_3(M_Z) in eV for y_nu = y_t and M_R = c3^3 Mbar, bracketed inputs.""" g1, g2, g3 = [math.sqrt(4 * math.pi / a) for a in (59.01, 29.59, a3_inv)] yt, lam = math.sqrt(2) * mt_msbar / V_EW, LAM_MZ T = math.log(MR_RUNG / MZ) t_ps = math.log(M_PS / MZ) h = T / n k = 1 / (16 * math.pi ** 2) b = (41 / 10, -19 / 6, -7) I_alpha = 0.0 for i in range(n): t = i * h I_alpha += (-3 * g2 * g2 + 6 * yt * yt + lam) * h scale = ps_beta_scale if t > t_ps else 1.0 dg1 = k * b[0] * g1 ** 3 dg2 = k * b[1] * g2 ** 3 dg3 = k * b[2] * g3 ** 3 dyt = scale * k * yt * (4.5 * yt ** 2 - 8 * g3 ** 2 - 2.25 * g2 ** 2 - (17 / 20) * g1 ** 2) dlam = k * (24 * lam ** 2 - 6 * yt ** 4 + 12 * lam * yt ** 2 - 3 * lam * (3 * g2 ** 2 + 0.6 * g1 ** 2) + 0.375 * (2 * g2 ** 4 + (g2 ** 2 + 0.6 * g1 ** 2) ** 2)) g1 += h * dg1 g2 += h * dg2 g3 += h * dg3 yt += h * dyt lam += h * dlam R_down = math.exp(-I_alpha / (16 * math.pi ** 2)) * kappa_band return (yt * V_EW / math.sqrt(2)) ** 2 / MR_RUNG * R_down * 1e9 def run(): reset() print("v482 FLAV.NUSCALE.03: the v481 decision computation, executed " "(bracketed exclusion)") m3_c = m3_rung() F_req = M3_OBS / m3_c check("THE GAP [E-num]: central m_3(rung) = %.4f eV vs observed %.4f eV -- " "rescue factor F_req = %.3f (+%.0f%%), i.e. 0.154 c3-rungs" % (m3_c, M3_OBS, F_req, 100 * (F_req - 1)), 1.5 < F_req < 1.9) shifts = { "m_t +3": m3_rung(mt_msbar=165.5) / m3_c, "m_t -3": m3_rung(mt_msbar=159.5) / m3_c, "a3inv -0.10": m3_rung(a3_inv=8.34) / m3_c, "a3inv +0.10": m3_rung(a3_inv=8.54) / m3_c, "kappa +10%": 1.10, "kappa -10%": 0.90, "PS-leg x1.5": m3_rung(ps_beta_scale=1.5) / m3_c, "PS-leg x0.5": m3_rung(ps_beta_scale=0.5) / m3_c, } F_best = m3_rung(mt_msbar=165.5, a3_inv=8.34, kappa_band=1.10, ps_beta_scale=0.5) / m3_c max_up = max(shifts.values()) check("BRACKETED EXCLUSION [E-num]: max single band shift x%.3f, " "ALL-favourable combined x%.3f, required x%.3f -- NO generous input " "band (m_t +-3 GeV >3sig, alpha_s >3sig, kappa-run +-10%%, PS-leg " "beta envelope x[0.5,1.5]) bridges the gap: the UNSTRUCTURED rung " "M_R = c3^3 Mbar is EXCLUDED conditional on [P] y_nu = y_t (the " "v481 miss is not an RG artifact); bands: %s" % (max_up, F_best, F_req, "; ".join(f"{kk} x{v:.3f}" for kk, v in shifts.items())), max_up < 1.15 and F_best < 1.25 and F_best < 0.8 * F_req) five_thirds = g_car / N_fam rel = abs(F_req - five_thirds) / five_thirds check("NAMED ESCAPE + POST-HOC NOTE [C declined]: only a third-generation " "Majorana STRUCTURE factor r = M_R/M_R3 ~ %.3f revives the rung; " "post-hoc r_needed is %.2f%% from g_car/N_fam = 5/3 -- NO mechanism " "forces a 3/5 Clebsch on M_R3 today, so this is a named coincidence " "with a named missing mechanism (PS Majorana-sector Clebsch), " "DECLINED per v354/v355 -- the same discipline as the t0 ~ 30 " "near-miss (v478)" % (F_req, 100 * rel), rel < 0.02) check("CANDIDATE UNAFFECTED [O]: v481's one-parameter window statement " "(M_R free in [M_PS, M_GUT]; required M_R = 9.3e13 GeV at rung " "3.15; NO floor Sigma m_nu = 0.059 eV) never used the integer rung " "and stands unchanged; FLAV.NUSCALE stays a window-bracketed [O] " "candidate; frozen record (v84) untouched; no gate closes", True) return summary("v482 FLAV.NUSCALE.03: the named decision computation " "executed -- the integer rung c3^3 Mbar is EXCLUDED as an " "unstructured pin (needs x1.67 in m_3; generous input bands " "give at most x1.165 combined), conditional on y_nu = y_t; " "the r = 5/3-proximate structure escape is recorded and " "DECLINED (0.18%, no mechanism); the v481 one-parameter " "window candidate stands; nothing closes") if __name__ == "__main__": raise SystemExit(1 if run() else 0)