"""v481 -- FLAV.NUSCALE.02: the absolute neutrino-mass scale under the CARRIER Yukawa normalisation y_nu = y_t -- FLAV.NUSCALE.01's two-parameter (y_nu, M_R) trade-off collapses to ONE parameter, the required M_R lands INSIDE the compiler's own PS window, and the nearby integer c3-rung is explicitly DECLINED at 1-loop (anti-numerology, v354/v355). A CANDIDATE-class sharpening (genre v467/v468); the frozen record (v84/REG.FREEZE.01) is untouched and NO gate closes. Background. FLAV.NUSCALE.01 (v272) typed the absolute scale as ONE open UV input with the trade-off m_3 = (y_nu v)^2 / (2 M_R), and recorded that the y_nu = 1 inversion gives log_c3(Mbar/M_R) ~ 2.6 -- non-integer, "not a compiler output". But y_nu = 1 is not the carrier normalisation: TFPT's own carrier structure (one SO(10) 16 per family, PS algebra v245/v248/v249) with the MINIMAL Yukawa sector (one 10_H / PS (1,2,2)) forces the third-family Dirac neutrino Yukawa to equal the top Yukawa at the matching scale: y_nu = y_t. This module redoes the inversion with that normalisation at explicit 1-loop RG: up: g1, g2, g3 (GUT-normalised, b = (41/10, -19/6, -7), the v273 EG coefficients), y_t, lambda from M_Z to M_R; down: the Weinberg operator kappa with the ADKLR coefficient 16 pi^2 dkappa/dt = (-3 g2^2 + 6 y_t^2 + lambda) kappa + flavor terms (Antusch-Drees-Kersten-Lindner-Ratz, Phys. Lett. B519 (2001) 238, hep-ph/0108005; tau-Yukawa flavor term negligible here). [P] 1. CARRIER NORMALISATION (named premise): y_nu = y_t at M_R from the minimal 16.16.10 Yukawa sector -- the trade-off collapses to M_R alone. [N] 2. INVERSION INSIDE THE COMPILER WINDOW: the observed m_3 = sqrt(dm2_atm) = 0.0503 eV demands M_R ~ 9.3e13 GeV -- INSIDE the PS two-step window [M_PS, M_GUT] = [4.2e13, 2.4e15] (v249), at log_c3(Mbar/M_R) = 3.15. [X] 3. INTEGER-RUNG HONESTY GATE: the rung M_R = c3^3 Mbar = 1.53e14 GeV predicts m_3 = 0.030 eV -- 40% LOW at 1-loop. NEAR (3.15 vs 3), NOT ON: the ladder pin is DECLINED per v354/v355; the named decision computation is 2-loop SM running + explicit PS threshold matching. [N] 4. FALSIFIABLE BAND: over the PS window the carrier-normalised seesaw spans m_3(M_GUT) = 0.002 .. m_3(M_PS) = 0.115 eV, bracketing the observation; the low-M_R half is already in tension with DESI Sigma m_nu ~ 0.072 eV -- cosmology cuts the window from below; the NO floor Sigma = m_2 + m_3 = 0.059 eV stays the falsifiable edge (v272). [C]/[O] 5. Scope: candidate-class; the premise is the minimal Yukawa sector [P]; the absolute scale stays formally open until the decision computation lands; the frozen registry is untouched. NET EFFECT: the absolute neutrino scale is now a ONE-parameter statement bracketed by the compiler's own UV window instead of a two-parameter trade-off. Numerical (explicit 1-loop RG integration), Python-only by nature. """ import math from tfpt_constants import check, summary, reset, c3, Mbar MZ = 91.1876 V_EW = 246.22 YT_MZ = math.sqrt(2) * 162.5 / V_EW # MSbar m_t(M_Z) ~ 162.5 GeV LAM_MZ = 0.130 # m_h = 125 GeV quartic at M_Z A_INV_MZ = (59.01, 29.59, 8.44) # v246 GUT-normalised inputs M3_OBS = 0.0503 # eV (NuFIT NO, sqrt dm2_atm) DM2_21 = 7.42e-5 # eV^2 M_PS, M_GUT = 4.2e13, 2.4e15 # v249 PS window C3 = float(c3) MBARF = float(Mbar) def run_sm_up(mu_hi, n=20000): g1, g2, g3 = [math.sqrt(4 * math.pi / a) for a in A_INV_MZ] yt, lam = YT_MZ, LAM_MZ T = math.log(mu_hi / MZ) h = T / n k = 1 / (16 * math.pi ** 2) b = (41 / 10, -19 / 6, -7) I_alpha = 0.0 # integral of alpha_SM dt for _ in range(n): I_alpha += (-3 * g2 * g2 + 6 * yt * yt + lam) * h dg1 = k * b[0] * g1 ** 3 dg2 = k * b[1] * g2 ** 3 dg3 = k * b[2] * g3 ** 3 dyt = 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)) return yt, R_down def m3_pred_eV(MR): """m_3(M_Z) for y_nu(MR) = y_t(MR): seesaw at MR + ADKLR running down.""" yt, R = run_sm_up(MR) return (yt * V_EW / math.sqrt(2)) ** 2 / MR * R * 1e9, yt, R def run(): reset() print("v481 FLAV.NUSCALE.02: seesaw with the carrier normalisation y_nu = y_t") MR_int = C3 ** 3 * MBARF m3_int, yt_int, R_int = m3_pred_eV(MR_int) # 1. carrier normalisation premise check("CARRIER NORMALISATION [P named]: one SO(10) 16 per family + minimal " "Yukawa sector (10_H / PS (1,2,2)) => y_nu = y_t at the matching scale " "(y_t(1.5e14 GeV) = %.3f at 1-loop) -- FLAV.NUSCALE.01's (y_nu, M_R) " "trade-off collapses to M_R alone; premise NAMED, not proven" % yt_int, 0.2 < yt_int < 0.7) # 2. inversion inside the compiler window lo, hi = 1e13, 1e16 for _ in range(60): mid = math.sqrt(lo * hi) if m3_pred_eV(mid)[0] > M3_OBS: lo = mid else: hi = mid MR_req = math.sqrt(lo * hi) rung_req = math.log(MBARF / MR_req) / math.log(1 / C3) MR_ynu1 = (V_EW / math.sqrt(2)) ** 2 / (M3_OBS * 1e-9) # ledger convention m_D = v/sqrt2 rung_ynu1 = math.log(MBARF / MR_ynu1) / math.log(1 / C3) check("INVERSION INSIDE THE COMPILER WINDOW [N]: the observed m_3 = 0.0503 eV " "demands M_R = %.2e GeV -- INSIDE the PS two-step window [4.2e13, 2.4e15] " "(v249) -- at log_c3(Mbar/M_R) = %.3f (the y_nu = 1 inversion gives the " "structureless %.2f, the FLAV.NUSCALE.01 number)" % (MR_req, rung_req, rung_ynu1), M_PS < MR_req < M_GUT and abs(rung_req - 3.15) < 0.05 and abs(rung_ynu1 - 2.57) < 0.02) # 3. integer-rung honesty gate ratio = m3_int / M3_OBS check("INTEGER-RUNG HONESTY GATE [X declined]: M_R = c3^3 Mbar = %.2e GeV " "predicts m_3 = %.4f eV -- ratio %.2f to observation (40%% low at " "1-loop; kappa run-down factor %.3f). NEAR the rung (%.2f vs 3), NOT " "ON: the ladder pin is DECLINED per v354/v355; decision computation " "named: 2-loop SM + explicit PS threshold matching" % (MR_int, m3_int, ratio, R_int, rung_req), 0.4 < ratio < 0.8) # 4. falsifiable band m3_lo = m3_pred_eV(M_GUT)[0] m3_hi = m3_pred_eV(M_PS)[0] m2 = math.sqrt(DM2_21) sigma_floor = M3_OBS + m2 check("FALSIFIABLE BAND [N]: over the PS window m_3 spans [%.4f, %.4f] eV, " "bracketing 0.0503; Sigma at the M_PS end = %.3f eV is already in tension " "with DESI ~0.072 -- cosmology cuts the window from below; the NO floor " "Sigma = m_2 + m_3 = %.4f eV stays the falsifiable edge (v272)" % (m3_lo, m3_hi, m3_hi + m2, sigma_floor), m3_lo < M3_OBS < m3_hi and sigma_floor < 0.072) # 5. scope check("SCOPE [C]/[O]: CANDIDATE class (genre v467/v468) -- the premise is the " "minimal Yukawa sector [P]; the absolute scale stays formally open until " "the named decision computation lands; frozen record (v84/REG.FREEZE.01) " "untouched; no gate closes, no marker moves", True) return summary("v481 FLAV.NUSCALE.02: carrier normalisation y_nu = y_t collapses " "the (y_nu, M_R) trade-off to one parameter -- required M_R = " "9.3e13 GeV INSIDE the PS window at log_c3(Mbar/M_R) = 3.15; " "integer rung c3^3 Mbar declined at 1-loop (m_3 40% low; decision " "= 2-loop + PS thresholds); falsifiable band brackets observation, " "NO floor Sigma m_nu = 0.059 eV; candidate class, nothing closes") if __name__ == "__main__": raise SystemExit(1 if run() else 0)