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Original ledger classification: Candidate [P]/[N]/[X]/[C]/[O] (carrier normalisation collapses the trade-off; window bracketing; integer rung declined at 1-loop; decision computation named)

Recorded statement: ABSOLUTE NEUTRINO SCALE UNDER THE CARRIER YUKAWA NORMALISATION (2026-07-14, bird's-eye round; CANDIDATE class, genre v467/v468): FLAV.NUSCALE.01 typed the absolute scale as one open UV input with the two-parameter trade-off (y_nu, M_R) and…

Statement, assumptions and sources

Paper context: Standard Model and flavor structure

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FLAV.NUSCALE.02

Original ledger classification: Candidate [P]/[N]/[X]/[C]/[O] (carrier normalisation collapses the trade-off; window bracketing; integer rung declined at 1-loop; decision computation named)

Original claim text

ABSOLUTE NEUTRINO SCALE UNDER THE CARRIER YUKAWA NORMALISATION (2026-07-14, bird's-eye round; CANDIDATE class, genre v467/v468): FLAV.NUSCALE.01 typed the absolute scale as one open UV input with the two-parameter trade-off (y_nu, M_R) and recorded the y_nu = 1 inversion at the structureless log_c3(Mbar/M_R) ~ 2.6. But y_nu = 1 is not the carrier normalisation: one SO(10) 16 per family + the MINIMAL Yukawa sector (10_H / PS (1,2,2), the v245/v248/v249 structure) forces y_nu = y_t at the matching scale [P named premise]. With explicit 1-loop RG (gauge/y_t/lambda up; ADKLR Weinberg-operator kappa down, hep-ph/0108005): [N] the trade-off COLLAPSES to M_R alone and the observed m_3 = 0.0503 eV demands M_R = 9.3e13 GeV -- INSIDE the compiler's own PS window [4.2e13, 2.4e15] (v249), at log_c3(Mbar/M_R) = 3.15. [X] 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 (kappa run-down factor 0.794): NEAR the rung (3.15 vs 3), NOT ON -- the ladder pin is DECLINED per v354/v355; the decision computation is NAMED (2-loop SM + explicit PS threshold matching). [N] FALSIFIABLE BAND: over the PS window m_3 spans [0.002, 0.115] eV bracketing the observation; the M_PS end (Sigma ~ 0.124 eV) is already in tension with DESI ~0.072 -- cosmology cuts the window from below; the NO floor Sigma = m_2 + m_3 = 0.059 eV stays the falsifiable edge (v272). [C]/[O] candidate class: the premise is the minimal Yukawa sector [P]; the absolute scale stays formally open until the decision computation lands; the frozen record (v84/REG.FREEZE.01) is untouched. NET: the absolute neutrino scale is now a ONE-parameter statement bracketed by the compiler's own UV window, not a two-parameter trade-off. UPDATE 2026-07-14 (v482/FLAV.NUSCALE.03): the named decision computation is EXECUTED -- the integer rung is EXCLUDED as an unstructured pin (bracketed envelopes reach x1.165 vs required x1.670); the 5/3-proximate structure escape is recorded and declined; the one-parameter window candidate stands.

Original classification detail

Open [O] candidate (parameter-reduced): y_nu = y_t [P] collapses (y_nu, M_R) to M_R alone; required M_R inside the PS window at rung 3.15; c3^3 rung declined at 1-loop (m_3 40% low); NO floor Sigma m_nu = 0.059 eV falsifiable edge

Dependencies as recorded

FLAV.NUSCALE.01; PS.RGTEST.01; PS.ALGEBRA.01; QFT4D.MATTER.01; FLAV.PMNS.CLOSE.01; v245; v248; v249; v272; v273

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Registered verification modules

  • v481_seesaw_carrier_ladder.pyRegistered verification module · neutrinos
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    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, and the required M_R lands INSIDE the compiler's own PS window; the nearby integer c3-rung is explicitly DECLINED at 1-loop (anti-numerology). [P] carrier normalisation (named premise): one SO(10) 16 per family + minimal Yukawa sector (10_H / PS (1,2,2)) => y_nu = y_t at the matching scale. [N] inversion: m_3 = 0.0503 eV demands M_R = 9.3e13 GeV, inside [4.2e13, 2.4e15] (v249), at log_c3(Mbar/M_R) = 3.15 (y_nu = 1 gives the structureless 2.58). [X] integer-rung honesty gate: M_R = c3^3 Mbar predicts m_3 = 0.030 eV (40% low at 1-loop; ADKLR run-down 0.794) -- NEAR, not ON: pin DECLINED; decision computation named (2-loop + PS thresholds). [N] falsifiable band [0.002, 0.115] eV brackets the observation; DESI cuts the window from below; NO floor Sigma = 0.059 eV. [C]/[O] candidate class (genre v467/v468); frozen record untouched; nothing closes.

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