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Original ledger classification: Enumeration/decision [E]/[O] (the 3/5 Clebsch door closed; negative result; window candidate stands)

Recorded statement: THE 3/5 CLEBSCH DOOR ENUMERATED AND CLOSED (2026-07-15; executes the mechanism search behind FLAV.NUSCALE.03's named escape): v482 recorded that only a third-generation Majorana structure factor r ~ 1.6696 (0.18% from g_car/N_fam = 5/3)…

Statement, assumptions and sources

Paper context: Standard Model and flavor structure

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FLAV.NUSCALE.04

Original ledger classification: Enumeration/decision [E]/[O] (the 3/5 Clebsch door closed; negative result; window candidate stands)

Original claim text

THE 3/5 CLEBSCH DOOR ENUMERATED AND CLOSED (2026-07-15; executes the mechanism search behind FLAV.NUSCALE.03's named escape): v482 recorded that only a third-generation Majorana structure factor r ~ 1.6696 (0.18% from g_car/N_fam = 5/3) could revive the integer rung M_R = c3^3 Mbar, and declined it for lack of mechanism. The mechanism search is now EXECUTED at the group-theory level with a clean NEGATIVE. [E] NO RENORMALISABLE CHANNEL: sym^2(16) = 136 = 10 + 126; the 126bar is NOT in the E8 hull {1, 10, 16, 45} (v247) -- M_R only via the d=5 operator (16_F 16bar_H)(16_F 16bar_H)/Lambda with the E8-allowed 16_H. [E] CHANNEL LIST: 16 x 16bar = 1 + 45 + 210; the hull admits singlet + 45 insertion channels (210 absent). [E] CHARGE TABLE: Y = T_3R + (B-L)/2 verified on all 16 states; Tr_16 Y^2 = 10/3 (v485); (B-L, T_3R, Y)(nu^c) = (+1, -1/2, 0). [E] THE {2,3}-SMOOTH THEOREM (the door closes): every available nonzero nu^c channel weight -- singlet 1, T_3R^2 = 1/4, (B-L)^2 = 1, T_3R(B-L) = -1/2, SU(4)-15 weight 3/8 -- is a {2,3}-smooth rational, and the multiplicative closure of {2,3}-smooth rationals never contains 5/3 (a factor 5 cannot appear); the UNIQUE natural 5 of the embedding is k_Y = Tr_16 Y^2 / Tr_16 T_3L^2 = 5/3 (Ginsparg, v470) -- a FULL-MULTIPLET trace, and its carrier direction has Y(nu^c) = 0 EXACTLY, so the only 5-carrying group number is structurally decoupled from the Majorana operator. [E] GENERATION-BLINDNESS: the Clebsch multiplies the whole family matrix c_ij (identical 16's); a per-generation ratio is a flavor texture, never a Clebsch -- the required diag(1, 1, 3/5) cannot arise from group theory by construction. [O] COMPILER-FLAVOR INVENTORY (typed, declined): exact 3/5's in the frozen address tables sit only in WRONG slots (K lepton row (5,3,2): gen2/gen1; R (2,5,3) and L (8,5,3) lepton rows: gen3/gen2); the escape needs gen3 vs a DEGENERATE gen1 = gen2 base, which no frozen table has; no mechanism links M_R to the address tables (v354/v355). NET: the rung + 5/3 rescue is DEAD as a mechanism candidate; the v481 one-parameter window candidate (M_R free inside the PS window; Sigma m_nu = 0.059 eV floor as kill test) stands as the honest endpoint. Contract provenance: experiments/theory-contracts/clebsch01_majorana_35_door.py. No gate closes; the frozen record is untouched.

Original classification detail

Door closed [E]: no renormalisable channel (126 E8-forbidden); nu^c channel weights {2,3}-smooth -> 5/3 unreachable; k_Y = 5/3 decoupled (Y(nu^c) = 0); Clebsches generation-blind; [O] wrong-slot compiler 3/5's typed and declined

Dependencies as recorded

FLAV.NUSCALE.03; FLAV.NUSCALE.02; PS.E8BRANCH.01; v247; v249; v470; v481; v482; v485

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Registered verification modules

  • v488_majorana_clebsch_door.pyRegistered verification module · flavor
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    FLAV.NUSCALE.04: the 3/5 Clebsch door of the seesaw rung, enumerated and CLOSED -- v482's named escape (a third-generation Majorana factor r ~ 1.6696, 0.18% from g_car/N_fam = 5/3) is decided NEGATIVE at the group-theory level. [E] no renormalisable channel: sym^2(16) = 136 = 10 + 126 and the 126bar is not in the E8 hull (v247) -- M_R only via the d=5 operator (16 16bar_H)^2/Lambda; [E] channel list 16 x 16bar = 1 + 45 + 210 with only singlet + 45 admissible; [E] charge table: (B-L, T_3R, Y)(nu^c) = (+1, -1/2, 0), Tr_16 Y^2 = 10/3; [E] the {2,3}-smooth theorem: every nu^c channel weight is {2,3}-smooth, so no channel combination reaches 5/3 -- and the unique natural 5 of the embedding (k_Y = 5/3, v470) is decoupled because Y(nu^c) = 0 exactly; [E] Clebsches are generation-blind (family-space scalars) -- diag(1,1,3/5) cannot arise from group theory; [O] compiler-flavor 3/5 inventory typed and declined (wrong slots only). The rung + 5/3 rescue is dead; the v481 window candidate stands.

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