Publication history: 2026-07-15

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• v488_majorana_clebsch_door.py (FLAV.NUSCALE.04). v482 named ONE escape for the integer seesaw rung M_R=c_3^3\Mbar: a third-generation Majorana factor r\approx1.6696, 0.18\% from \gcar/\Nfam=5/3 — declined for lack of mechanism. The mechanism search is now EXECUTED: [E]NO RENORMALISABLE CHANNEL — \operatorname{sym}^2(\mathbf{16})=136=\mathbf{10}+\mathbf{126} and the \overline{\mathbf{126}} is NOT in the E_8 hull \{1,10,16,45\} (v247), so M_R only via the d{=}5 operator (\mathbf{16}_F\overline{\mathbf{16}}_H)^2/\Lambda; channels \mathbf{16}\times\overline{\mathbf{16}}=\mathbf{1}+\mathbf{45}+\mathbf{210} with only singlet + \mathbf{45} admissible. [E]CHARGE TABLE: (B{-}L,T_{3R},Y)(\nu^c)=(+1,-\tfrac12,0), \operatorname{Tr}_{16}Y^2=\tfrac{10}3 (v485). [E]THE \{2,3\}-SMOOTH THEOREM (the door closes): every nonzero \nu^c channel weight \{1,\tfrac14,1,-\tfrac12,\tfrac38\} is \{2,3\}-smooth, and the multiplicative closure of \{2,3\}-smooth rationals never contains \tfrac53 (no factor 5); the UNIQUE natural 5 of the embedding, k_Y=\tfrac53 (Ginsparg, v470), is a full-multiplet trace whose direction has Y(\nu^c)=0 EXACTLY — structurally decoupled from the Majorana operator. [E] GENERATION-BLINDNESS: Clebsches are family-space scalars; \operatorname{diag}(1,1,\tfrac35) cannot arise from group theory by construction. [O]compiler-flavor inventory typed and declined: exact \tfrac35's only in wrong slots (K lepton gen2/gen1; R+L lepton gen3/gen2; never gen3 vs a degenerate base). 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, the \Sigma m_\nu=0.059 eV floor as kill test) stands. Contract provenance: experiments/theory-contracts/clebsch01_majorana_35_door.py. Integrated in tfpt_2_standard_model (new paragraph closing the seesaw arc); ledger row FLAV.NUSCALE.04 + update note on .03; Python-only (Fraction/sympy exact), mirrorable, deferred to the next verified engine run.

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• v487_transfer_clock_rungs.py (HYP.REWRITE.03). v486 left the split selection open (“(\tfrac12,\tfrac16) vs uniform (\tfrac13,\tfrac13) is selected by the physical spectrum, not yet derived”; named candidate: the vague “sheet-symmetric choice”). Closed: [E]RUNG READING — the lazy rule's one-step spectrum is EXACTLY the complete resummed-clock ladder below the wall (v124: \lambda_n^{1/p_2}=1-n/\Nfam, pole at n{=}\Nfam): \operatorname{eig}(M)=\{1,\tfrac23,\tfrac13\}=\{1-n/3:n=0,1,2\}, while v327's uniform rule puts its second pair mode ON the wall (0=1-3/3) — the v486 degeneracy re-read as “odd channel collapsed to the wall”. [E]DECK PARITY = RUNG INDEX: [B,\sigma]=0; the \sigma-even pair mode carries rung n{=}1 (survival \tfrac23), the \sigma-odd mode rung n{=}2 (survival \tfrac13) — each clock step flips the deck parity; this is the structural home of the v486 parity assignment (\omega_1 even-channel, \omega_2 odd-channel) that experiments/frb-parity-comb tests. [E]FORCING: demanding the faithful ladder (no rung missing, no physical mode on the wall — definitional for a full-spectrum generator) + \Z_2 equivariance + non-negative rates forces UNIQUELY both the split (\tfrac12,\tfrac16) AND the rung assignment even\to1, odd\to2 (the swapped assignment needs h=-\tfrac16<0); the “sheet-symmetric choice” candidate is superseded by this proof. [E]BEND COROLLARY: \omega_1/\omega_2=\mathrm{rate}(2)/\mathrm{rate}(1)=\log_{3/2}3=2.70951\ldots — the parity-comb tone ratio IS the v107/v124 bend of the pulsar-clock search. [O]what remains open is exactly what was open before v486: the arity \{2,3\} (anchor input) and the clock's semiclassical derivation (R1); no independent choice remains at the walk level. Contract provenance: experiments/theory-contracts/lazy01_clock_rung_forcing.py. Integrated in origin_theory (new paragraph after the v486 block); ledger row HYP.REWRITE.03 + update note on .02; Python-only (sympy exact), mirrorable, deferred to the next verified engine run.

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• v486_transfer_full_rule.py (HYP.REWRITE.02). The verified seam transfer spectrum is \{1,(2/3)^6,(1/3)^6\} (v54/v221), but the only local generator in the suite (v327) produces \{1,\tfrac23,0\} — its zero mode persists under every power, so no iterate reaches the third mode. [E]UNIQUENESS: for the symmetric 3-channel rule M(s,h)=[[1,0,0],[0,s,h],[0,h,s]] (one absorbing family channel + \Z_2 pair) the survival spectrum is \{s{+}h,s{-}h\}; demanding the PHYSICAL pair \{\tfrac23,\tfrac13\} forces UNIQUELY (\mathrm{stay},\mathrm{hop},\mathrm{leak})=(\tfrac12,\tfrac16,\tfrac13)=(1/|\Z_2|,1/(|\Z_2|\Nfam), 1/\Nfam) — the lazy \Z_2-pair walk, every rate an atom expression (honest direction: spectrum \to rates). [E]SIX-HAND GENERATION: over the order-6=2\Nfam=|R^+(A_3)| hand, \operatorname{eig}(B^6)=\{\tfrac{64}{729},\tfrac1{729}\} exactly — both decay gaps now have one recursive generator: 6\ln\tfrac32 (recovery, v76) and 6\ln3 (subdominant, previously generator-less). [E]SUPERSESSION: the uniform rule's zero mode is power-persistent; its \lambda_2 arity story (\tfrac23=|\Z_2|/\Nfam) is unchanged. [O]the arity \{2,3\} stays the anchor input; the lazy-vs-uniform split is SELECTED by the physical spectrum, not yet first-principles-derived (named candidate: stay =1/|\Z_2| as the sheet-symmetric choice). Discovery provenance: experiments/tfpt-discovery/generator_hunt_full_transfer_rule.py (plus a typed anchor-bilinear coverage inventory — known hits a^TKa{=}41, Koide 53, and the recorded-only \mathbf1^TQa{=}16 — and the lepton-exponent observation (5,3,2)= K-row = atom triple; no unforced claims, v354/v355 discipline). Integrated in origin_theory (new paragraph after the v327 rewrite block); ledger rows HYP.REWRITE.02 + update note on .01; Python-only (sympy exact), mirrorable, deferred to the next verified engine run.