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A registered result in its source context

Original ledger classification: Identity [I] + Physical [P] (sector id)

Recorded statement: Anchor-placement splitting trichotomy - the clean rational double cover is NON-GENERIC (anchor-first hardening) [I] + [P] (sector id). The splitting-type exponents (2,1,1) (= the anchor (1,1,2); v32 splitting O(-2)+O(-1)^2) placed across…

Statement, assumptions and sources

Paper context: Standard Model and flavor structure

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FLAV.PENCIL.04

Original ledger classification: Identity [I] + Physical [P] (sector id)

Original claim text

Anchor-placement splitting trichotomy - the clean rational double cover is NON-GENERIC (anchor-first hardening) [I] + [P] (sector id). The splitting-type exponents (2,1,1) (= the anchor (1,1,2); v32 splitting O(-2)+O(-1)^2) placed across the three family slots give three DIFFERENT covers: (1,1,2) heavy-in-fam3 (lepton) det B(K+xQ)=(3x+2)(3x+5) disc=81=N_fam^4 -> SPLIT (individually rational branch labels {2,5}); (2,1,1) heavy-in-fam1 det B=(x+2)(9x+11) disc=49=scalaron^2 -> SPLIT; (1,2,1) heavy-in-fam2 det B=5x^2+10x+3 disc=40=|R(D5)|=det B(L) -> NON-SPLIT (Galois-conjugate IRRATIONAL branch points -1 +/- sqrt(10)/5, centered EXACTLY on the sheet x=-1 (q=3), separation 2 sqrt(A_Lambda)). The three discriminants are themselves compiler atoms (N_fam^4, scalaron^2, |R(D5)|). Negative control (cf. v81): the R-pencil disc=153 is not a square either => Koide & carrier as SEPARATE RATIONAL singularities is a special feature of the canonical anchor placement, not generic. Restates the basis-invariant core T=3 B(Q)^-1 B(K)=[[5,11/3],[0,2]] (Spec{2,5}, tr=7=scalaron, det=10=A_Lambda). The physical fermion-sector identification of the placements is NOT claimed and stays [P]

Original classification detail

Identity [I] (discriminant trichotomy, non-genericity, negative control) + [P] (physical sector identification of the placements)

Dependencies as recorded

FLAV.PENCIL.02; FLAV.PENCIL.03; v32; v80; v81

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Registered verification modules

  • v82_koide_attractor_splitting.pyRegistered verification module · frontier
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    Koide attractor FORCED, not postulated: the branch-preserving map fixing q=2,5 is unique, and its multiplier (2/3)⁶ = the established transfer gap λ₂ (v54/56) ⇒ 3 Koide postulates → 1; + splitting trichotomy disc 81/49/40 (clean split is non-generic)

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