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A registered result in its source context

Original ledger classification: Identity [I] (finite-model selection theorem + ladder control) + Physical [P] (residue typing)

Recorded statement: CALDERON-SHEET SELECTION THEOREM (which Calderon involutions certify a scalar kernel; the v109 follow-up): on the carrier H = S+ (+) S- the certified bilinear data of an involution eps (eps^2 = 1) are the matrix elements <f, eps g>; the…

Statement, assumptions and sources

Paper context: Architecture, E8 and the electromagnetic fixed point

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CAR.PAIR.02

Original ledger classification: Identity [I] (finite-model selection theorem + ladder control) + Physical [P] (residue typing)

Original claim text

CALDERON-SHEET SELECTION THEOREM (which Calderon involutions certify a scalar kernel; the v109 follow-up): on the carrier H = S+ (+) S- the certified bilinear data of an involution eps (eps^2 = 1) are the matrix elements <f, eps g>; the v109 singlet counts per sheet block (0, 0, 1, 1) give the exact selection statement - (1) SELECTION THEOREM [I] (finite model): a sheet-ODD involution (swapping S+ <-> S-) certifies EXACTLY 1+1 = 2 = |Z2| invariant scalar kernels (one per orientation), a sheet-EVEN involution certifies NONE: 'a scalar two-point datum exists IFF eps is sheet-odd'. (2) THE TWO KERNELS = THE GLUE AMBIGUITY [I]: the kernel count 2 = |Z2| matches exactly the two Lagrangian glues (GLUE.LAGR.01, swapped by single spinor conjugation) - the Calderon scalar channel carries precisely the glue ambiguity, resolved by the same sheet choice. (3) LADDER GENERICITY [I] (anti-overclaim control): for g = 3, 5, 7 the within-sheet zero-weight count is 0 and the cross count is 2^{g-1}; sheet-oddness forces the half-spinor relation K = (g-1)/2, NOT the value g = 5 - the g-selection stays with the independent rank-8/integrality closure (CAR.RANK / CAR.LADDER.01). (4) QBL RESIDUE SPLIT [P] (recorded, not claimed): (a) INTERFACE 'the seam Calderon involution is sheet-odd' - structurally natural, because the one-sided collar / double-cover deck is the SAME |Z2| that halves c3 = 1/(2 x 4pi) (exchanging cover sides is sheet-odd by construction); (b) ANALYTIC CORE 'the two-point kernel certifies only slot-degrees <= 2' - the genuine locality statement. Two named parts; proving both closes QBL => K=2 <=> g=5

Original classification detail

Identity: scalar kernel exists iff involution is sheet-odd; 2 = |Z2| kernels = glue ambiguity; QBL residue split into interface + analytic core

Dependencies as recorded

CAR.PAIR.01; CAR.LADDER.01; ARCH.QUAD.01 (QBL); GLUE.LAGR.01 (two glues); GATE.METRIC.07 (sheet Z2)

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Registered verification modules

  • v110_calderon_sheet.pyRegistered verification module · registry
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    CALDERÓN-SHEET SELECTION THEOREM (the v109 follow-up): the certified bilinear data of a Calderón involution ε (ε²=1) on H = S⁺⊕S⁻ are ⟨f, εg⟩; with the v109 singlet counts per sheet block (0,0,1,1) the exact statement is 'a scalar two-point datum exists ⟺ ε is sheet-odd' — sheet-odd certifies exactly 1+1 = 2 = |ℤ₂| invariant kernels (one per orientation), sheet-even certifies NONE; THE TWO KERNELS = THE GLUE AMBIGUITY: 2 = |ℤ₂| = the two Lagrangian glues (v92) — the Calderón scalar channel carries exactly the glue ambiguity, resolved by the same sheet choice; LADDER GENERICITY (anti-overclaim): for g = 3,5,7 sheet-oddness forces the half-spinor relation K = (g−1)/2, NOT g=5 — the g-selection stays with rank-8/integrality (v14/v108); QBL residue split into two named parts [P]: (a) interface 'the seam Calderón involution is sheet-odd' (natural: the one-sided collar / double-cover deck is the SAME ℤ₂ that halves c₃ = 1/(2·4π)), (b) analytic core 'the 2-point kernel certifies only slot-degrees ≤ 2'

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