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Original ledger classification: Physical/operator [O] (open constructive obligation)

Recorded statement: THE SEAM CALDERON-KERNEL OBLIGATION (genuine open obligation 2 of 2; the structural residual of the theory, NOT a finite computation): the RAW RP seam Calderon operator must equal the mu4-equivariant free c=8 gapped one-particle…

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QGEO.KERNEL.01

Original ledger classification: Physical/operator [O] (open constructive obligation)

Original claim text

THE SEAM CALDERON-KERNEL OBLIGATION (genuine open obligation 2 of 2; the structural residual of the theory, NOT a finite computation): the RAW RP seam Calderon operator must equal the mu4-equivariant free c=8 gapped one-particle contraction on that boundary AS AN OPERATOR (C_Sigma = U^{-1} C_mu4 U), not merely as the same spectral list. Rails already laid: the DtN/Calderon symbol is universally |k| (free chiral dispersion, v156); a scalar seam datum exists iff the Calderon involution is sheet-odd (v110); the free c=8 fixed point is isolated with no relevant/marginal drift (v158); mu4-equivariance diagonalises the transfer in the cusp basis with weights {0,1/3,2/3} => spectrum {1,(2/3)^6,(1/3)^6} (v162); the fixed space is the rank-8 Calderon polarisation K_Sigma (v113). Proof route: conformal collar normal form (same principal Calderon symbol as the standard mu4 collar) + sheet-odd selection + no-lower-order-drift (c=8 rigidity) + mu4 diagonalisation + rank-8 identification. Given QGEO.KERNEL.01, the net side closes via QGEO.NET.01 (v154/v175, [E]). The operator identity from RAW seam data is NOT a finite computation; left honestly OPEN

Original classification detail

Open [O]: raw RP seam Calderon kernel = the mu4-equivariant free gapped contraction as an operator (one of the two genuine obligations)

Dependencies as recorded

QGEO.TREE.01; QGEO.NET.01; GATE.METRIC.13; GATE.METRIC.18; v110; v113; v156_seam_net_construction.py; v158_fixed_point_stable.py; v162_seam_transport_identification.py

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Registered verification modules

  • v177_seam_marking_kernel.pyRegistered verification module · registry
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    the QGEO proof tree — the v176 'one realisation premise' split into its honest constituents: REALIZE = MARKS · UNIFORM · COHOM · MODULE · KERNEL · NET, with FOUR nodes closed CONSTRUCTIVELY as [E] and the open residual sharpened into exactly TWO named obligations. [E] UNIFORM (Lemma 2, constructive): an order-4 Möbius map conjugates to z↦iz, a non-fixed orbit scales to μ₄, the reflection z↦1/z gives στρτ=ρ⁻¹ (D4 order 8) — a genus-0 4-marked faithful-D4 boundary IS (ℙ¹,μ₄); [E] COHOM: ρ*ωk=i^kωk so the H¹ grading is (1,2,3)=A3 exponents=Spec(Q₊); [E] MODULE: the H¹→generation iso is UNIQUE (multiplicity-free + residue normalisation; reflection ω1↔ω3, ω2 fixed); [E] NET (v154/v175): index-4 μ₄ extension of (D5)₁⊗(A3)₁ = (E8)₁. The TWO genuine open obligations [O]: QGEO.MARKS.01 (raw seam → genus-0 four-marked D4 boundary) and QGEO.KERNEL.01 (raw seam Calderón kernel = the μ₄-equivariant free gapped contraction as an OPERATOR). Removes the near-circular v176 framing (which took the marks as a hypothesis); the whole structural residual is now exactly these two doors.

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