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Original ledger classification: Decomposition [E] (chain + L3/L4/L5) + [C] (L1 literature) + [O] (L2 Flat-Away)

Recorded statement: RAW MARK-LOCALITY DECOMPOSITION (2026-06-18): decompose the ONE remaining Route-B residual after v288 ('why is the raw seam sub-principal term mark-local?') into an explicit 5-lemma chain, discharge the four standard/established lemmas and…

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MARKLOCAL.RAW.01

Original ledger classification: Decomposition [E] (chain + L3/L4/L5) + [C] (L1 literature) + [O] (L2 Flat-Away)

Original claim text

RAW MARK-LOCALITY DECOMPOSITION (2026-06-18): decompose the ONE remaining Route-B residual after v288 ('why is the raw seam sub-principal term mark-local?') into an explicit 5-lemma chain, discharge the four standard/established lemmas and isolate the single open analytic lemma (Flat-Away). The best closing lever for Route B; does NOT close mark-locality. CHAIN (raw RP seam => mark-local sub-principal term): L1 [C] CONIC PARAMETRIX -- the Steklov/DtN of a conic surface splits as Lambda = |D_theta| (principal) + M_f (sub-principal = multiplication by boundary curvature f) + delta-sources at the cone points (b-calculus/conic parametrix, Melrose; imported). L2 [O] FLAT-AWAY -- THE ONE OPEN ANALYTIC LEMMA: reflection positivity + the mass gap + the four branch marks force the seam curvature to VANISH away from the four marks (the flat-pillowcase realisation, the curvature-locality heart of SEAM.EQUIV.01). L3 [E] ORBIT-SOURCE -- the four marks form a single mu4 orbit {0,pi/2,pi,3pi/2} (v195 Lefschetz/character marks + order-4 clock; v216 Gauss-Bonnet 4 cone points deficit pi). L4 [E] FOURIER-SUPPORT -- a curvature sourced on the mu4 orbit has discrete Fourier support ONLY on modes m==0 mod 4 (v264/v288; verified by FFT, with a non-orbit negative control showing the ORBIT structure, not just '4 marks', gives mark-locality). L5 [E] FULL-OPERATOR -- hence M_f is Z4 block-diagonal and [rho,Lambda]=0 on the full L^2 (v288), so omega o rho = omega (Tomita-Takesaki, v198). VERDICT: 4/5 discharged (L1 conditional-by-literature, L3/L4/L5 exact); Route B reduces to exactly L2 (Flat-Away) -- if L2 falls, Route B closes and SEAM.EQUIV.01 needs only the holomorphy half (Route A).

Original classification detail

[E] the chain typing + L3 (orbit) + L4 (Fourier support) + L5 (full operator); [C] L1 (conic parametrix, literature); [O] L2 (Flat-Away), the single open analytic lemma. A finer decomposition of the v288 residual, NOT a closure.

Dependencies as recorded

SEAM.EQUIV.B01; SEAM.EQUIV.01; QGEO.ENERGY.03; QGEO.SUBPRIN.01; FORM.QGEO.04

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Registered verification modules

  • v289_marklocal_raw.pyRegistered verification module · frontier
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    MARKLOCAL.RAW.01 — decompose the ONE remaining Route-B residual ('why is the raw seam sub-principal term mark-local?') into a 5-lemma chain and isolate the single open analytic lemma. [C] L1 conic parametrix: conic Steklov DtN = |D_θ| + M_f + cone sources (b-calculus/Melrose, imported); [O] L2 FLAT-AWAY — the one open analytic lemma: RP+gap+4 marks ⇒ curvature vanishes away from the marks (the flat-pillowcase realisation); [E] L3 orbit-source: the 4 marks form one μ4 orbit (v195/v216); [E] L4 Fourier-support: μ4-orbit curvature ⇒ support only on 4ℤ (v264/v288, FFT, with a non-orbit negative control); [E] L5 full-operator: ⇒ [ρ,Λ]=0 on full L² (v288). 4/5 discharged; Route B reduces to exactly L2 — if it falls, Route B closes and SEAM.EQUIV.01 needs only the holomorphy half (Route A).

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