A registered result in its source context
Original ledger classification: Numerical experiment [E] (geometric chain) + [C] (RP-state) + [O] (premise)
Recorded statement: FLAT tau=i PILLOWCASE DtN EXPERIMENT (2026-06-18): a direct numerical experiment on the actual seam orbifold, realising the QGEO chain on the geometric side (does NOT prove the premise). [E] the pillowcase = the Z2-even sector of the flat…
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Paper context: Research contracts
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QGEO.STEKLOV.01
Original ledger classification: Numerical experiment [E] (geometric chain) + [C] (RP-state) + [O] (premise)
Original claim text
FLAT tau=i PILLOWCASE DtN EXPERIMENT (2026-06-18): a direct numerical experiment on the actual seam orbifold, realising the QGEO chain on the geometric side (does NOT prove the premise). [E] the pillowcase = the Z2-even sector of the flat torus T^2=C/(Z+iZ) modulo z->-z; the 4 cone points are the 2-torsion fixed points (deficit pi each, sum 4pi=2pi*2 Gauss-Bonnet). [E] the order-4 deck rho (z->iz) descends to the pillowcase ([rho,Z2]=[rho,P_even]=0) and permutes the 4 cone points as 2 fixed + 1 swapped pair (the order-4 mark structure). [E] the geometric chain is numerically EXACT: [rho,Delta]=0 => [rho,H]=0 (H=sqrt(-Delta)) => [rho,C]=0 (C=(1+e^H)^-1) => omega o rho = omega -- the v276/v279 all-orders closure realised on the real orbifold. [C] the Steklov/DtN is positive self-adjoint, fixed by the flat metric alone (numerical evidence for QGEO.OBLIG.01 route (i), RP-state uniqueness). [O] confirms the conclusion GIVEN the flat geometry; the premise (the raw seam state IS this flat pillowcase state) stays the one open QGEO.SYM.01 input.
Original classification detail
[E] the pillowcase orbifold + order-4 orbit + the exact geometric chain omega o rho = omega numerically realised; [C] the RP-state is metric-determined (route-(i) evidence); [O] the premise stays open. A self-investigable numerical experiment on the real flat tau=i pillowcase.
Dependencies as recorded
QGEO.SYM.01; QGEO.SYM.03; QGEO.OBLIG.01; QGEO.PILLOW.01; QGEO.MARKS.03
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- Research contracts
Sections that explicitly cite this claim
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- 2026-06-18 (self-investigation round: pillowcase DtN, modular data, the E8-at- [formula in source] unification, live scorecard, v280– v283)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- Honest statusinput 4 origin theory
- 2026-06-18 (the two proof routes decomposed: Route (i) and Route (ii) into lemma chains, v284/ v285)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- Honest statusorigin theory
- Honest statusOrigin Theory
- 2026-06-18 (closing sprint: the Seam Equivalence Theorem named + both routes attacked, v286– v288)Research changelog; TFPT — Introduction and reading guide
- 2026-07-21 (XIII) ( v503 — the v215 deferred emergence test (lever 7) executed light and promoted as QGEO.EMERGE.LIGHT.01: NO dynamical selection of the square modulus — the free field's global [formula in source] winner is the hexagonal torus, [formula in source] is a saddle, criticality at the square is Palais symmetry; the square is pinned by rigidity alone (the raw DtN is mod- [formula in source] block-diagonal iff [formula in source] , an isolated zero); and the residual converges: QGEO-R1 [formula in source] P2-R1 [formula in source] one common rest, ``why does the raw seam carry the order- [formula in source] clock''; Wolfram extension [formula in source] (verified engine run); NO marker moves — QGEO.REALIZE.01 stays / , AX.P2.01 stays a declared axiom)Research changelog; TFPT — Introduction and reading guide
- Honest statusinput 4 origin theory
All 10 linked sections
Registered verification modules
- v280_pillowcase_steklov.pyRegistered verification module · registry
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QGEO.STEKLOV.01 — a direct numerical experiment on the flat τ=i pillowcase orbifold (the seam geometry): the self-investigable test of the QGEO.SYM.01 obligation (does NOT prove the premise). [E] pillowcase = Z2-even sector of the flat torus, 4 cone points (2-torsion, deficit π each, sum 4π=2π·2 Gauss-Bonnet); [E] the order-4 deck ρ (z→iz) descends ([ρ,Z2]=[ρ,P_even]=0) and permutes the 4 cone points as 2 fixed + 1 swapped pair; [E] the geometric chain is exact: [ρ,Δ]=0 ⇒ [ρ,H]=0 (H=√(−Δ)) ⇒ [ρ,C]=0 (C=(1+e^H)⁻¹) ⇒ ω∘ρ=ω (the v276/v279 all-orders closure on the real orbifold); [C] the Steklov DtN is positive self-adjoint, fixed by the flat metric (route-(i) evidence for RP-state uniqueness); [O] confirms the conclusion given flat geometry, the premise stays open.
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