A registered result in its source context
Original ledger classification: Synthesis/reduction [E]/[O] (keystone-as-one-theorem)
Recorded statement: THE SEAM KEYSTONE AS ONE CITABLE THEOREM (2026-06-22): the raw seam state is the flat tau=i pillowcase state, with EXACTLY ONE open lemma. Assembles the keystone pieces into one statement -- IF (raw RP-collar seam state = flat tau=i…
Statement, assumptions and sources
Paper context: Origin Theory
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QGEO.KEYSTONE.01
Original ledger classification: Synthesis/reduction [E]/[O] (keystone-as-one-theorem)
Original claim text
THE SEAM KEYSTONE AS ONE CITABLE THEOREM (2026-06-22): the raw seam state is the flat tau=i pillowcase state, with EXACTLY ONE open lemma. Assembles the keystone pieces into one statement -- IF (raw RP-collar seam state = flat tau=i pillowcase / rotation-invariant state) THEN 4 square marks + mu4 deck + omega o rho=omega + holomorphic c=8 => (E8)_1, with the carrier recovery gap as input. [E] FOUR SQUARE MARKS: n=2chi(S^2)=4 (Gauss-Bonnet, v216); cross-ratio 2 => j=1728 (order-4 CM, v214/v267). [E] FLAT PILLOWCASE: S^2(2,2,2,2), chi_orb=2-4(1-1/2)=0 => flat tau=i (Troyanov). [E] MU4 FINGERPRINT: DtN sub-principal at m=0 mod 4 (v201/v280). [E] HOLOMORPHY SELECTOR: det Cartan(E8)=1 vs D8=4 (v83/v143/v308). [E] INPUT GAP: Delta=6 ln(3/2)>0 (v76/v302). [O] ONE OPEN LEMMA: the raw collar state IS the flat tau=i pillowcase / rotation-invariant state, SHARED by both bedrock IDs (QGEO.SYM.01, SEAM.EQUIV.01; v323), machine-pinned in Lean (FORM.SEAMEQUIV.01 + FORM.QGEO.BW.01). An assembly/reduction certificate (like v176/v261), NOT a closure.
Original classification detail
[E] the assembled keystone theorem with all exact pieces machine-checked (marks=4, j=1728, chi_orb=0, det Cartan E8=1, gap>0, mod-4 fingerprint); [O] the single open lemma (raw seam = flat tau=i pillowcase / rotation-invariant state) shared by both bedrock IDs and Lean-pinned. An assembly certificate (like v176/v261), does NOT close the bedrock.
Dependencies as recorded
QGEO.SYM.01; SEAM.EQUIV.01; QGEO.BW.01; v214; v216; v280; v308; v323; v76
Open the original ledger source, row 424Location recorded in the ledger
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- Origin Theory
Sections that explicitly cite this claim
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- 2026-06-22 (next-steps round: the keystone collapsed to one shared premise (Lean [formula in source] one citable theorem), the [formula in source] solver suite, the cusp weight derived from a minimal rewrite, and the [formula in source] pressure point: FORM.QGEO.BW.01, v325, v326, v327, v328)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- Honest statusinput 4 origin theory
- 2026-06-22 (keystone unification + status reframe: ONE open theorem, ONE decoupled foreign problem: v335, FORM.QGEO.BW.01 qgeoSymIsCorollary)Research changelog; TFPT — Introduction and reading guide
- Honest statusorigin theory
- Honest statusOrigin Theory
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Honest statusinput 4 origin theory
Registered verification modules
- v325_pillowcase_keystone.pyRegistered verification module · frontier
Read the description recorded in the module registry
The seam keystone as ONE citable theorem: the raw seam state is the flat tau=i pillowcase state, with EXACTLY ONE open lemma. IF (raw RP-collar seam state = flat tau=i pillowcase / rotation-invariant state) THEN 4 square marks + mu4 deck + omega o rho=omega + holomorphic c=8 => (E8)_1, with the carrier recovery gap as input. Pieces (all exact): n=2chi(S^2)=4 (v216); cross-ratio 2 => j=1728 (v214/v267); flat orbifold S^2(2,2,2,2), chi_orb=0 (Troyanov); DtN sub-principal at m=0 mod 4 (v201/v280); det Cartan(E8)=1 vs D8=4 (v83/v143/v308); gap 6 ln(3/2)>0 (v76/v302). The ONE open lemma -- the raw collar state IS the flat tau=i pillowcase / rotation-invariant state -- is SHARED by both bedrock IDs (QGEO.SYM.01, SEAM.EQUIV.01; v323), machine-pinned in Lean (FORM.SEAMEQUIV.01 + FORM.QGEO.BW.01). An assembly/reduction certificate (like v176/v261), not a closure.
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