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Original ledger classification: Obligation lemma [E] (proof-tree complete) + [C] (routes) + [O] (one residual)

Recorded statement: QGEO.SYM.01 AS ONE PRECISE CONSTRUCTIVE-QFT LEMMA + PROOF-TREE COMPLETENESS (2026-06-18): the formal write-up of the one human math obligation (does NOT close it). LEMMA (constructive-QFT form): let Sigma = P^1 minus mu_4 carry the free…

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QGEO.OBLIG.01

Original ledger classification: Obligation lemma [E] (proof-tree complete) + [C] (routes) + [O] (one residual)

Original claim text

QGEO.SYM.01 AS ONE PRECISE CONSTRUCTIVE-QFT LEMMA + PROOF-TREE COMPLETENESS (2026-06-18): the formal write-up of the one human math obligation (does NOT close it). LEMMA (constructive-QFT form): let Sigma = P^1 minus mu_4 carry the free c=8 RP/OS quasi-free state omega_Sigma with DtN Lambda_Sigma; PREMISE (the one open input, QGEO.SYM.01): the raw seam carries the FLAT tau=i pillowcase metric g_flat (the Troyanov-unique constant-curvature representative, cone angles pi, of the conformal class fixed by the order-4 deck), so Lambda_Sigma = sqrt(-Delta_{g_flat}); CONCLUSION: omega_Sigma o rho = omega_Sigma (the carrier clock is a symmetry of the seam STATE) -> mark-locality -> metric-sector inclusion -> E8. [E] PROOF-TREE COMPLETENESS: the reduction DAG from 'free RP seam' (v155/v175 -> marks v195/v216 -> conformal class tau=i v214/v267 -> Troyanov flat -> commutator all orders v276/Lean -> state-invariance v198/v201/SeamDeckClosure -> mark-locality v210/v264 -> E8 v154/v277) has EXACTLY ONE un-discharged leaf: 'the raw seam state IS the flat g_flat state' (Lambda_Sigma = sqrt(-Delta_flat)). [E] the GEOMETRIC SIDE is fixed (flat DtN diagonal in Fourier modes, rho commutes with any spectral function to all orders, Lean FORM.QGEO.04), so the obligation is STATE-IDENTIFICATION not geometric ambiguity. [C] two proof routes: (i) RP-state uniqueness on the flat tau=i orbifold, (ii) Troyanov + OS reconstruction. [O] one constructive-QFT statement closes QGEO.SYM.01.

Original classification detail

[E] the precise lemma + proof-tree completeness (exactly one open leaf) + the fixed geometric side; [C] the two proof routes; [F] the all-orders step in Lean; [O] the one constructive-QFT residual. The formal obligation write-up; does NOT close QGEO.SYM.01.

Dependencies as recorded

QGEO.SYM.01; QGEO.SYM.02; QGEO.SYM.03; FORM.QGEO.04; QGEO.MARKLOCAL.01; QGEO.PILLOW.01

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  • v279_qgeo_obligation_lemma.pyRegistered verification module · registry
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    QGEO.OBLIG.01 — the QGEO.SYM.01 bedrock written as ONE precise constructive-QFT lemma with a proof-tree completeness check (the formal obligation write-up; does NOT close it). Lemma: given the premise 'the raw seam carries the flat τ=i pillowcase metric g_flat (Troyanov-unique, cone angles π), so Λ_Σ=√(−Δ_flat)', then ω_Σ∘ρ=ω_Σ → mark-locality → E8. [E] the reduction DAG from 'free RP seam' has 8 closed nodes and EXACTLY ONE open leaf ('the raw seam state IS the flat state'); [E] the geometric side is fixed (flat DtN diagonal, ρ commutes to all orders, Lean FORM.QGEO.04), so the obligation is STATE-IDENTIFICATION not geometric ambiguity; [C] two proof routes (RP-state uniqueness on the flat orbifold, or Troyanov + OS); [F] the all-orders step is a Lean theorem (SeamDeckClosure.flat_all_orders_clock, standard axioms, no sorry); [O] one constructive-QFT statement closes QGEO.SYM.01.

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