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Original ledger classification: Reduction certificate [E] (five steps established) + [O] (the one realisation premise)

Recorded statement: THE SEAM COLLAR REALISATION THEOREM, ASSEMBLED AS ONE CENTRAL STATEMENT + REDUCTION CERTIFICATE (the single structural proof obligation of the whole theory, formulated cleanly; NOT a fabricated proof): THEOREM -- given (1) an oriented…

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QGEO.REALIZE.02

Original ledger classification: Reduction certificate [E] (five steps established) + [O] (the one realisation premise)

Original claim text

THE SEAM COLLAR REALISATION THEOREM, ASSEMBLED AS ONE CENTRAL STATEMENT + REDUCTION CERTIFICATE (the single structural proof obligation of the whole theory, formulated cleanly; NOT a fabricated proof): THEOREM -- given (1) an oriented one-sided RP seam collar, (2) a sheet-odd Calderon involution, (3) quasi-free one-particle seam data with gap (2/3)^6, (4) a faithful D4 action on the boundary marks, (5) four parabolic marks with mu4 character decomposition, (6) an admissible c=8 boundary net, THEN the conformal boundary of the seam collar is Moebius-equivalent to P^1 minus mu4, its H^1 character basis is canonically the generation basis with grading (1,2,3), the seam Calderon contraction is the rank-8 K_Sigma polarisation, and the index-4 simple-current extension is (E8)1. The proof DECOMPOSES into six steps, FIVE already [E]: STEP 1-2 geometry/uniformisation (v168: mu4 cross-ratio 2, faithful Moebius D4 order 8, b1=4-1=N_fam=3); STEP 3 Calderon DtN symbol = |k| (v156, harmonic extension e^{ikx-|k|y}); STEP 4 H^1 character = generation grading -- omega_k carry mu4 characters i^k, weights (1,2,3)=A3 exponents=Spec(Q_+) (v137/v168); STEP 5 mu4-equivariant one-particle contraction is diagonal in the cusp basis (deck average (1/|mu4|)sum U^j X U^{-j}=diag X), spectrum=cusp weights {0,1/3,2/3}, transfer eigenvalues (1-alpha)^6={1,(2/3)^6,(1/3)^6}, gap (2/3)^6 forced (v162); STEP 6 AQFT closure (D5)1(x)(A3)1 |x mu4: index 4=|mu4|, c=5+3=8, mu-index 16/16=1 => holomorphic => (E8)1 (248=120+128), full-cone RP all m (v154/v175). THE ONE OPEN PREMISE [O] (QGEO.REALIZE.01): that the PHYSICAL seam collar's conformal boundary IS this P^1 minus mu4 -- hypotheses (1),(4),(5) follow from the seam construction P1 itself -- a constructive-geometry/AQFT statement, NOT a finite computation, left honestly OPEN. NET: the whole structural residual of the theory reduces to this single realisation premise; everything else in the central theorem is machine-verified

Original classification detail

Reduction certificate [E]/[O]: the central theorem reduces to ONE open realisation premise (QGEO.REALIZE.01); five of six steps are [E]

Dependencies as recorded

QGEO.REALIZE.01; QGEO.RIGID.01; GATE.METRIC.13; GATE.METRIC.18; QFT.NETRP.01; v137_qplus_cohomology.py; v156_seam_net_construction.py; v162_seam_transport_identification.py; v168_qgeo_rigidity.py; v175_net_existence_full_cone.py

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Registered verification modules

  • v176_seam_collar_realisation.pyRegistered verification module · registry
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    the Seam Collar Realisation Theorem assembled as ONE central statement + reduction certificate (the single structural proof obligation of the theory, formulated cleanly — NOT a fabricated proof): the theorem 'the seam collar's conformal boundary is ℙ¹∖μ₄ with H¹ grading (1,2,3), Calderón contraction = rank-8 K_Σ, index-4 extension = (E8)₁' decomposes into six steps, FIVE already [E] — geometry/uniformisation (v168: cross-ratio 2, faithful Möbius D4 order 8, b₁=N_fam=3), Calderón DtN symbol |k| (v156), H¹ character = generation grading (1,2,3)=A3 exponents=Spec(Q₊) (v137/v168), μ₄-equivariant one-particle contraction diagonal in the cusp basis with gap (2/3)⁶ (v162), AQFT closure (D5)₁⊗(A3)₁⋊μ₄=(E8)₁ + full-cone RP all m (v154/v175) — so the WHOLE structural residual reduces to EXACTLY one open premise: that the physical seam collar's conformal boundary IS this ℙ¹∖μ₄ (QGEO.REALIZE.01), a constructive-geometry statement left honestly OPEN.

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