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Original ledger classification: Open (research route [O]: the Costello-Li construction; preparation [E]/[C] via the CELEST.SEAM.01 work packages v492-v518)

Recorded statement: THE TWISTOR ROUTE OF THE SEAM EQUIVALENCE TARGET (2026-07-22 route split, the second continuum route named in its own right -- an ID restructuring, NO status change in substance): the open Costello-Li-grade construction -- the interacting…

Statement, assumptions and sources

Paper context: TFPT — Introduction and reading guide

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SEAM.EQUIV.TWISTOR.01

Original ledger classification: Open (research route [O]: the Costello-Li construction; preparation [E]/[C] via the CELEST.SEAM.01 work packages v492-v518)

Original claim text

THE TWISTOR ROUTE OF THE SEAM EQUIVALENCE TARGET (2026-07-22 route split, the second continuum route named in its own right -- an ID restructuring, NO status change in substance): the open Costello-Li-grade construction -- the interacting holomorphic open+closed twistorial algebra on PT/Gamma (the global BCOV+SDYM quantisation, WP5e proper of CELEST.SEAM.01) whose boundary partition function is E4/eta^8 INCLUDING the q^{-1/3} prefactor, OS-reconstructed to the ACTUAL (E8)_1 seam net (not only its character). PREPARED, NOT CONSTRUCTED: the CELEST.SEAM.01 work packages (v492-v518) fix the null ideal, the deleting operator, the GNS limit state, the two-interval index, the KLM triple, both faces of the inflow, the level (a theorem of clock invariance, value pinned by the sector counter), the bulk-axion slot, the back-reacted Omega_N (M1, v515: closed form, (2 pi i)^2-integral lockstep periods, forced source charge 4 = |mu4|), the twisted KS measure on the declared completion reading (M2, v516: per-sector Okubo squares, the 32 T3 cancelled, psi = 64 supplied) and the a0 uplift (M3, v517: log correction coupled to the centre count on four scales); the delta-1 chain is DECIDED by v518 (CELEST.WP5E.DELTA1.01: the derived chiral measure kills the delta-1 route; the stated v516 tension -- declared vs derived measure -- is the sharp named [O] the global quantisation must resolve); the global quantisation and the OS/real-structure bridge (WOIT.OS.TWISTOR.01) stay open. [O] throughout; nothing executed so far moves it; the parent SEAM.EQUIV.01 stays [O] as an unconditional claim. UPDATED 2026-08-27 (v973): the declared measure is RIGID on the computable sector -- an 18-parameter deformation of the declared measure data (contact normalisation, 4 sector weights, residue normalisation, 4 linking charges, 4 centre positions) with 4 gauge directions has executed-constraint Jacobian ranks C1 clock 9 / C2 lockstep+integrality 8 / C3 charge 2 / C4 null-ideal 2, joint rank 13 => the moduli kernel is EXACTLY 1 = the uniform sector-weight shift dv = (1,1,1,1), mapping to the untwisted Okubo square Q0 = 36(1,2,1,0,0) and annihilated by every executed certificate functional BY CONSTRUCTION (exactly flat to all orders); ablation ledger (full,-C1,-C2,-C3,-C4,-C1&C2) = (1,3,1,2,3,10); byproduct Phi_P = 3 Phi_T5 + (9/4) Phi_T3 on the deformation image. HONEST: this is sector-level rigidity, NOT a BCOV derivation -- the computable sector is the finite v508/v515 shadow, C4 pins level sets of EXECUTED functionals only, and the W2:W13 = 4:3 Harvey-Moore tester is typed NOT-TRANSCRIBABLE; the global quantisation stays the open closure condition; status UNCHANGED [O].

Original classification detail

Open [O]: the twistor/Costello-Li route of SEAM.EQUIV.01; the CELEST.SEAM.01 work packages are preparation; closes only with the global BCOV quantisation + the WOIT.OS.TWISTOR.01 bridge

Dependencies as recorded

SEAM.EQUIV.01; CELEST.SEAM.01; WOIT.OS.TWISTOR.01; CELEST.WP1.01; CELEST.WP4.01; CELEST.WP5A.01; CELEST.WP5B.01; CELEST.WP5C.01; CELEST.WP5D.01; CELEST.WP5DB.01; CELEST.WP5E.ALPHA.01; CELEST.WP5E.BETA.01; CELEST.WP5E.GAMMA.01; CELEST.WP5E.DELTA2.01; CELEST.WP5E.EPS2.01; CELEST.WP5E.EPS1.01; CELEST.WP5E.M1.01; CELEST.WP5E.M2.01; CELEST.WP5E.M3.01; CELEST.WP5E.DELTA1.01

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Registered verification modules

  • v492_celestial_z4_orbifold.pyRegistered verification module · frontier
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    CELEST.WP1.01: WP1 of the celestial-holographic research contract CELEST.SEAM.01 -- the E8 mu4-glue grading (v128) IS the flat Z4 monodromy of the glue-equivariant celestial chiral algebra on the A3 ALE space C^2/Z4 (Bittleston-Homans-Sharma, arXiv:2305.09451, the Z2/Eguchi-Hanson case; Kronheimer-Nakajima flat connection). [E] inner grading: h = (2,2,2,2,2;0^4) reads the glue class mod 4 on all 240 roots => glue = Ad(exp(2 pi i h/4)) = flat Z4 monodromy; A3-side h' = (0^5;1,1,1,-3) = the diagonal (1,1) glue of Z4 x Z4 (v92/v125); Z2 halfway 120 = SO(16) / 128 = spinor. [E] C^2/Z4 IS the A3 singularity XY = Z^4 (Molien + Hilbert (1+t^4)/((1-t^2)(1-t^4)) exact). [E] equivariant SDYM(E8) sector closes: D[d] = 60(d+1) even / 64(d+1) odd -- works ONLY because dim g_j = (60,64,60,64); zero modes = carrier D5+A3+Cartan = 60; density 1/4 = 1/|Z4|. [E] (E8)_1 character = sum of the 4 glue-coset sectors (1+248q+4124q^2+34752q^3, v377); sector weights = the v92/v125 discriminant form (5x^2+3y^2)/8; glue diagonal h = (0,1,1,1) integer = local extension. [E] correction: the A3 deck acts on the celestial sphere as z -> -z (order 2); the order-4 clock z -> iz is the U(2) phase diag(i,1) (normalises the deck, det = i rotates omega by the mu4 generator), spin bridge (spin clock)^2 = deck, Z8 with 8 = 2|mu4|. [E] clock-invariant A3 deformation = 1-parameter XY = Z^4 + a0, branch points = ONE mu4 orbit, cross-ratio 2 (v168/v214 pillowcase). [E] negative controls: diag(i,i) killed 3 ways; false glue breaks additivity 3112/6720; rigidity = Aut(Z4). [C] verdict B: match under the ONE named identification clock^2 = deck. [O] structural arithmetic only -- no celestial duality constructed; CELEST.SEAM.01 stays a research contract; SEAM.EQUIV.01 stays [O]. Exact (sympy).

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