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CELEST.WP5E.M3.01: milestone M3 of the celestial-holographic research contract CELEST.SEAM.01 (WP5e back-reaction programme) -- 'the a0 uplift', executed (SUCCESS on the preregistered v514 S8.3 criterion): the (4, +-4) GH multipole uplifted to the twistor-potential kernel chi = log P4 (the log of the v515 family polynomial) with the induced Kahler-potential correction. Exact sympy, no floats (23 checks, ~7 s). [E] KERNEL BRIDGE: the O(2) section is a NULL coordinate -- Laplacian(3d) G(eta_p) = 0 identically for an ARBITRARY kernel G (the uplift is well-typed); RESIDUE IDENTITY d_x [transform(log eta_p)] = 1/r_p EXACTLY (residue 1/(2r) at zeta_-): the GH potential V = sum_p 1/r_p IS the x-derivative of the contour transform of chi; flux -4 pi per centre, total source charge 4 = |mu4| (the V-ledger matched). [E] FOUR COUPLED CENTRE-COUNT SCALES: (1) asymptotic kernel log chi = 4 log eta + a2/eta^2 + (a0 - a2^2/2)/eta^4 + ... -- LOG COEFFICIENT 4 = |mu4| = centre count (the CPS 'N log' analogue at kernel level); at the clock-fixed seam fibre zeta = 0 the a2 slot closes and the first correction is EXACTLY a0/eta^4 = the (4, +-4) multipole in kernel clothes; exact m-grading (the term zeta^k/eta^4 carries field charge m = 4 - k: m = +-4 pieces PURE a0, m = 0 piece -6 t0^4 phi0-free -- the U(1) -> Z4 breaking sits exclusively in the a0 pieces); NO log x power terms in the Laurent tower (the v514 honest zero -- no asymptotic METRIC log -- is preserved); (2) the once-integrated GLT kernel sum_p eta_p log eta_p = 4 eta log eta + p_4/(12 eta^3) + p_8/(56 eta^7) + ... with p_n = 0 unless n = 0 mod 4 (selection rule at potential level) and p_{4k} = 4 (-a0)^k: EVERY correction carries the prefactor 4 = centre count; (3) the exceptional-locus log chi(eta = 0) = log a0 = 4 log t0 + i(4 phi0 + pi) -- t0-coefficient 4 = |mu4|, clock phase 4i; the modulus response a0 d/da0 chi = a0/(eta^4 + a0) equals 1 AT the exceptional locus and falls off as a0/eta^4 at infinity (no constant, no log): the a0-log lives at the exceptional locus, exactly as v514 S6.3 demanded; (4) periods (v515 consistency): Pi_j(la) LINEAR in t0 (uniform first-order shift, lockstep + phase ratios (1, i, i^2) preserved exactly); d log Pi_j / d log a0 = 1/4 = 1/|mu4| uniformly; integrated over the a0 circle: monodromy e^{2 pi i/4} = i = ONE Coxeter clock step (the v493 monodromy REPRODUCED from the perturbative period shift; the finite monodromy is the cyclic centre permutation q_p -> q_{p+1}); node la-support t0-FREE (the Z8 seam bridge is a0-rigid); all 6 pair discriminants ~ t0^2 != 0 (K4 connectivity: the forced uniform flux vector persists); the BM kernel is modulus-free with int_{S^3} K = (2 pi i)^2 (the quantised fluxes cannot move). [E] NEGATIVE CONTROLS: the (4, 0) multipole is phi0-independent in V AND in the kernel (-6 t0^4): clock-invariant, breaks nothing; Z2/Eguchi-Hanson analogue: EVERY dial reads 2 = |Z2| ((2, +-2) amplitude (3/2) sin^2 th, kernel log 2, exceptional log 2 log t0, period response 1/2, monodromy -1 = the Z2 clock); wrong centre counts k = 3, 5: kernel log coefficient k, modulus slot O(6)/O(10) != O(8) -- the observable MOVES with the centre count; forbidden family Z^4 - Z: p3 = 3 != 0 (selection rule broken), e4 = 0 (no a0-log at the exceptional locus) -- fails BOTH uplift dials. [C] THE GLT DICTIONARY: 'eta_p log eta_p = THE GH Kahler-potential kernel' is the generalized-Legendre-transform dictionary (Lindstrom-Rocek / Ivanov-Rocek), typed [C]. [O] the full nonlinear Kahler potential of the resolved A3 ALE (no closed form exists); the quantised BCOV coefficient stays with the delta-1 strand; SEAM.EQUIV.TWISTOR.01 untouched. VERDICT: SUCCESS -- the log-type correction delivered on four coupled dials (kernel log 4, exceptional-locus log 4 log t0, tower prefactor 4, period response 1/4 -> monodromy i), every one tied to the centre count (EH: 2, k-orbit: k); the KILL branch (decoupling from the centre count) does NOT fire; NO marker moves anywhere.

Linked claims

CELEST.WP5E.M3.01

Paper sections

Source section 1Source section 2Source section 3Source section 4Source section 5Source section 6Source section 7Source section 8Source section 9Source section 10Source section 11Source section 12Source section 13Source section 14Source section 15Source section 16Source section 17Source section 18Source section 19