Celestial wp5e eps1 axion slot
v514_celestial_wp5e_eps1_axion_slot.py · frontier
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CELEST.WP5E.EPS1.01: WP5e-epsilon-1 of the celestial-holographic research contract CELEST.SEAM.01 -- 'the O(-2) bulk-axion slot', executed (verdict B): build the s = 0 tower field explicitly, pin lambda~ = 6 as a residue with explicit factor bookkeeping on PT/Z4, and take the first honest back-reaction step (Gibbons-Hawking A3). Exact sympy/Fraction, no floats (34 checks, ~4 s). [E] EQUIVARIANT O(-2) SLOT: pushforward ledger pi_* O(-2) on PT' = tot(O(1)+O(1) -> P^1): per spacetime degree d exactly (d+1)^2 = nullspaces of the wave operator (1, 4, 9, 16, 25, 36 for d = 0..5); the v492 action on the fibre coordinates (mu1, mu2) -> (i mu1, i^-1 mu2), incidence forces column weights (+1, +1, -1, -1); the equivariant bookkeeping closes BLOCK BY BLOCK (all d <= 6, all 4 characters); character series P_0 = 1 + 3t^2 + 15t^4 + 21t^6 + 45t^8 + ..., P_1 = P_3 = 2t + 8t^3 + 18t^5 + ..., P_2 = 6t^2 + 10t^4 + 28t^6 + ...; the d = 0 slot has multiplicity (1, 0, 0, 0) -- THE BULK AXION SURVIVES THE PROJECTION; Molien invariant ring = (1 - t^8)/((1 - t^4)^2 (1 - t^2)) -- Z in O(2), X, Y in O(4), relation degree 8 = the a0 weight (v492/v493 bridge); E3 bijection sharpened: twisted characters {i, -1, -i} with minimal content (2t, 6t^2, 2t) and NO degree-0 mode = the Coxeter eigenvalues on H^2(ALE), det(A-1) = -4; graviton control: the O(+2) slot starts invariant only at fibre degree 4 with multiplicity 3 = {X, Z^2, Y} (the cohomological form of v505 X = -2 != +2 = Y). [E] LAMBDA~ = 6 TRIPLY PINNED: (1) Okubo: Tr_adj X^4 = 36<x,x>^2 = (6<x,x>)^2 on the 240 glue roots, 36 = h_vee + 6, lambda~ = 6 = |Z2| N_fam; (2) measure cancellation: mu = 1/4 enters three times (vertex^2 mu^2, propagator 1/mu, anomaly mu) and cancels EXACTLY -- lambda~_eff^2 = 36 for ARBITRARY mu; wrong bookings quantified and excluded: anomaly-only => lambda~ = 3, missing propagator renormalisation => lambda~ = 12; (3) flux: minimal CPS quantum N = 1, a single exchange channel exactly at k = 1 (#primaries), (kappa/c3)^2 = 36/3 = 12 exact. [E] GH/A3 BACK-REACTION STEP: invariant 4-centre configurations = exactly 2 branches (axis^4 or ONE free mu4 orbit); free orbit => prod(Z - i^p z0) = Z^4 - z0^4 => XY = Z^4 + a0 with a0 = -z0^4 (the v493 family RE-DERIVED from the geometry); monodromy a0 -> e^{2 pi i} a0 = one clock step; the GH point of charge k is EXACTLY R^4/Z_k (k = 4 => seam boundary S^3/Z4); periods int omega = 4 pi (x_q - x_p), free orbit: Pi_j = 4 pi t0 (i-1)(1, i, i^2), |Pi_j| equal (LOCKSTEP, counter-check of v509); the Coxeter clock FROM THE GEOMETRY (A^4 = 1, det(A-1) = -4, Pi.A = i Pi); the CPS 'N log' analogue = source charge 4 = |mu4| (flux -4 pi per centre); HONEST SHARPENING: for the Ricci-flat ALE the asymptotic log coefficient is EXACTLY 0 (EH: u K' = sqrt(u^2 + a^4), det g = 1) -- the log lives at the exceptional locus; Burns contrast (K = u + N log u => det g != 1, only scalar-flat); bonus: multipole selection rule m = 0 mod 4, first symmetry-breaking multipole (4, +-4) carries -a0 with amplitude (35/16) sin^4 th. [E] NEGATIVE CONTROLS: so8 (lambda~^2 = 12 irrational; perfect squares in the Deligne series only {9, 36} = {sl3, e8}); diag(i, i) (Veronese, 5 generators, no hypersurface, the bijection collapses); k = 2 (three channels; honest: lambda~^2 = 36 is k-independent, the kill is the closure dial). [C] conditional on Costello's flat-PT matching lambda_g^2 E = A. [O] the quantised BCOV one-loop coefficient on PT/Z4; the twisted channels (32 T3) are not covered by the bulk axion -- M1-M3 preregistered VERBATIM: M1 the A3 Omega_N on PT/Z4 (success: (2 pi i)^2 periods with lockstep phases; kill: unequal fluxes => the v509 dial dies); M2 the twisted KS measure (success: bulk 36 + sphere axions cancel 32 T3; kill: a leftover T3); M3 the a0 uplift of the (4, +-4) multipole (success: log correction prop 4 = |mu4|; kill: decoupling from the centre count). No marker moves anywhere.
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