Celestial wp5e delta2 tensor ledger
v511_celestial_wp5e_delta2_tensor_ledger.py · frontier
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CELEST.WP5E.DELTA2.01: WP5e-delta-2 of the celestial-holographic research contract CELEST.SEAM.01 -- 'the full-tensor ledger', the named escape route of the v508 exchange no-go, executed (intermediate verdict, exact): does the FULL adjoint tensor structure of e8 (non-Cartan external legs, higher-arity vertices) open a sphere-axion channel to the rigid 32 T3 residual of the Atiyah-Bott ledger (A_fix = (9, -30, -15, 0, 32) in (P1, P2, P3, T5, T3), v505 S3.7)? The collapse is CONFIRMED full-tensorially, but one cubic door opens. Exact integer-scaled weight multisets + Kostant/Weyl alternating sums + sympy/Fraction, no floats (41 checks, ~4 s). [E] STRUCTURE: g0 = d5 (+) a3 is SEMISIMPLE with NO u(1) factor (the 52 class-0 roots split 40 + 12 into pure D5 + pure A3 roots, root span rank 8 = rank E8); the twisted sectors factorise multiplicity-free into minuscule Weyl orbits g1 = (16_s, 4), g2 = (10, 6), g3 = (16_c, 4bar) = (g1)^*, each an irreducible g0-module (64, 60, 64); INNERNESS THEOREM: h = (2,2,2,2,2;0^4) lies in the CARTAN OF g0, so every g0-invariant tensor automatically carries total sector charge 0 mod 4 -- the v508 collapse is a full-tensor statement AND holds across arities (all 15 non-neutral sector triples: Hom = 0). [E] HOM TABLES: bilinear dim Hom_{g0}(g_j x g_j') nonzero ONLY at j' = -j (dims 2/1/1/1, Killing blocks); trilinear neutral multisets {0,0,0}: 3 (= 1 sym + 2 antisym), {0,1,3}: 2, {0,2,2}: 2, {1,1,2}: 1, {2,3,3}: 1 -- ALL cross-sector trilinears are pure brackets (antisymmetric in the repeated legs); the ONLY totally symmetric survivor on all of e8 is the su(4) d-symbol (so(10) has no cubic Casimir: Inv(S^3 45) = 0 protects T5). [E] THE NEW CHANNEL: the quartic projection of the d-symbol exchange is Q_dd = (0, 0, -1/240, 0, 1/60) = (1/60)(T3 - P3/4), computed by TWO independent routes (Killing-propagator contraction, 2 h_vee = 60 verified from the roots; hand route |x^2 - (tr x^2/4) 1|^2/60); Phi_T3(Q_dd) = 1/60 != 0 -- v508's master-kill functional does NOT annihilate the trilinear exchange (the product theorem covers quadratic vertices only); brackets, tadpoles and mixed d x f die exactly; no T5 analogue. [E] NEW CERTIFICATE: M = [E13, E22, E00, Q_dd] has rank 3, augmented rank 4 -- the pairing in the charge reading remains OBSTRUCTED, but with the WEAKER certificate {Phi_T5, psi = Phi_P - Phi_T3/4}, psi(A_fix) = 72 - 8 = 64; the RELAXED reading becomes EXACTLY solvable: A_fix = -u + 8v + 2w + 1920 Q_dd (residual 0) -- where v508 found T5 = T3 = 0 persisting even relaxed, the d-channel closes the T3 gap with small integer coefficients. [C] number fences: 64 = dim g1 = 2^6; 1920 = |W(D5)| = 2^7 x 3 x 5 = 8 x 240. [O] the arity >= 4 ledger; the physical justification of the cubic GS term (c_d = 1920 under the e8-Killing propagator); ch2-naturalness for CUBIC vertices UNDECIDED (no canonical geometric datum for a cubic vertex); the burden on delta-1 (twisted BCOV contact terms) is SHARPENED: it must supply either the psi = 64 slice or the selection-rule relaxation. [E] NEGATIVE CONTROLS: (a) Killing control = v508 replication (A_fix, E13 = (16, -96, 144, 0, 0), E22 = (16, 32, 16, 0, 0), E00 = 225 E22); (b) SO(16)/D8: bilinears (1, 0, 1), trilinears (1, 0, 1, 0), Inv(S^3 adj_d8) = 0 -- no symmetric cubic, no odd sectors, no A3 block: the delta-2 channel cannot even be posed (E8/mu4 doubly special); (c) false g0 = d5+a2+u(1): (5, 2, 2) != (2, 1, 1) and Inv(S^3 g0) = 6 != 1; false sector content (16_s, 4bar) kills every pairing. SEAM.EQUIV.01 stays [O]; NO marker moves. Exact (sympy/Fraction).
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