Entropic hodge carrier
v474_entropic_hodge_carrier.py · frontier
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GRAV.ENTROPIC.HODGE.01: the OPERATOR level of the entropic-action bridge (work packages 1 + 4-algebra of v473). [E] CAR => Clifford: ten Gamma's on the carrier Fock space Lambda^* C^5 (dim 2^g_car = 32) satisfy {Gamma_a,Gamma_b} = 2 delta_ab exactly -- the so(10) = D5 Clifford algebra acts on the carrier exterior algebra. [E] S+ = Lambda^even as D5-module: the 45 bilinears commute with (-1)^N, span exactly 45 = dim so(10), zero leak from the 16-dim even subspace -- the half-spinor IS the even exterior algebra WITH its spinor structure (operator level of v2/v44/v197). [E] Hodge-Dirac symbol: c(xi)^2 = -|xi|^2 Id for symbolic xi -- Bianconi's D = d + delta is Clifford multiplication at symbol level. [E] the fold is 5 -> 5bar: traceless u(5) weights of Lambda^4 = negatives of Lambda^1, so the Hodge fold conjugates the vector block -- her fiber 1+5+10 becomes the GUT half-spinor 16 = 1 + 5bar + 10 (the SM carrier decomposition). [E] honest obstruction: Omega^{<=2} is NOT Clifford-invariant (Lambda^2 -> Lambda^3 leak); only Lambda^even is -- the bridge must go through the fold, never degree truncation. [E] Q-target enumeration (the v473 conjecture DECIDED): d k^2 = 32 with integer k has exactly the supports (2,4), (8,2), (32,1) = {|Z2|, rank E8, 2^g_car}; minimal uniform q = c3^2 = 1/(64 pi^2) per Fock mode; the two-form block 10 and the fiber 16 need irrational multipliers => the naive pair-block reading is KILLED; bonus Tr Q^2/delta_top = 32/48 = 2/3. [C] physical Q choice; [O] AP2 compression + R^2 mechanism open, no marker moves. Mixed exact (numpy integer Fock + sympy; Wolfram-mirrored where cheap).
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