Celestial wp5a null ideal
v497_celestial_wp5a_null_ideal.py · frontier
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CELEST.WP5A.01: WP5a of the celestial-holographic research contract CELEST.SEAM.01 -- 'the null ideal from the limit', first constructive milestone of WP5 (the v496 boundary-limit shadow made precise). [E] Base: v492/v496 replication (glue dims (60,64,60,64), tower D[d], chi = E4/eta^8 through q^6, mu4 period sum 248). [E] STABILISATION THEOREM: family chi_w of graded Fock characters on the chiral jet generators (loop energy m + w*radial number r, quarter units u = q^{1/4}); w = 2 IS the chiral jet grading (generators 64,120,128,180,192,240,256,300 per degree); u^n coefficient of chi_w = quarter-moded loop Fock for ALL w >= n+1, strictly larger for w <= n (n <= 8, w <= 10) -- the boundary reading is the precise coefficientwise limit eps = 1/w -> 0 with explicit threshold w = n+1; convention: 897266 = loop Fock at u^4 = integer level 1. [E] NULL IDEAL DERIVED (not cited): Freudenthal + Weyl + character peeling give Sym^2(248) = V(2 theta) + V(omega) + V(0) = 27000 + 3875 + 1 (residual exactly 0, orbit-sum cross-check); 27000 = 30^3 = h_vee^3; C2 = (124, 96, 0), Dynkin indices 6750/750; level-1 integrability <2 theta,theta_vee> = 4, <omega,theta_vee> = 2 => only level-1 primary = vacuum ([C] Kac, counting consequence); quotient 31124 - 27000 = 4124 = 1 + 248 + 3875 exactly. [E] TWO ROUTES, ONE NUMBER: mu4 theta-split sector sum at q^2 = (1036,1024,1040,1024) = 4124 -- independent lattice route hits the Fock quotient exactly; q^3: 34752 = chi_3. [E] NEGATIVE CONTROLS: SO(16)_1 through the SAME pipeline: Sym^2(120) = 5304+1820+135+1 (FOUR components), 5304 != 14^3 (h_vee^3 not generic), quotient 7380-5304 = 2076 = Theta_D8/eta^8 at q^2 (second algebra validated), block weights (0,1/2,1,1) do NOT fuse vs E8 (0,1,1,1) fusing; false periodisation: only P = 4 = |mu4| gives 248; swapped glue breaks the zero-mode anchor (64 != 60). [C] identifications: 'radial decoupling = MMST collar thickness -> 0' (v336/v449 same two-step shape); Kac singular vector via counting consequence only. [O] HONEST LIMIT: the limit does NOT generate the truncation -- singular vector as operator in the limit net open (WP5b); GNS limit state, local normality/Haag duality open (WP5c/d); the celestial route now has the same two-step shape as MMST (limit + maximal ideal) with the ideal quantitatively fixed; SEAM.EQUIV.01 stays [O]. Exact (integer/Fraction).
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