Celestial wp5c gns limit state
v500_celestial_wp5c_gns_limit_state.py · frontier
Read the original description and evidence links
CELEST.WP5C.01: WP5c of the celestial-holographic research contract CELEST.SEAM.01 -- 'the GNS limit state', the third constructive milestone of WP5 (WP5a made the limit precise, WP5b built the deleting operator; WP5c constructs the STATE whose GNS kernel contains the ideal). Exact integer/Fraction, no floats, deterministic. [E] CONSTRUCTION: quasi-free family omega_w -- loop sector = affine k=1 vacuum functions via the MACHINE-determined compact anti-involution theta(e_a) = -e_{-a} (the UNIQUE sign that is an anti-automorphism on all 61504 basis pairs; contravariance exact); radial sector = oscillator pairings x^{w r} (exact Gibbs regulator, x-adic). [E] CONVERGENCE SHARP: omega_w = omega_inf mod x^{N+1} for ALL w >= N+1 (N = 8), NOT yet at w = N (r = 1 modes at order N) -- the WP5a threshold holds identically at the state level; positivity of every omega_w checked. [E] KERNEL (core, fully machine): FULL exact level-2 Gram -- 31124 monomials in 9361 weight blocks (profile 164:1, 37:240, 7:2160, 1:6960), each block exact: level-1 rank 248 positive definite (Cartan block = E8 Cartan, det 1); level-2 rank 4124, kernel 27000, every block PSD; rank per Weyl orbit (norm 8/6/4/2/0) = (0,0,1,8,44); kernel = V(2 theta) WEIGHT BY WEIGHT (Freudenthal cross-check on all 9361 weights); h.w. norms (3844, 49, 2, 0) at (0, omega, theta, 2theta); direct ideal checks F_i|s>, F_j F_i|s> norm 0. [E] MU4 EQUIVARIANCE: omega_w o clock = omega_w for all w; the clock descends to GNS; GNS level-2 rank by clock class = (1036,1024,1040,1024) = Theta_Cj/eta^8 at q^2 (two-routes identity at the STATE level); level-1 split (60,64,60,64). RESOLUTION of WP5b S4.10: |s> IS the ZERO VECTOR of GNS(omega_inf) -- the twisted two-C1-mode floor (6 quarters = q^{3/2}) concerns only pre-limit objects (GNS has no state there, 6 mod 4 != 0). [E] NEGATIVE CONTROLS: k = 2 (<s|s> = +4, dominant blocks full rank -- no ideal in the kernel); k = 0 (level-1 Gram = 0 -- no 248 layer without the central extension); D8 (level-2 rank 2076 = 7380 - 5304, kernel = V(2 theta_D8) PSD, but h = (0,1/2,1,1): vacuum GNS is 1 of 4 blocks -- one-block completeness stays E8/mu4-specific); wrong family E'_w = m w + r (level-1 limit rank 0, the 248 layer ERASED, u^4 content 710955 != 248 -- the kill has teeth); no damping (897266 != 248); CCR OBSTRUCTION: at FIXED radial pairing c > 0 positivity forces omega(bb*) >= c -- NO w-uniform damping state exists: the family formulation is NECESSARY and the family EXISTS => preregistered KILL not triggered. [C] quasi-free extension to the full *-algebra, Kac positivity beyond level 2. [O] local normality of omega_inf, net structure/Haag duality (WP5d), Costello-Li (WP5e), operator-algebraic closure beyond the graded topology; SEAM.EQUIV.01 stays [O]. VERDICT: SUCCESS on the preregistered criterion (dim GNS level-2 = 4124 exactly). Exact (integer/Fraction).
Read the original Python source- Linked claims