Celestial wp5d two interval index
v501_celestial_wp5d_two_interval_index.py · frontier
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CELEST.WP5D.01: WP5d-alpha of the celestial-holographic research contract CELEST.SEAM.01 -- 'the two-interval index from the lattice' (the local-net question, alpha stage). numpy/scipy Gaussian machinery + exact Fractions. [E-machine]/[L] SETUP: critical Majorana ring (v450 style), 16 layers = seam carrier c_- = 8; Peschel-exact; three prescriptions (fermionic / orbifold sector sum {1,P_A,P_B,P_AB} / dual algebra {1,P_AB}); superselection [rho, P_AB] = 0 machine-exact; every Gaussian formula validated against exact diagonalisation (<= 1.5e-15). [L/N] FERMIONIC MI EXTENSIVE (mu = 1 reference): c fit 0.5000, max |F(x)| = 5.97e-5 (N = 512), |F| falling monotonically to 1.3e-6 (N = 1024) -- Casini-Huerta extensivity as a lattice witness. [L/N] THE MU-OFFSET: Renyi-2 exactly Delta_2 = -ln[(1+R)/2]; the 16-layer carrier saturates ln 2 to MACHINE PRECISION (|Delta_2 - ln 2| = 1.1e-15 at N = 512; R falls as N^-0.500); index reading [F : F_even] = 2.000000, mu_gauged = 4.000000 = the v490 census (two independent lattice witnesses); per-layer gauging costs 16 ln 2 (the offset measures ln[index], not a blob). [L/N] HAAG-DUALITY INDICATOR: fermionic S(E) = S(E') to 8.2e-12; the orbifold BREAKS complementarity (D(E) - D(E') = 0.427 at a = 64); the pair sum is exchange-symmetric and <= ln 4 with max 1.2637 at x = 1/2 -> the ln 4 budget is a DOUBLE-LIMIT statement (the first naive fixed-x check was wrong and was replaced -- honestly typed). [E] CONDENSATION ARITHMETIC: det Cartan(D5) x det Cartan(A3) = 16; KLM/Longo-Rehren 16/4^2 = 1 and 16/2^2 = 4 -> 4/2^2 = 1 (both routes exact); Sigma d^2 (Ising 4, SO(16)_1 4, (E8)_1 1); theta_v = 1 exactly at nu = 16, rivals != 1. Anchored chain: mu = 1 (graded, MEASURED) -> 4 (gauged, MEASURED + v490) -> 1 (arithmetic, [C]; the condensed net is interacting -- v490 fence). [E/N] NEGATIVE CONTROLS: nu = 1 single Majorana (offset non-trivial, theta_v = e^{i pi/8} not removable -- the kill discriminator has teeth); trivial phase (everything <= 1e-7); wrong sector sum {1,P_AB} (offset exactly 0 instead of ln 2). [C] the dictionary 'offset = ln index' (KLM/Longo-Xu/CHMP) + the condensation step. [O] continuum Haag duality, local normality, split/strong additivity (WP5d-beta runs as exploration), Costello-Li (WP5e); SEAM.EQUIV.01 stays [O]. VERDICT: the mu = 1 indicator chain PASSES; preregistered KILL ('mu-offset != 0 after condensation') not triggered. Python (numpy + scipy + Fractions).
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