nx_linalg_chol_gate.nx

nx_linalg_chol_gate.nx -- THE REFEREE FOR THE Q30 CHOLESKY (graphics GR47). The done-rule GR47 declared BEFORE this was written, quoted from graphics.plan so the bar cannot drift: "a Q30 fixed-point Cholesky over nx_fixq30_lib arithmetic factors any SPD matrix up to the identity-space dimension, L times L-transposed reproduces the input within a stated Q30 band on random SPD fixtures, a non-SPD input is refused by name rather than producing garbage, and GR24 composes it for its draw (one ruler, never a second decomposition)" This gate proves the first three clauses. The fourth is GR24's own rung and is NOT claimed here. THE LOAD-BEARING TOOTH IS THE TEXTBOOK 3x3, because its factor is known by hand and INDEPENDENTLY of this implementation: A = [[4,12,-16],[12,37,-43],[-16,-43,98]] has L = [[2,0,0],[6,1,0],[-8,5,3]] exactly. A residual check alone would pass for any L whose product happens to reconstruct A; comparing against a hand-derived L tests that this is THE Cholesky factor and not merely A factor. license_tier: ORIGINAL No hw writes (Rule 26).