nx_mathspec_erf.nx

nx_mathspec_erf.nx -- SOVEREIGN SPEC EMITTER for the ERF kernel (DLMF ch7 rung 1, ME2-ERF-001). Every constant from the 120-bit bigfloat -- no python, no minimax: 2/sqrt(pi) via bf_pi (Machin) + NEWTON square root (8 iterations from the f64 seed, doubling precision each step: bf_div exists, so s <- (s + pi/s)/2); Taylor reciprocals r_n = 1/(n!(2n+1)) by factor-by-factor bf_div_small with the sign (-1)^n BAKED into the emitted bits (the sinhcosh P_k sign gene). REFUSAL RAILS (refuse > fabricate): R1: (2/sqrt(pi)) * sqrt(pi) must equal 2 to ~100 bits, else exit 2 no emit; R2: the derived 2/sqrt(pi) f64 bits must equal the KNOWN-GOOD libm constant 0x3FF20DD750429B6D bit-exactly (derive sovereignly, verify vs the world). Layout: c[0]=one c[1]=two_over_sqrt_pi c[2]=tosp_hi(32-bit split) c[3]=tosp_lo c[4..35]=32 SIGNED Taylor reciprocals hi-first: (-1)^n/(n!(2n+1)) n=31..0 (24 terms left the tail at ~2^-42 at the cut; 32 puts it past 2^-67 -- ULP-clean) c[36]=series_cut 1.75 c[37]=one_cut 6.0 (|x|>=6 -> erf=+-1 sub-ulp) Emits runtime/_hdl_build/_pm_erf_spec.nx :: pm_erf_spec_fill(c)->30 license_tier: ORIGINAL