sketch_tdigest_v2.nx

sketch_tdigest_v2.nx -- T-Digest with Dunning k1 arcsin-based scale. V2 vs V1 (sketch_tdigest.nx): V1 scale: w_max_norm(q) = 4·q·(1-q) · π / δ (parabolic approx) V2 scale: w_max_norm(q) = (1 - cos(2π/δ))·(1/2 - q) + sin(2π/δ)·sqrt(q(1-q)) The V2 form is the closed-form expansion of Dunning's k1(q) = (δ/2π) · arcsin(2q - 1) inverse-difference w_max = k1⁻¹(k1(q)+1) - q, via the sin-of-sum identity. At q=0.5 V1 and V2 agree; in the tails V2 is LOOSER than V1 (fewer centroids needed for the same global rank guarantee), the canonical memory-efficiency T-Digest property. V1 trades memory for tighter tail recall. V2 trades tail recall for tighter memory. Both ship -- caller picks the right tool. Per cardinal 25 ("Build Intelligence, Never Strip Features"). TRIG CONSTANTS: sin(2π/δ) and cos(2π/δ) precomputed at alloc time as Q14 fixed-point (1.0 = 16384), via Taylor series: sin(x) ≈ x - x³/6 cos(x) ≈ 1 - x²/2 + x⁴/24 For δ ∈ [10, 500] -> x ∈ [0.0126, 0.628] -> Taylor error < 1e-4 in Q14, well below the 1-LSB sketch noise floor. LOSSLESS-LANGUAGE DISCIPLINE (doc 20): Query returns ApproxI64 same NX_ENV_RANK_ERROR envelope as V1, param_a interpolates the V2-specific bound: V2 rank_err ≈ 1.5 / δ at p=0.5, ≈ 0.3 / δ at p=0.99 (tail roughly 5x looser than V1; still tighter than KLL globally).