nx_bigfloat120_sinh.nx

nx_bigfloat120_sinh.nx -- SOVEREIGN sinh/cosh oracle on the 120-bit bigfloat. cosh = (E + 1/E)/2 with E = exp(x) from the pow organ's bigfloat exp core (bfp_exp_pm) -- no cancellation anywhere. sinh uses the same form for x >= 1 (cancellation there costs < 1 bit) and the EXACT-RATIONAL Taylor series x + x^3/3! + ... for x < 1, where the exp difference would cancel catastrophically at 120 bits. Positive-only core; sinh odd / cosh even handled at the boundary. Overflow: |x| > 711 decided as inf (true cut ~710.476 lands inside bf_to_f64's natural overflow rounding). Self-anchor (see _bf_sinhcosh_gate_authored): double-angle identities sinh(2u) = 2 sinh u cosh u and cosh(2u) = 1 + 2 sinh^2 u (cancellation-free, valid across the whole domain), the pythagorean strip at small |x|, and an f64 tie sinh+cosh = e^x against the BLESSED bf_exp_f64 organ. license_tier: ORIGINAL