C-D26-DIRECT-CRT

D26 direct-CRT theorems PROVED and double-verified: a unique canonical labeled tuple exists (sort ascending breaking S_13 once, positive representative, primitive, duplicates kept) with sign, permutation and scale fixed ONCE globally; and each labeled coordinate V_i below B13 is pinned by direct CRT once the modulus product exceeds 2*B13 = 969 bits, versus the squared-coefficient threshold 2H = 1946 bits. The direct threshold is provably about half, cutting the certified prime product from about 205 to about 109 primes. Back-conversion re-symmetrizes to the same e_j(V^2) object the coefficient route uses

In plain language

Direct coordinate CRT is proved and double-verified: each speed in the canonical labeled tuple is pinned once the modulus product exceeds about 969 bits, against about 1946 bits for the coefficient route, roughly half the certified primes.

Exact statement

D26 direct-CRT theorems PROVED and double-verified: a unique canonical labeled tuple exists (sort ascending breaking S_13 once, positive representative, primitive, duplicates kept) with sign, permutation and scale fixed ONCE globally; and each labeled coordinate V_i below B13 is pinned by direct CRT once the modulus product exceeds 2*B13 = 969 bits, versus the squared-coefficient threshold 2H = 1946 bits. The direct threshold is provably about half, cutting the certified prime product from about 205 to about 109 primes. Back-conversion re-symmetrizes to the same e_j(V^2) object the coefficient route uses