Κ = 0.003 for integer multiplication crossed

A repository contribution applies a verified "fresh-helper retiming" across 19 full native calls inside a previously thinned p17 complex controller and reports an improved conditional complexity bound for integer multiplication. The claimed bound becomes T(n) = O(n (log n)^(1 - 0.00300105)), with the update keeping 16 paid query shears, whole idle calls, all main operators and a stronger BIT supplier intact. The author-check asserts the change is a net optimization to the controller's helper structure while preserving the controller's core operator and scalar arrangements.

The submission gives precise construction and accounting: independent productive fields remain 11,560; paid calls drop from 72,902 to 69,273 (saving 3,629); productive and paid rank masses are 260,798 and 259,998 respectively, preserving a surplus of 800. Each full native unit uses an exact 117-entrance, 42-exit, 395-scalar-frame patch and the exact intervals produce κ = 0.0030010541830. That κ is +0.00004105 (+1.3868%) above a recent 0.00296 baseline, +11.7098% above 0.00268647, and +30.4804% above a pinned 0.0023 value. Related branches and follow-up PRs report nearby κ values (e.g., ~0.00302015), and there are no reviewers or assignees listed.