Status: unrefereed candidate theoretical and computer-assisted result offered for scrutiny.This release develops a localized fixed-seed calculus for polynomial exponential periods. It gives complete depressed-quartic rank strata and a finite exact odd-quintic reduction certificate containing the full matrix, reduction witnesses, determinant and all sixteen size-three minors. It also distinguishes persistent tangent-family defects from pointwise derivative-frame failures and uses the known Chebyshev–Bessel family as a prior-art benchmark.Producer-side replay passes 129/129 ordinary checks, 129/129 under optimized Python, 17/17 coefficient-matching checks, 47/47 finite certificate checks and 9/9 mutation or negative controls. These checks do not constitute independent reproduction, formal verification, specialist peer review, analytic contour validation, or a novelty or priority determination.Original content is dedicated under CC0 1.0 Universal.