Effective eventual monotonicity on the (2,2,m) tensor slice

Abstract

Let a(n_1,...,n_p) denote the expected number of real critical rank-one approximations to a standard Gaussian tensor, in the normalization of Draisma and Horobeţ. We prove a(2,2,m) < a(2,2,m-1) for every integer m >= 3*10^103+3. The proof converts the Kac--Rice integral into an absolute determinant of a normalized random walk in 2-by-2 symmetric matrices, uses its exact moment-generating function to obtain a weighted Edgeworth expansion, certifies positivity of the first even correction, and supplies explicit low-, middle-, and high-frequency remainder estimates. This is an effective asymptotic tail theorem. It does not settle the finite range below the threshold, including m=4 and the r=1 comparison, and does not resolve the full Draisma--Horobeţ conjecture. No global-first claim is made. Status: Public Beta. Internal writing-preparation proof audit, bounded novelty review, final-manuscript review, reproducible artifact construction and full-page inspection passed within their stated scopes. External mathematical review and formal peer review have not been completed. The archive contains the frozen manuscript, accepted TeX/PDF, verification code, analytic constant ledgers, reproduction instructions, artifact reports and checksums. The separately downloadable PDF is identical to the accepted PDF inside the archive.