Research paperAcceptedARR-2026-54Q3HMFJ0Z8CZB4T · v1 · 2026-09-05

Polynomial vertex reduction and optimal stability at balanced inertia (4,4)

Lluis Eriksson

Abstract

For every balanced sign multiplicity N and fixed ambient dimension, we reduce the optimal forward stability coefficient for inverse self-commutator cost to a rational list of O(N^5) spectral pairs. This counts Horn linear programs, not their size or total running time. At inertia (4,4), exact rational certificates for 89 ordered vertices establish the optimal coefficient 4/7 in every fixed ambient dimension at least eight. An ambient-independent Horn obstruction and a boundary perturbation prove sharpness. We classify the full equality set on the compact spectral closure and show strictness throughout the exact inertia stratum. Together with the previously sharp reverse coefficient 3/2, this completes both stability constants at multiplicity four. Constants for N at least five remain unevaluated. All finite certificates and replay programs are supplied; classical Horn sufficiency and written polyhedral arguments are explicit dependencies.

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Related ARR records

  • ARR-2026-24M24KDPZK8HDBQ9Extends · Evaluates the previously open balanced multiplicity-four forward constant, proves a general finite vertex reduction and classifies the multiplicity-four equality cases.

AI assistance statement

OpenAI Codex assisted with derivation, exact replay, literature comparison, typesetting and separate internal critical review. Lluis Eriksson authorized improvements and publication of the final version; his subsequent individual Astra checks are pending at deposit. The producing model family participated in the internal review. No independent human editorial review or independent-model numerical rating is claimed.

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Author-directed founder-pilot deposit implementing the current instruction to improve and publish this paper. The author and editorial signer are the same person. DEPOSIT_DECISION.json records a new exception scoped to this exact record/version/PDF; the ordinary independent-human-editor requirement is not fulfilled. Authorization to prepare and publish does not claim that the author already inspected the new final bytes. No independent editorial acceptance or peer review is claimed.