Sharp Cyclicity of Neutral Entry–Exit Cycles with Quadratic Grazing

Abstract

This record archives version 1.2.0 of the research materials for the preprint “Sharp Cyclicity of Neutral Entry–Exit Cycles with Quadratic Grazing.” It contains a standalone 42-page arXiv-layout PDF and a curated reproducibility archive with manuscript source, proof modules, interval certificates, numerical research assets, and supporting notes. The SIADS submission manuscript and all journal-specific material are excluded; the associated GitHub repository remains private. We determine sign-sharp local cyclicity bounds for planar continuous piecewise-smooth slow–fast return circuits that combine an invariant-line entry–exit delay with quadratic grazing. The archive distinguishes the mathematical proof, finite symbolic certificates, validated interval computations, and ordinary positive-parameter numerical illustrations. An arXiv replacement for arXiv:2607.27464 was submitted on 2026-08-02 and remains subject to arXiv moderation. Frozen source commit: fc4e0a7ec1244cb1a7c10b441f252ab2a1cd63b0.Standalone PDF SHA-256: 5e7b4d695b59bfe99576618d7168e69765162fdec8ff86b11b7a4f6ee6fb6e25.Reproducibility archive SHA-256: 5a30613ac7e43479ff5e881b953ed2aa1dcd3c6ba222057f109fa5538bd00dfc.