{ "schemaVersion": "1.6", "slug": "wilhelm-heinrich-large-gain", "title": "One rhythm at large gain", "shortTitle": "Wilhelm–Heinrich large-gain uniqueness", "url": "https://evidencepress.org/releases/wilhelm-heinrich-large-gain/", "oneLine": "Convex geometry and exact stability formulas establish one attracting cycle in an explicit parameter region; the full uniqueness question remains open.", "abstract": "For positive rates r0 >= 1000 max(a0,b0)^2/min(a0,b0), this candidate proves one attracting positive periodic orbit of the Wilhelm–Heinrich oscillator. The positive-interior attractor is a convex-function graph, with a disk domain only above Hopf. Exact Floquet formulas and a source-mapped local slow-graph result accompany the large-gain theorem. Selected scalar constants have rational interval bounds; finite orbit computations remain diagnostics. The intermediate parameter region is unresolved.", "datePublished": "2026-10-03", "dateModified": "2026-10-03", "version": "3.1.0-candidate", "doi": "10.5281/zenodo.23126164", "doiUrl": "https://doi.org/10.5281/zenodo.23126164", "conceptDoi": "10.5281/zenodo.23126163", "pdfUrl": "https://github.com/ipitchford/wilhelm-heinrich-large-gain/releases/download/v3.1.0-candidate/paper.pdf", "altPdfUrl": "https://zenodo.org/records/23126164/files/paper.pdf?download=1", "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23126164", "repoUrl": "https://github.com/ipitchford/wilhelm-heinrich-large-gain", "releaseUrl": "https://github.com/ipitchford/wilhelm-heinrich-large-gain/releases/tag/v3.1.0-candidate", "markdownUrl": "https://evidencepress.org/releases/wilhelm-heinrich-large-gain/index.md", "bibtexUrl": "https://evidencepress.org/releases/wilhelm-heinrich-large-gain/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/wilhelm-heinrich-large-gain.mp3?v=05bda7f919", "imageUrl": "https://evidencepress.org/assets/og/wilhelm-heinrich-large-gain.png?v=be7e2bdece", "coverArtUrl": "https://evidencepress.org/assets/art/wilhelm-heinrich-large-gain.svg?v=81b3db931c", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/wilhelm-heinrich-large-gain.mp3", "name": "Wilhelm–Heinrich large-gain briefing", "description": "Synthetic OpenAI fable narration; not additional scientific evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/wilhelm-heinrich-large-gain.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed written-proof candidate with internal model checking, exact symbolic tests and selected rational interval bounds. Not formal verification or external specialist review." }, "assurance": [ { "dimension": "availability", "label": "Availability and archiving", "question": "Is the evidence package publicly retrievable from an archive under a persistent identifier?", "state": "passed", "evidenceUrl": "https://zenodo.org/records/23126164", "note": "All four release assets checked against GitHub and Zenodo public provider checksums and full public downloads on 3 October 2026." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "Full required suite passed in the pinned local environment, from a fresh extraction of the frozen archive, and in hosted CI. Selected rational endpoints and correction controls passed normally and with Python -O. 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No unaffiliated environment reproduction established." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI-assisted research; original model identity not established", "Supplied model review and audit", "Codex scoped revision, exact checks and publication" ], "humanRole": "Publication authorised by the user; no human scientific role is inferred.", "disclosure": "Anonymous is the scholarly creator. Evidence Press is the publisher. 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Permanence, finiteness and convergence; the cycle-count question remains open in this source.", "url": "https://doi.org/10.1007/s10910-011-9946-9", "doi": "10.1007/s10910-011-9946-9" }, { "citation": "Boros and Hofbauer (2023). Some minimal bimolecular mass-action systems with limit cycles. Theorem 13 summarizes the original model; its mass-conserving extension is a different system.", "url": "https://doi.org/10.1016/j.nonrwa.2023.103839", "doi": "10.1016/j.nonrwa.2023.103839" }, { "citation": "Baigent (2019). Convex geometry of the carrying simplex for the May-Leonard map. A related convexity mechanism for face-preserving competitive maps, not a direct theorem for this flow.", "url": "https://doi.org/10.3934/dcdsb.2018288", "doi": "10.3934/dcdsb.2018288" }, { "citation": "Mierczyński (2020). The C1 property of convex carrying simplices for competitive maps. A regularity antecedent with different face-invariance hypotheses.", "url": "https://doi.org/10.1017/etds.2018.85", "doi": "10.1017/etds.2018.85" }, { "citation": "Eldering (2013). Normally hyperbolic invariant manifolds: the noncompact case. Theorem 3.2 and Remark 3.3 support the source-mapped local slow-graph repair.", "url": "https://doi.org/10.2991/978-94-6239-003-4", "doi": "10.2991/978-94-6239-003-4" }, { "citation": "Wilhelm and Heinrich (1996). Mathematical analysis of the smallest chemical reaction system with Hopf bifurcation. 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