{ "schemaVersion": "1.6", "slug": "davis-yin-gap-sharpness", "title": "Exact finite-horizon gap constants and non-attainment for Davis–Yin splitting", "shortTitle": "The exact Davis–Yin gap constant", "url": "https://evidencepress.org/releases/davis-yin-gap-sharpness/", "oneLine": "An exact decomposition gives the sharp averaged comparison-gap coefficient across the full unrelaxed step range and explains why the worst case is usually approached but not attained.", "abstract": "This research candidate determines the exact worst-case coefficient of an averaged primal-dual comparison gap for Davis–Yin three-operator splitting over the full unrelaxed range 0=2, no finite-dimensional positive-denominator instance attains either open-range supremum. At the endpoint alpha L=2 and K>=2 the exact denominator becomes alpha(K-1); strict convexity of f rules out attainment, while the general endpoint attainment question remains open. The sharpness quantifier permits arbitrary admissible comparison pairs and does not establish saddle-pair sharpness, last-iterate rates, objective-error rates or lower bounds for other algorithms.", "datePublished": "2026-10-20", "dateModified": "2026-10-20", "version": "1.0.0-candidate", "doi": "10.5281/zenodo.23505130", "doiUrl": "https://doi.org/10.5281/zenodo.23505130", "conceptDoi": null, "pdfUrl": "https://github.com/ipitchford/davis-yin-gap-sharpness/releases/download/v1.0.0/davis-yin-gap-sharpness-v1.0.0.pdf", "altPdfUrl": null, "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23505130", "repoUrl": "https://github.com/ipitchford/davis-yin-gap-sharpness", "releaseUrl": "https://github.com/ipitchford/davis-yin-gap-sharpness/releases/tag/v1.0.0", "markdownUrl": "https://evidencepress.org/releases/davis-yin-gap-sharpness/index.md", "bibtexUrl": "https://evidencepress.org/releases/davis-yin-gap-sharpness/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/davis-yin-gap-sharpness.mp3", "imageUrl": "https://evidencepress.org/assets/og/davis-yin-gap-sharpness.png?v=f88f132ed1", "coverArtUrl": "https://evidencepress.org/assets/art/davis-yin-gap-sharpness.svg?v=8d929a496d", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/davis-yin-gap-sharpness.mp3", "name": "Plain-English audio briefing", "description": "Communication aid; not additional research evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/davis-yin-gap-sharpness.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed AI-assisted mathematical candidate. Internal reviews and exact checks have their stated scope; external specialist review, independent external reproduction and formal verification have not been established." }, "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/23505130", "note": "The frozen paper and research package are public on GitHub and Zenodo, with matching asset hashes." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "Ordinary and optimized exact replay agree; trajectory and constant corruptions are rejected in both modes." }, { "dimension": "independentRerun", "label": "Independent rerun", "question": "Has someone else run the supplied implementation and obtained the stated result?", "state": "not-assessed", "note": "No unaffiliated rerun has been established." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "No separate external implementation is claimed." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "No proof-assistant formalisation." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "AI-assisted review is not external specialist review." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "No external editorial peer review." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "partial", "note": "Code and environment are supplied; finite replay does not establish the analytic theorem." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI-assisted mathematical research", "OpenAI Codex: review, revision, extensions and publication" ], "humanRole": "Publication authority only; no human research contribution inferred.", "reviewStatus": "Internal AI-assisted assessment, not external peer review." }, "attributionBoundary": null, "problem": null, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Prepared from the frozen v1.0.0 manuscript, claims, assurance records and replay receipts. GitHub and Zenodo assets were checked byte-for-byte against the sealed local release on 20 October 2026.", "grandfatheredAtSchemaVersion": null, "keywords": [ "Davis–Yin splitting", "three-operator splitting", "performance estimation", "sharp constants", "non-attainment", "convex optimisation" ], "keyResults": [ "For 0=2 no finite-dimensional positive-denominator instance attains either open-range supremum.", "At alpha L=2 and K>=2 the exact denominator is K-1; general endpoint attainment remains unresolved." ], "reviews": [], "evidencePackage": "Exact analytic slack identity and sharpness family; exact rational ordinary/optimized replay, two semantic mutation controls in both modes and matched receipts.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Davis and Yin (2017), A three-operator splitting scheme and its optimization applications.", "url": "https://doi.org/10.1007/s10957-016-0917-z", "doi": "10.1007/s10957-016-0917-z" }, { "citation": "Nguyen et al. (2025), source averaged-gap bound and tightness conjecture.", "url": "https://arxiv.org/abs/2506.23475", "doi": "10.48550/arXiv.2506.23475" }, { "citation": "Taylor, Hendrickx and Glineur (2017), exact worst-case performance of first-order methods.", "url": "https://doi.org/10.1137/16M1081143", "doi": "10.1137/16M1081143" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:davis-yin-gap-sharpness", "attemptIds": [ "ep-attempt:davis-yin-gap-sharpness-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "communication" ], "lineageId": null, "accelerationPrimitives": [ "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "bound", "description": "Exact finite-horizon averaged comparison-gap constants and attainment classification for the specified Davis–Yin ordering.", "scope": "Arbitrary admissible comparison pairs in finite-dimensional convex instances; not saddle-only sharpness or a lower bound for other algorithms." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "The quantity is an averaged comparison gap, not automatically an objective error or maximised duality gap.", "remainingRisks": [ "General endpoint attainment is unresolved.", "The bounded literature search is not exhaustive priority certification." ] }, "humanJudgmentGates": [ "Publication is authorised; scientific endorsement is not inferred.", "External specialist review and independent reproduction remain open." ], "parentLinks": [], "assuranceTarget": { "dimensions": [ "independentRerun", "specialistReview", "formalVerification", "priorityAssessment" ], "nextAction": "Independently check the slack identity and the non-attainment implications.", "claimCeiling": "Only the stated comparison-gap quantifiers and algorithm; internal replay is not external assurance." }, "impactClaims": [ { "id": "davis-yin-gap-no-impact", "aim": "science", "outcome": "An openly inspectable mathematical candidate and continuation target.", "setting": "AI-assisted mathematical research", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "None registered.", "estimand": "No research-speed or scientific-impact effect is estimated.", "evidenceRefs": [], "registeredDesignRef": null, "independentAssessment": null } ] }, "researchMetrics": { "schemaVersion": "1.0", "policyUrl": "https://evidencepress.org/api/research-metrics-policy.json", "outcomePolicyUrl": "https://evidencepress.org/api/v2/research-metrics-policy.json", "workLedgerUrl": "https://evidencepress.org/api/work-ledger.json", "claimCeiling": "These records describe scoped workflow inputs and outcomes. 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