{ "schemaVersion": "1.6", "slug": "finite-signal-quadratic-substitutes", "title": "Finite convex certificates for quadratic informational substitutes", "shortTitle": "Finite tests for information substitutes", "url": "https://evidencepress.org/releases/finite-signal-quadratic-substitutes/", "oneLine": "A finite convex criterion decides a specified diminishing-returns property for two finite signals and a scalar quadratic prediction target, including impossible signal combinations.", "abstract": "This unrefereed candidate characterises quadratic informational substitution for a scalar square-integrable target and two finite signals with arbitrary joint support. At each distinct source mean, one auxiliary completion vector must satisfy a weighted squared-distance budget for every source state. Compact minimax duality and scalar interpolation establish equivalence with every admissible randomised disclosure. The sharp residual-variance coefficient is an attained convex-program value when finite; full support reduces it to explicit directed pairwise ratios. Sparse scalar examples have exact coefficients 4/9 and 16/9. A full-support vector counterexample shows that pairwise sufficiency does not extend automatically to multicategory quadratic scoring.", "datePublished": "2026-10-15", "dateModified": "2026-10-15", "version": "0.1.0-candidate", "doi": "10.5281/zenodo.23401650", "doiUrl": "https://doi.org/10.5281/zenodo.23401650", "conceptDoi": null, "pdfUrl": "https://github.com/ipitchford/finite-signal-quadratic-substitutes/releases/download/v0.1.0-candidate/paper.pdf", "altPdfUrl": null, "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23401650", "repoUrl": "https://github.com/ipitchford/finite-signal-quadratic-substitutes", "releaseUrl": "https://github.com/ipitchford/finite-signal-quadratic-substitutes/releases/tag/v0.1.0-candidate", "markdownUrl": "https://evidencepress.org/releases/finite-signal-quadratic-substitutes/index.md", "bibtexUrl": "https://evidencepress.org/releases/finite-signal-quadratic-substitutes/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/finite-signal-quadratic-substitutes.mp3", "imageUrl": "https://evidencepress.org/assets/og/finite-signal-quadratic-substitutes.png?v=22a132159c", "coverArtUrl": "https://evidencepress.org/assets/art/finite-signal-quadratic-substitutes.svg?v=d057be26e9", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/finite-signal-quadratic-substitutes.mp3", "name": "Plain-English audio briefing", "description": "Communication aid; not additional research evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/finite-signal-quadratic-substitutes.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": false, "detail": "Unrefereed AI-assisted candidate with written analytic proofs and internal exact checks. Simulated academic assessment is not external peer review, independent reproduction, formal verification or priority clearance. Public archive availability is verified separately from scientific assurance." }, "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/23401650", "note": "Public GitHub and Zenodo manifest, archive and PDF verified against frozen local files by full downloads on 15 October 2026. Availability is not correctness or peer review." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "partial", "note": "Internal normal and optimized finite checks support their stated scope, not formal verification of the universal proof or unaffiliated reproduction.", "evidenceUrl": "https://github.com/ipitchford/finite-signal-quadratic-substitutes/blob/v0.1.0-candidate/review-evidence/REVISION_VERIFICATION.md" }, { "dimension": "independentRerun", "label": "Independent rerun", "question": "Has someone else run the supplied implementation and obtained the stated result?", "state": "not-assessed", "note": "No unaffiliated replay established." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "Coordinated checking is not unaffiliated reimplementation." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "Universal claims use written proofs, not a proof assistant." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "Internal simulated reviewers do not establish 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 journal peer review established." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "partial", "evidenceUrl": "https://github.com/ipitchford/finite-signal-quadratic-substitutes/blob/v0.1.0-candidate/ENVIRONMENT.txt", "note": "Rational inputs, code and recorded environment are archived publicly; no unaffiliated rerun established." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "OpenAI Codex coordinated research, checking and drafting" ], "humanRole": "Publication authority only; no human research contribution inferred from ownership.", "reviewStatus": "Internal simulated academic assessment with disclosed development familiarity; no external human peer review or unaffiliated reproduction established." }, "attributionBoundary": null, "problem": { "name": "Finite scalar quadratic informational substitutes", "url": "https://arxiv.org/abs/1703.08636" }, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Prepared from the revised version-3 manuscript and internal academic assessment on 15 October 2026 for version 0.1.0-candidate. Final DOI, repository tag and public assets bound to full-download GitHub/Zenodo parity observed on 15 October 2026. No historical discovery clocks reconstructed.", "grandfatheredAtSchemaVersion": null, "keywords": [ "informational substitutes", "quadratic scoring", "convex certificates", "finite signals", "randomised disclosure", "minimax" ], "keyResults": [ "Finite scalar-knot completion feasibility is necessary and sufficient for the universal disclosure inequality with arbitrary finite signal support.", "The sharp residual-variance coefficient is an attained convex-program value whenever finite; equal-mean compatibility characterises finiteness.", "Full rectangular support forces the completions and yields an explicit directed-pair formula and sharp normalised gap, not a minimum absolute disclosure gap.", "Sparse scalar examples distinguish coefficients 4/9 and 16/9; in one orientation every two-state posterior restriction of A can pass while a three-state posterior fails.", "A full-support vector example defeats pairwise sufficiency and admits a strictly positive four-category Brier realisation." ], "reviews": [], "evidencePackage": "Self-contained analytic manuscript, rational examples and finite checks, normal/optimized producer replay, bounded source comparisons and internal AI-assisted assessment. GitHub and Zenodo archive assets match the frozen local files by full-download verification.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Chen and Waggoner, Informational Substitutes, Definition 2.2.3: the precise disclosure quantifiers.", "url": "https://arxiv.org/abs/1703.08636", "doi": "10.48550/arXiv.1703.08636" }, { "citation": "Anonymous, Four tests for binary informational substitutes: binary-source predecessor, including sparse support and vector targets.", "url": "https://doi.org/10.5281/zenodo.23238557", "doi": "10.5281/zenodo.23238557" }, { "citation": "Ordentlich and Polyanskiy, Strong Data Processing Constant is Achieved by Binary Inputs: adjacent binary extremal reduction, not the same fixed-target coefficient.", "url": "https://arxiv.org/abs/2010.01987", "doi": "10.48550/arXiv.2010.01987" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:finite-signal-quadratic-substitutes", "attemptIds": [ "ep-attempt:finite-signal-quadratic-substitutes-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "communication" ], "lineageId": null, "accelerationPrimitives": [ "structural-compression", "certificate-first", "counterexample-proxy-first", "assurance-vector" ], "decisionObject": { "type": "certificate", "description": "Finite convex completion systems or a strict rational failure witness.", "scope": "Two finite signals, arbitrary support, one partially disclosed base signal and fixed scalar quadratic value." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "Conditional variance, compact minimax and scalar-knot interpolation connect disclosure inequalities to simultaneous completion budgets.", "remainingRisks": [ "Written proof is not formal verification.", "Numerical feasibility at a boundary is not an exact certificate.", "No direct inference for estimated tables or vector targets." ] }, "humanJudgmentGates": [ "User has authorised publication; scientific interpretation and assurance remain bounded by the evidence.", "Development-independent specialist interpretation and priority scrutiny remain open." ], "parentLinks": [ { "relation": "extends-result", "workId": "ep-work:binary-quadratic-informational-substitutes", "legacyReleaseSlug": null, "externalUrl": null, "inheritedClaim": "Binary-source endpoint and posterior-disclosure framework; current scalar arbitrary-cardinality proof is self-contained.", "inheritedAssuranceCeiling": "Unrefereed AI-assisted predecessor; reuse is not independent confirmation." } ], "assuranceTarget": { "dimensions": [ "availability", "internalReplay", "specialistReview", "noveltyAssessment" ], "nextAction": "Bind final frozen release evidence and verified public assets; seek development-independent specialist scrutiny separately.", "claimCeiling": "Unrefereed mathematical candidate; no external peer review, formal verification, priority clearance, measured impact or acceleration claim." }, "impactClaims": [ { "id": "finite-signal-substitutes-no-impact", "aim": "science", "outcome": "Inspectable finite characterisation in the stated mathematical model", "setting": "Coordinated AI-assisted theory research", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "None registered.", "estimand": "No causal research-speed or empirical forecasting effect 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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