{ "schemaVersion": "1.6", "slug": "binary-quadratic-informational-substitutes", "title": "Four tests for binary informational substitutes", "shortTitle": "Four tests for information substitutes", "url": "https://evidencepress.org/releases/binary-quadratic-informational-substitutes/", "oneLine": "For two yes-or-no signals, four exact inequalities decide whether every partial disclosure preserves a specified diminishing-returns property.", "abstract": "A candidate classification gives four necessary-and-sufficient weighted-square inequalities for a binary event and two binary signals under a quadratic score, using Chen–Waggoner March 2017 Definition 2.2.3. A conditional-variance identity and concavity reduce arbitrary measurable disclosures to two endpoints in each orientation, including zero-probability cells. Rational failures have explicit two-report witnesses. The package also gives an oriented finite-signal extension, strong-complements tests, and a reviewer-derived strict separation from projective substitutes.", "datePublished": "2026-10-08", "dateModified": "2026-10-08", "version": "1.1.0-candidate", "doi": "10.5281/zenodo.23238557", "doiUrl": "https://doi.org/10.5281/zenodo.23238557", "conceptDoi": "10.5281/zenodo.23238556", "pdfUrl": "https://github.com/ipitchford/binary-quadratic-informational-substitutes/releases/download/v1.1.0-candidate/binary-quadratic-informational-substitutes-v1.1.0-candidate.pdf", "altPdfUrl": "https://zenodo.org/records/23238557/files/binary-quadratic-informational-substitutes-v1.1.0-candidate.pdf?download=1", "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23238557", "repoUrl": "https://github.com/ipitchford/binary-quadratic-informational-substitutes", "releaseUrl": "https://github.com/ipitchford/binary-quadratic-informational-substitutes/releases/tag/v1.1.0-candidate", "markdownUrl": "https://evidencepress.org/releases/binary-quadratic-informational-substitutes/index.md", "bibtexUrl": "https://evidencepress.org/releases/binary-quadratic-informational-substitutes/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/binary-quadratic-informational-substitutes.mp3", "imageUrl": "https://evidencepress.org/assets/og/binary-quadratic-informational-substitutes.png?v=05a171630d", "coverArtUrl": "https://evidencepress.org/assets/art/binary-quadratic-informational-substitutes.svg?v=67cca2f24d", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/binary-quadratic-informational-substitutes.mp3", "name": "Audio briefing", "description": "Synthetic speech; communication, not additional mathematical evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/binary-quadratic-informational-substitutes.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed candidate with a written universal proof and internally replayed exact finite checks. No external peer review, independent reproduction, formal verification or historical-priority proof is claimed. The supplied review recommended minor revisions; reviewer identity and external independence are not 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/23238557", "note": "Public GitHub/Zenodo assets verified against the frozen archive, including full downloads. Availability is not proof or peer review." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "Exact internal normal/optimized replay and finite semantic controls; not the universal proof or external reproduction.", "evidenceUrl": "https://github.com/ipitchford/binary-quadratic-informational-substitutes/blob/v1.1.0-candidate/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 qualifying evidence establishing this dimension." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "No qualifying evidence establishing this dimension." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "No qualifying evidence establishing this dimension." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "No qualifying evidence establishing this dimension." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "No qualifying evidence establishing this dimension." }, { "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/binary-quadratic-informational-substitutes/blob/v1.1.0-candidate/ENVIRONMENT.txt", "note": "Standard-library rational checks, complete input records and fresh extraction; no unaffiliated rerun established." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI-assisted supplied research; originating model identity not established", "OpenAI Codex assistant: review actions, internal checks and publication" ], "humanRole": "Publication authority only; no human research contribution asserted.", "reviewStatus": "Unrefereed candidate with a written universal proof and internally replayed exact finite checks. No external peer review, independent reproduction, formal verification or historical-priority proof is claimed." }, "attributionBoundary": null, "problem": { "name": "Binary fixed-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": "Supplied mathematical package and review; publication revisions and internal replay on 8 October 2026. Earlier discovery effort and reviewer identity are not reconstructed.", "grandfatheredAtSchemaVersion": null, "keywords": [ "informational substitutes", "quadratic scoring", "Bayesian disclosure", "concavity", "exact rational witnesses" ], "keyResults": [ "Four weighted-square inequalities are necessary and sufficient for Chen–Waggoner strong substitutes for binary E, A and B under the fixed quadratic score, including zero-support cases.", "A failed rational-input inequality yields an explicit rational two-report disclosure and a directly checked negative score gap.", "The conditional-variance argument extends in one direction to a binary source and finite second signal, including square-integrable targets.", "Reviewer-derived Proposition 4 proves strong substitutes imply projective substitutes in this model, strictly; Appendix A gives endpoint/vertex tests for strong complements." ], "reviews": [], "evidencePackage": "Written proof and precise source comparison; exact rational classifier and failure witnesses; finite algebraic, support and direct-score checks; separately implemented checker; optimized replay and semantic negative controls; review response, AI index and manifest.", "openProblems": [ "An unaffiliated replay and specialist assessment would strengthen assurance.", "A full two-sided classification with nonbinary signals is not established.", "Other scoring rules and empirically estimated probability tables require separate work." ], "mathObjects": [], "relatedWorks": [ { "citation": "Chen and Waggoner (2017), Informational Substitutes. Definition 2.2.3 supplies the precise strong-substitutes target; full continuous-lattice submodularity is different.", "url": "https://arxiv.org/abs/1703.08636", "doi": "10.48550/arXiv.1703.08636" }, { "citation": "Kong and Schoenebeck (2018), Optimizing Bayesian Information Revelation Strategy in Prediction Markets. Finite-disclosure reduction and approximation machinery.", "url": "https://doi.org/10.4230/LIPIcs.ITCS.2018.14", "doi": "10.4230/LIPIcs.ITCS.2018.14" }, { "citation": "Anunrojwong, Chen, Waggoner and Xu, Computing Equilibria of Prediction Markets via Persuasion. Posterior optimisation and approximation, not this exact endpoint criterion.", "url": "https://arxiv.org/abs/2009.03607", "doi": "10.48550/arXiv.2009.03607" }, { "citation": "Börgers, Hernando-Veciana and Krähmer (2013), When are signals complements or substitutes? Characterisation across all decision problems, a different quantifier.", "url": "https://doi.org/10.1016/j.jet.2012.12.012", "doi": "10.1016/j.jet.2012.12.012" }, { "citation": "Neyman and Roughgarden, Are You Smarter Than a Random Expert? The Robust Aggregation of Substitutable Signals. Definition 2.8 gives projective substitutes.", "url": "https://arxiv.org/abs/2111.03153", "doi": "10.48550/arXiv.2111.03153" }, { "citation": "Frongillo, Neyman and Waggoner, Agreement Implies Accuracy for Substitutable Signals. Definition 2.6 gives rectangle substitutes.", "url": "https://arxiv.org/abs/2111.03278", "doi": "10.48550/arXiv.2111.03278" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:binary-quadratic-informational-substitutes", "attemptIds": [ "ep-attempt:binary-quadratic-informational-substitutes-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "evidence-assessment", "communication" ], "lineageId": null, "parentLinks": [], "accelerationPrimitives": [ "structural-compression", "certificate-first", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "certificate", "description": "Four exact inequalities or a rational counter-disclosure for a supplied binary probability table.", "scope": "Fixed quadratic score; binary event and two binary signals; Chen–Waggoner March 2017 Definition 2.2.3." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "Conditional variance expresses every disclosure gap through a concave posterior residual whose two endpoints are the reversed row margins.", "remainingRisks": [ "Written proof and runtime are trusted; finite computations are not a universal formal proof." ] }, "humanJudgmentGates": [ "External specialist assessment remains open; no human research judgement claimed." ], "assuranceTarget": { "dimensions": [ "independentRerun", "independentReimplementation", "formalVerification", "specialistReview" ], "nextAction": "Unaffiliated exact replay and specialist scrutiny of the quantifiers and conditional-variance proof.", "claimCeiling": "Unrefereed candidate with a written universal proof and internally replayed exact finite checks. 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