{ "schemaVersion": "1.6", "slug": "cross-polytope-signaling-dimension-six", "title": "The six-dimensional cross-polytope has signaling dimension three", "shortTitle": "Six dimensions, three classical symbols", "url": "https://evidencepress.org/releases/cross-polytope-signaling-dimension-six/", "oneLine": "An exact computer-assisted candidate closes the dimension-six gap: three classical symbols with free shared randomness simulate every allowed input–output correlation.", "abstract": "The candidate proves signaling dimension three for the six-dimensional cross-polytope in the full affine measurement model. Complete classification of 133,130 rooted representatives yields 217 valid measurement records, comprising 49 full cube-symmetry classes. The 130 difficult rooted records comprise 28 full classes. Rational simulator distributions and a separate orbit audit support the finite upper-bound proof; the lower bound and small-facet construction are prior work.", "datePublished": "2026-10-11", "dateModified": "2026-10-11", "version": "1.1.0-candidate", "doi": "10.5281/zenodo.23296390", "doiUrl": "https://doi.org/10.5281/zenodo.23296390", "conceptDoi": "10.5281/zenodo.23296389", "pdfUrl": "https://zenodo.org/records/23296390/files/cross-polytope-signaling-dimension-six-v1.1.0-candidate.pdf", "altPdfUrl": "https://github.com/ipitchford/cross-polytope-signaling-dimension-six/releases/download/v1.1.0-candidate/cross-polytope-signaling-dimension-six-v1.1.0-candidate.pdf", "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23296390", "repoUrl": "https://github.com/ipitchford/cross-polytope-signaling-dimension-six", "releaseUrl": "https://github.com/ipitchford/cross-polytope-signaling-dimension-six/releases/tag/v1.1.0-candidate", "markdownUrl": "https://evidencepress.org/releases/cross-polytope-signaling-dimension-six/index.md", "bibtexUrl": "https://evidencepress.org/releases/cross-polytope-signaling-dimension-six/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/cross-polytope-signaling-dimension-six.mp3", "imageUrl": "https://evidencepress.org/assets/og/cross-polytope-signaling-dimension-six.png?v=cab976f034", "coverArtUrl": "https://evidencepress.org/assets/art/cross-polytope-signaling-dimension-six.svg?v=c8df759166", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/cross-polytope-signaling-dimension-six.mp3", "name": "Audio briefing — Six dimensions, three classical symbols", "description": "Synthetic plain-English explanation; not additional scientific evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/cross-polytope-signaling-dimension-six.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed computer-assisted candidate. Fresh internal replay passed; no formal verification, external specialist review or unaffiliated reproduction 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/23296390", "note": "Public GitHub and Zenodo assets match the frozen release package; 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": "Fresh complete classification and exact inequality and transport checks passed in normal and optimized Python, with eight rejected corruptions; separate orbit coverage and optional byte-identical graph regeneration passed. All are coordinated internal checks.", "evidenceUrl": "https://github.com/ipitchford/cross-polytope-signaling-dimension-six/blob/v1.1.0-candidate/REPLAY_RECEIPT.md" }, { "dimension": "independentRerun", "label": "Independent rerun", "question": "Has someone else run the supplied implementation and obtained the stated result?", "state": "not-assessed", "note": "Not established at draft intake." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "Not established at draft intake." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "Not established at draft intake." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "Not established at draft intake." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "Not established at draft intake." }, { "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/cross-polytope-signaling-dimension-six/blob/v1.1.0-candidate/ENVIRONMENT.txt", "note": "Inputs, replay programs and environment details are archived. No unaffiliated reproduction is established." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "OpenAI Codex: source comparison, internal checking and publication preparation" ], "humanRole": "Publication authority only; no human research contribution asserted.", "reviewStatus": "Unrefereed computer-assisted candidate. Fresh internal replay passed; no formal verification, external specialist review or unaffiliated reproduction established." }, "attributionBoundary": null, "problem": { "name": "Dimension-six cross-polytope signaling dimension", "url": "https://arxiv.org/abs/2610.05924v1" }, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Supplied manuscript and AI-assisted review, exact certificate package and bounded extension assessment. Historical research clocks not reconstructed.", "grandfatheredAtSchemaVersion": null, "keywords": [ "signaling dimension", "cross-polytope", "classical simulation", "rational certificates", "balanced collections" ], "keyResults": [ "Signaling dimension of the six-dimensional cross-polytope equals three.", "Combined with known results, signaling dimension three occurs exactly in dimensions three through six.", "217 rooted records correspond to 49 full classes; 130 difficult rooted records correspond to 28 full classes." ], "reviews": [], "evidencePackage": "Complete exact support classification, 217 rational certificates, 2604 input-column transports, independent orbit accounting and full cube-symmetry catalogue; fresh internal replay passed.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Bencze and Frenkel (2026), On the signaling dimension of the cross-polytope: imported criterion, bounds and small-facet construction.", "url": "https://arxiv.org/abs/2610.05924v1", "doi": "10.48550/arXiv.2610.05924" }, { "citation": "Kai and Dall’Arno (2024), The signaling dimension of two-dimensional and polytopic systems: preceding computed dimensions.", "url": "https://doi.org/10.26421/QIC24.11-12-3", "doi": "10.26421/QIC24.11-12-3" }, { "citation": "Laplace Mermoud, Grabisch and Sudhölter, Minimal balanced collections and their application to core stability and other topics of game theory.", "url": "https://arxiv.org/abs/2507.05898v1", "doi": "10.48550/arXiv.2507.05898" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:cross-polytope-signaling-dimension-six", "attemptIds": [ "ep-attempt:cross-polytope-signaling-dimension-six-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "evidence-assessment", "communication" ], "lineageId": null, "accelerationPrimitives": [ "certificate-first", "structural-compression", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "certificate", "description": "Exact three-state simulation of all primitive measurements of the six-dimensional cross-polytope.", "scope": "Full affine model with free shared randomness; finite exact support coverage and rational feasibility." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "Primitive measurements reduce to positive balanced binary supports; one input-independent simulator distribution must satisfy all facet-subset inequalities.", "remainingRisks": [ "Unrefereed computer-assisted proof; no formal verification.", "No uniform structural explanation of all hard cases.", "Bounded prior-art search is not exhaustive priority determination." ] }, "humanJudgmentGates": [ "External scrutiny of the finite reduction and complete coverage remains open; no human research contribution asserted." ], "parentLinks": [], "assuranceTarget": { "dimensions": [ "independentRerun", "specialistReview" ], "nextAction": "Reproduce exact support coverage and simulator checks outside the producer workflow.", "claimCeiling": "Unrefereed computer-assisted candidate. Fresh internal replay passed; no formal verification, external specialist review or unaffiliated reproduction established." }, "impactClaims": [ { "id": "cross-polytope-signaling-dimension-six-no-impact", "aim": "science", "outcome": "Exact dimension-six classical simulation boundary", "setting": "Producer-coordinated theoretical research", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "None.", "estimand": "No measured acceleration, reuse or downstream scientific benefit.", "evidenceRefs": [], "registeredDesignRef": null, "independentAssessment": null } ] }, "researchMetrics": { "schemaVersion": "1.0", "policyUrl": "https://evidencepress.org/api/research-metrics-policy.json", "workLedgerUrl": "https://evidencepress.org/api/work-ledger.json", "claimCeiling": "These records describe scoped workflow inputs and outcomes. They support calibration and reference-class construction, but do not by themselves establish research acceleration, theorem correctness, novelty, independent assurance or impact.", "attempts": [ { "attemptId": "ep-attempt:cross-polytope-signaling-dimension-six-publication", "status": "result-ready", "resultClass": "positive", "metrics": { "schemaVersion": "1.0", "measurementScope": "assurance-through-publication", "scopeBoundary": "Work after this registration; research, extension, review and package-freezing actions are left-censored. No historical clocks or resource telemetry are reconstructed.", "forecast": { "frozenAt": "2026-10-11T09:51:28Z", "procedureClass": "full-candidate", "targetOutcome": "Immutable research publication and canonical site readback", "expectedActiveMinutes": 150, "plausibleLowMinutes": 120, "plausibleHighMinutes": 210, "expectedUnattendedWaitMinutes": 30, "referenceClass": { "label": "Full candidate publication", "sampleSize": 0, "basis": "Prospective procedural estimate, not a measured benchmark." }, "fermiComponents": [ { "component": "Remaining assurance, provider, media and guarded publication stages", "count": 1, "lowMinutesPerUnit": 120, "centralMinutesPerUnit": 150, "highMinutesPerUnit": 210, "basis": "Mandatory remaining publication stages; no assurance gate is waived for time" } ], "probabilityPositiveSignal": 0.9, "probabilityTargetClosure": 0.8, "probabilityHorizonMinutes": 480, "assumptions": [ "The frozen candidate remains unchanged and provider, CI and deployment routes remain accessible." ], "reforecastTriggers": [ "A substantive integrity finding, provider failure or CI failure." ], "stopRule": "No hard cap; complete mandatory gates or report a precise blocker." }, "outcome": null }, "missingnessReason": null } ] } }