{ "schemaVersion": "1.6", "slug": "wmy5-graded-obstructions", "title": "Five-variable weak Markus–Yamabe: graded compression and affine-Hessian obstructions", "shortTitle": "What two natural five-variable routes cannot do", "url": "https://evidencepress.org/releases/wmy5-graded-obstructions/", "oneLine": "Exact certificates exclude two complete graded compression families and a uniform Hessian family, while leaving the global five-dimensional problem open.", "abstract": "This unrefereed AI-assisted mathematical candidate investigates whether a polynomial vector field on real five-space can have characteristic polynomial (lambda+1)^5 everywhere and two distinct zeros. It does not construct such a field or prove global nonexistence. Instead it gives exact exclusions for two complete stated bigraded compression families derived from a known six-dimensional example. In the unequal-weight family, eight affine-linear coefficient equations force the parameters and a ninth has exact residual 16,367,616. It also proves that a specified uniform family of five-variable potentials has full nonconstant Hessian coefficient span, excluding constant Jacobian trace after invertible affine source-target changes. Standard-library exact replay, optimized-mode replay, four corruption tests and two symbolic audits passed. No external specialist review, independent external rerun or proof-assistant formalisation is claimed.", "datePublished": "2026-10-19", "dateModified": "2026-10-19", "version": "1.0.2", "doi": "10.5281/zenodo.23478563", "doiUrl": "https://doi.org/10.5281/zenodo.23478563", "conceptDoi": "10.5281/zenodo.23477225", "pdfUrl": "https://github.com/ipitchford/wmy5-graded-obstructions/releases/download/v1.0.2/wmy5-graded-compression-affine-hessian-v1.0.2.pdf", "altPdfUrl": null, "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23478563", "repoUrl": "https://github.com/ipitchford/wmy5-graded-obstructions", "releaseUrl": "https://github.com/ipitchford/wmy5-graded-obstructions/releases/tag/v1.0.2", "markdownUrl": "https://evidencepress.org/releases/wmy5-graded-obstructions/index.md", "bibtexUrl": "https://evidencepress.org/releases/wmy5-graded-obstructions/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/wmy5-graded-obstructions.mp3", "imageUrl": "https://evidencepress.org/assets/og/wmy5-graded-obstructions.png?v=0f8cd78f9a", "coverArtUrl": "https://evidencepress.org/assets/art/wmy5-graded-obstructions.svg?v=5d380a907c", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/wmy5-graded-obstructions.mp3", "name": "Plain-English audio briefing", "description": "Communication aid; not additional research evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/wmy5-graded-obstructions.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. The stated finite identities and complete displayed family inventories have exact internal replay. The global five-dimensional weak Markus–Yamabe construction/nonexistence problem, exhaustive priority, external specialist review, independent external reproduction and formal verification remain open." }, "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/23478563", "note": "The frozen ZIP and standalone PDF are archived on GitHub and Zenodo. Archiving does not establish mathematical correctness." }, { "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, four mutation controls, the short-chain checker and two symbolic audits passed on the frozen package.", "evidenceUrl": "https://github.com/ipitchford/wmy5-graded-obstructions/blob/v1.0.2/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": "No unaffiliated execution has been established." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "partial", "evidenceUrl": "https://github.com/ipitchford/wmy5-graded-obstructions/blob/v1.0.2/ASSURANCE.md", "note": "A reviewer-supplied separate SymPy reconstruction and byte-identical certificate regeneration were checked within the same coordinated AI-assisted workflow; this is not external reproduction." }, { "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 has been established." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "Internal 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 journal or external editorial peer review has been 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/wmy5-graded-obstructions/blob/v1.0.2/ENVIRONMENT.md", "note": "The principal certificates replay with the Python standard library; optional symbolic audits require the recorded SymPy environment." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI-assisted mathematical research and certificate construction", "OpenAI Codex: review actioning, extension proof, checking and publication" ], "humanRole": "Publication authority only; no human research contribution inferred.", "reviewStatus": "Internal AI-assisted mathematical and adversarial 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 final manuscript and the metadata-only version 1.0.2 successor at Git commit 6dcbc74bd710952f8469e66fa2700cc22443d5a5. Version 1.0.2 changes archive and assurance metadata only; no theorem, proof, manuscript, certificate, verifier or scientific claim changed. GitHub and Zenodo carry the same ZIP, PDF and checksum manifest. Metadata preserves the restricted architecture boundaries and does not promote internal review to external assurance.", "grandfatheredAtSchemaVersion": null, "keywords": [ "weak Markus-Yamabe conjecture", "polynomial vector fields", "Jacobian spectrum", "Hessian coefficient span", "exact certificates" ], "keyResults": [ "The complete stated 17-parameter parallel bigraded compression family contains no constant-spectrum member.", "The complete stated 16-parameter unequal-weight chain family contains no constant-spectrum member.", "Eight coefficient equations in the final chain reduction force the variables, after which the ninth has exact residual 16,367,616.", "For nonzero kappa, r and t, the nonconstant Hessian coefficient matrices in the displayed auxiliary-affine potential family span all symmetric 5 by 5 matrices.", "A tempting direct compression preserves three zeros but has positive Jacobian eigenvalue minus one plus square root of six at an explicit point." ], "reviews": [], "evidencePackage": "Written exact arguments, three rational certificate files, a Hessian coefficient-minor certificate, standard-library reconstruction, ordinary and optimized replay, four mutation controls, an independent short-chain checker, a monomial-inventory audit and a symbolic Hessian-minor audit. Frozen version 1.0.2 archive SHA-256 7cec4b353dc88862abdd5cf3738a3436da40498e2d493083541523d2b9f365ef.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Castañeda, Honorato and Valenzuela-Henríquez (2026), The weak Markus–Yamabe conjecture fails in dimension 14.", "url": "https://arxiv.org/abs/2608.05392", "doi": "10.48550/arXiv.2608.05392" }, { "citation": "Meng and Yang (2026), A five-variable counterexample to the Hessian conjecture, version 2.", "url": "https://arxiv.org/abs/2607.22198v2", "doi": "10.48550/arXiv.2607.22198" }, { "citation": "Liu (2026), On the Hessian conjecture in Lorentzian signature: Constant pivots and Hesse systems.", "url": "https://arxiv.org/abs/2608.19112", "doi": "10.48550/arXiv.2608.19112" }, { "citation": "liqsweep / blueberryvertigo (2026), An integer polynomial Hurwitz counterexample in dimension six.", "url": "https://github.com/blueberryvertigo/ArXiv-tryouts", "doi": null } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:wmy5-graded-obstructions", "attemptIds": [ "ep-attempt:wmy5-graded-obstructions-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "communication" ], "lineageId": null, "accelerationPrimitives": [ "certificate-first", "structural-compression", "adversarial-controls", "productive-failure", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "certificate", "description": "Exact exclusion certificates and coefficient-span obstruction for three specified five-variable search architectures.", "scope": "Two complete displayed bigraded compression families and one displayed auxiliary-affine Hessian family; not all five-variable polynomial vector fields." }, "bottleneckTargeted": [ "discovery", "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "The manuscript maps constant Jacobian spectrum to coefficient equations, exact rational certificates and a full symmetric-matrix Hessian span obstruction.", "remainingRisks": [ "The global five-dimensional problem remains open outside the stated architectures.", "The written reductions still require unaffiliated specialist scrutiny.", "The targeted literature audit is not exhaustive priority clearance." ] }, "humanJudgmentGates": [ "Publication is authorised; no scientific endorsement is inferred.", "External specialist review and independent reproduction remain open." ], "parentLinks": [ { "relation": "depends-on-claim", "workId": null, "legacyReleaseSlug": null, "externalUrl": "https://github.com/blueberryvertigo/ArXiv-tryouts", "inheritedClaim": "The explicit six-dimensional constant-spectrum baseline and its listed zeros.", "inheritedAssuranceCeiling": "The present package independently expands the characteristic identity and checks the three zeros; historical priority and broader claims are not inherited." } ], "assuranceTarget": { "dimensions": [ "independentRerun", "specialistReview", "formalVerification", "priorityAssessment" ], "nextAction": "Obtain unaffiliated scrutiny of the family-completeness reductions and semantic bridge, then formalise or independently reimplement the short contradictions.", "claimCeiling": "Exact internally replayed obstructions for the stated families; no global dimension-five conclusion, external specialist review, formal verification or exhaustive priority determination." }, "impactClaims": [ { "id": "wmy5-graded-obstructions-no-impact", "aim": "science", "outcome": "Inspectable exclusions that narrow several natural construction routes.", "setting": "AI-assisted mathematical research and exact certificate checking", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "None registered.", "estimand": "No causal research-speed or scientific-impact estimate.", "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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