{ "schemaVersion": "1.6", "slug": "two-host-dormancy-oscillations", "title": "Exact counterexamples and stable oscillations in a two-host dormancy model", "shortTitle": "Dormancy can sustain oscillations", "url": "https://evidencepress.org/releases/two-host-dormancy-oscillations/", "oneLine": "An exact parameter family overturns a proposed coexistence-convergence claim, and a certified local Hopf bifurcation creates attracting cycles.", "abstract": "This unrefereed mathematical candidate gives an explicit one-parameter counterexample family in a six-dimensional two-host dormancy–infection model. Both resident equilibria resist within-resident perturbations and can be invaded, yet the unique coexistence equilibrium is unstable. Every nonnegative equilibrium is hyperbolic, and almost every strictly positive trajectory fails to converge to an equilibrium. A separate dormancy-parameter calculation certifies a supercritical Hopf bifurcation and stable small periodic orbits locally beyond its threshold. This is a deterministic model result, not empirical validation or a proof that almost every trajectory becomes periodic.", "datePublished": "2026-10-18", "dateModified": "2026-10-18", "version": "1.0.0", "doi": "10.5281/zenodo.23448514", "doiUrl": "https://doi.org/10.5281/zenodo.23448514", "conceptDoi": null, "pdfUrl": "https://github.com/ipitchford/two-host-dormancy-oscillations/releases/download/v1.0.0-candidate/two-host-dormancy-oscillations.pdf", "altPdfUrl": null, "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23448514", "repoUrl": "https://github.com/ipitchford/two-host-dormancy-oscillations", "releaseUrl": "https://github.com/ipitchford/two-host-dormancy-oscillations/releases/tag/v1.0.0-candidate", "markdownUrl": "https://evidencepress.org/releases/two-host-dormancy-oscillations/index.md", "bibtexUrl": "https://evidencepress.org/releases/two-host-dormancy-oscillations/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/two-host-dormancy-oscillations.mp3", "imageUrl": "https://evidencepress.org/assets/og/two-host-dormancy-oscillations.png?v=6129b94ca0", "coverArtUrl": "https://evidencepress.org/assets/art/two-host-dormancy-oscillations.svg?v=3db08bc77b", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/two-host-dormancy-oscillations.mp3", "name": "Plain-English audio briefing", "description": "Communication aid; not additional research evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/two-host-dormancy-oscillations.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed AI-assisted candidate. No external peer review, unaffiliated reproduction or proof-assistant formalisation 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/23448514", "note": "GitHub and Zenodo preserve the exact frozen ZIP, PDF and checksum manifest; 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": "passed", "note": "Seven-program exact symbolic and outward-interval replay passes normally and with optimized Python, including semantic corruption controls and fresh archive extraction. Written dynamical arguments are not machine proofs.", "evidenceUrl": "https://github.com/ipitchford/two-host-dormancy-oscillations/blob/v1.0.0-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": "No external assurance established by this publication workflow." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "No external assurance established by this publication workflow." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "No external assurance established by this publication workflow." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "No external assurance established by this publication workflow." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "No external assurance established by this publication workflow." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "not-assessed", "note": "No external assurance established by this publication workflow." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI-assisted research workflow", "OpenAI Codex: checking, revision and publication" ], "humanRole": "Publication authority only; no human research contribution inferred.", "reviewStatus": "Internal AI-assisted assessment, not external peer review." }, "attributionBoundary": null, "problem": { "name": "Coexistence convergence in a two-host dormancy model", "url": "https://doi.org/10.1007/s00285-026-02372-8" }, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Prepared from the final version-1.0.0 manuscript, supplied substantive review and exact frozen archive. Research commit 82eb3858eac9f4742d1110027e86d60069b812c8; archive SHA-256 87bdf32dca9670ad900e09e3390727c19e5fa5e47691e320a3c314085190f276. Public GitHub and Zenodo assets verified byte-identical on 18 October 2026.", "grandfatheredAtSchemaVersion": null, "keywords": [ "dormancy", "host–virus dynamics", "Hopf bifurcation", "exact counterexample", "interval arithmetic" ], "keyResults": [ "An explicit admissible family for every C ≥ 1/2 has a unique positive coexistence equilibrium with two unstable directions.", "Both resident equilibria are stable within their resident subsystems and invasible by the other host.", "Almost every strictly positive trajectory fails to converge to any equilibrium.", "A certified supercritical Hopf bifurcation near q = 0.9769161486 gives stable small cycles locally on its upper side." ], "reviews": [], "evidencePackage": "Self-contained analytic manuscript with exact producer-side computations and scoped internal assessment; finite checks do not establish the full analytic theorem.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Blath and Tóbiás (2026), source two-host model and Conjecture 4.1(C)(iii).", "url": "https://doi.org/10.1007/s00285-026-02372-8", "doi": "10.1007/s00285-026-02372-8" }, { "citation": "Blath and Tóbiás (2023), earlier dormancy and virus model; a distinct one-host setting.", "url": "https://doi.org/10.1051/ps/2022022", "doi": "10.1051/ps/2022022" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:two-host-dormancy-oscillations", "attemptIds": [ "ep-attempt:two-host-dormancy-oscillations-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "communication" ], "lineageId": null, "accelerationPrimitives": [ "certificate-first", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "counterexample", "description": "Exact coexistence-instability counterexamples and a certified local supercritical Hopf branch.", "scope": "The specified deterministic two-host model; no global periodic-orbit claim or resolution of other source conjectures." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "Displayed ODEs, exact equilibrium and Routh-Hurwitz calculations, followed by local Hopf nondegeneracy and transversality checks.", "remainingRisks": [ "Written analytic arguments are not formally verified.", "Producer checks are not unaffiliated reproduction.", "Bounded source comparison is not exhaustive priority clearance." ] }, "humanJudgmentGates": [ "Publication is authorised; external specialist scrutiny and interpretation of the deterministic host–virus model remain open." ], "parentLinks": [ { "relation": "depends-on-claim", "workId": null, "legacyReleaseSlug": null, "externalUrl": "https://doi.org/10.1007/s00285-026-02372-8", "inheritedClaim": "The six-dimensional two-host dormancy model and the equilibrium-convergence claim in Conjecture 4.1(C)(iii).", "inheritedAssuranceCeiling": "Published source; the new candidate remains unrefereed." } ], "assuranceTarget": { "dimensions": [ "independentRerun", "specialistReview", "formalVerification", "priorityAssessment" ], "nextAction": "Unaffiliated reconstruction of the written argument and certificate replay, with specialist scrutiny of the stated boundary cases.", "claimCeiling": "The specified deterministic two-host model; no global periodic-orbit claim or resolution of other source conjectures. Unrefereed candidate, not formal verification, independent reproduction or exhaustive priority clearance." }, "impactClaims": [ { "id": "two-host-dormancy-oscillations-no-impact", "aim": "science", "outcome": "Exact coexistence-instability counterexamples and a certified local supercritical Hopf branch.", "setting": "AI-assisted theoretical research", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "None registered.", "estimand": "No causal research-speed or downstream scientific 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. 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:two-host-dormancy-oscillations-publication", "status": "published", "resultClass": "positive", "metrics": { "schemaVersion": "1.0", "measurementScope": "assurance-through-publication", "scopeBoundary": "Only remaining provider, media, site and readback stages from this registration; all earlier research and revision are left-censored.", "forecast": { "frozenAt": "2026-10-18T07:46:50.736Z", "procedureClass": "remaining-candidate-site-and-archive-delivery", "targetOutcome": "Accurately scoped archived candidate and canonical site readback if every mandatory gate passes.", "expectedActiveMinutes": 70, "plausibleLowMinutes": 35, "plausibleHighMinutes": 140, "expectedUnattendedWaitMinutes": 25, "referenceClass": { "label": "Remaining Evidence Press candidate publication stages", "sampleSize": 0, "basis": "Procedural planning judgement, not an empirical calibration." }, "fermiComponents": [ { "component": "Provider identity, media, guarded site delivery and readback", "count": 1, "lowMinutesPerUnit": 35, "centralMinutesPerUnit": 70, "highMinutesPerUnit": 140, "basis": "Revised papers and producer replays exist; exact archive gates and provider/site delivery remain mandatory." } ], "probabilityPositiveSignal": 0.95, "probabilityTargetClosure": 0.85, "probabilityHorizonMinutes": 360, "assumptions": [ "No provider outage or byte mismatch blocks delivery." ], "reforecastTriggers": [ "Provider failure, immutable-asset mismatch or site preservation regression." ], "stopRule": "Complete every mandatory gate or retain a precise blocker; never weaken assurance to meet the forecast." }, "outcome": { "status": "unavailable", "policyVersion": "2.0", "recordedAt": "2026-10-18T08:20:28.761Z", "reason": "Selected gate timings are not complete scoped effort or resource measurements; no retrospective estimate or calibration update is made.", "missingFields": [ { "field": "calendarElapsedMinutes", "reason": "Observed opening and delivery times are retained as milestones; elapsed wall time is not active effort and no numeric metrics series is emitted." }, { "field": "activeAgentMinutes", "reason": "The scoped activeAgentMinutes counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "unattendedWaitMinutes", "reason": "The scoped unattendedWaitMinutes counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "blockedMinutes", "reason": "The scoped blockedMinutes counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "reworkMinutes", "reason": "The scoped reworkMinutes counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "agentRuns", "reason": "The scoped agentRuns counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "maxParallelAgents", "reason": "The scoped maxParallelAgents counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "modelTurns", "reason": "The scoped modelTurns counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "researchCycles", "reason": "The scoped researchCycles counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "falsificationGatesRun", "reason": "The scoped falsificationGatesRun counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "candidateArchitecturesTested", "reason": "The scoped candidateArchitecturesTested counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "candidateArchitecturesRejected", "reason": "The scoped candidateArchitecturesRejected counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "substantiveReviewRounds", "reason": "The scoped substantiveReviewRounds counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "p0Findings", "reason": "The scoped p0Findings counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "p1Findings", "reason": "The scoped p1Findings counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "prepublicationClaimCorrections", "reason": "The scoped prepublicationClaimCorrections counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "resultState", "reason": "Published candidate delivery is observed in statusHistory; incomplete workflow telemetry does not negate publication." }, { "field": "positiveSignalObserved", "reason": "Candidate publication evidence is retained separately; no calibrated signal metric is inferred." }, { "field": "targetReached", "reason": "Delivery target is recorded in statusHistory; no calibrated target metric is inferred." }, { "field": "forecastErrorMinutes", "reason": "Active effort was not measured; forecast error cannot be computed from wall time." }, { "field": "forecastRatio", "reason": "Active effort was not measured; elapsed time is not a valid active-effort denominator." }, { "field": "withinForecastInterval", "reason": "Active effort was not measured, so interval membership is unknown." }, { "field": "activeHumanMinutes", "reason": "The scoped activeHumanMinutes counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "computeMinutes", "reason": "The scoped computeMinutes counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "deduplicatedModelTokens", "reason": "The scoped deduplicatedModelTokens counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." }, { "field": "uncachedInputTokens", "reason": "The scoped uncachedInputTokens counter was not instrumented or aggregated; unknown is not zero, and no estimate is inferred from logs, elapsed time or left-censored work." } ], "calibration": null } }, "missingnessReason": null } ] } }