{
  "schemaVersion": "1.6",
  "slug": "overpartition-congruences-and-towers",
  "title": "Overpartition congruences and class-restricted towers",
  "shortTitle": "When the remainders vanish",
  "url": "https://evidencepress.org/releases/overpartition-congruences-and-towers/",
  "oneLine": "Three linked papers certify overpartition congruences and explain infinite towers through exact modular-form structure.",
  "abstract": "Unrefereed computer-assisted proof collection: Wei congruences modulo 7, 17, 19 and 23; class-restricted square-prime towers modulo 13, 17 and 23; and an exact modulo-13 whole-class classification. Contains three revised papers, exact finite modular-form certificates, explicit overlap and prior-art attribution, and failure-sensitive verification. Universal claims depend on the written modularity and Sturm arguments, not finite testing alone. No formal verification, external peer review, independent reproduction or four-star significance is asserted.",
  "datePublished": "2026-10-12",
  "dateModified": "2026-10-12",
  "version": "1.1.0-candidate",
  "doi": "10.5281/zenodo.23319157",
  "doiUrl": "https://doi.org/10.5281/zenodo.23319157",
  "conceptDoi": "10.5281/zenodo.23319156",
  "pdfUrl": "https://github.com/ipitchford/overpartition-congruences-and-towers/releases/download/v1.1.0-candidate/overpartition-congruences-and-towers-v1.1.0-candidate.pdf",
  "altPdfUrl": "https://zenodo.org/records/23319157/files/overpartition-congruences-and-towers-v1.1.0-candidate.pdf?download=1",
  "altPdfLabel": null,
  "zenodoUrl": "https://zenodo.org/records/23319157",
  "repoUrl": "https://github.com/ipitchford/overpartition-congruences-and-towers",
  "releaseUrl": "https://github.com/ipitchford/overpartition-congruences-and-towers/releases/tag/v1.1.0-candidate",
  "markdownUrl": "https://evidencepress.org/releases/overpartition-congruences-and-towers/index.md",
  "bibtexUrl": "https://evidencepress.org/releases/overpartition-congruences-and-towers/cite.bib",
  "audioUrl": "https://evidencepress.org/assets/audio/overpartition-congruences-and-towers.mp3",
  "imageUrl": "https://evidencepress.org/assets/og/overpartition-congruences-and-towers.png?v=8e6a2e6198",
  "coverArtUrl": "https://evidencepress.org/assets/art/overpartition-congruences-and-towers.svg?v=622055b95e",
  "media": [
    {
      "type": "audio",
      "url": "https://evidencepress.org/assets/audio/overpartition-congruences-and-towers.mp3",
      "name": "Audio briefing — Overpartition congruences and class-restricted towers",
      "description": "Synthetic plain-English explanation, not additional scientific evidence.",
      "transcriptUrl": "https://evidencepress.org/assets/audio/overpartition-congruences-and-towers.txt"
    }
  ],
  "authors": [
    "Anonymous"
  ],
  "license": "CC0-1.0",
  "status": "unrefereed-candidate",
  "verification": {
    "peerReviewed": false,
    "independentlyReproduced": false,
    "formallyVerified": false,
    "internallyReplayed": true,
    "detail": "Unrefereed computer-assisted proof collection. Internal replay and implementation diversity do not establish formal verification, unaffiliated reproduction, external peer review or broad significance."
  },
  "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/23319157",
      "note": "Frozen ZIP, PDF and checksums were downloaded from GitHub and Zenodo and matched local assets. 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": "Complete declared exact certificates replayed. Universal conclusions also depend on written modularity and finite-determination arguments.",
      "evidenceUrl": "https://github.com/ipitchford/overpartition-congruences-and-towers/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 by internal checking or publication."
    },
    {
      "dimension": "independentReimplementation",
      "label": "Independent reimplementation",
      "question": "Has someone else reached the result from an independent implementation?",
      "state": "not-assessed",
      "note": "Not established by internal checking or publication."
    },
    {
      "dimension": "formalVerification",
      "label": "Formal verification",
      "question": "Is a formalised statement machine-checked, and over which trusted base?",
      "state": "not-assessed",
      "note": "Not established by internal checking or publication."
    },
    {
      "dimension": "specialistReview",
      "label": "Specialist review",
      "question": "Has a domain specialist assessed the argument?",
      "state": "not-assessed",
      "note": "Not established by internal checking or publication."
    },
    {
      "dimension": "editorialPeerReview",
      "label": "Editorial peer review",
      "question": "Has a journal or venue run peer review to a decision?",
      "state": "not-assessed",
      "note": "Not established by internal checking or publication."
    },
    {
      "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/overpartition-congruences-and-towers/blob/v1.1.0-candidate/requirements.txt",
      "note": "Pinned dependencies and exact source provided; local and CI execution remain producer-coordinated."
    }
  ],
  "provenance": {
    "aiGenerated": true,
    "aiAssisted": true,
    "generatedBy": [
      "AI-assisted research workflow",
      "Codex: source checks, revisions, exact structural refinements and publication"
    ],
    "humanRole": "Publication authority only; no human research contribution asserted.",
    "reviewStatus": "Unrefereed computer-assisted proof collection. Internal replay and implementation diversity do not establish formal verification, unaffiliated reproduction, external peer review or broad significance."
  },
  "attributionBoundary": null,
  "problem": {
    "name": "Wei overpartition congruences and class-restricted towers",
    "url": "https://arxiv.org/abs/2603.08510v1"
  },
  "orderedProductAverage": null,
  "corrections": [],
  "publicCorrections": [],
  "publicCorrectionIndexes": null,
  "pageStructureVersion": "2.0",
  "pageStructureVariant": "canonical-theorem",
  "pageStructureWaivers": [],
  "recordMaturity": "current",
  "metadataProvenance": "Three user-supplied research bundles and reviewer audit; revised 12 October 2026. Overlapping base cases are counted once.",
  "grandfatheredAtSchemaVersion": null,
  "keywords": [
    "overpartitions",
    "modular forms",
    "Sturm bound",
    "Hecke operators",
    "congruences"
  ],
  "keyResults": [
    "The specified Wei congruences modulo 7, 17, 19 and 23 have exact finite modular-form certificates.",
    "Correction eigenforms propagate the stated modulo-13/17/23 families through every power of four.",
    "The whole class pbar(13·4^i·(8n+7)) vanishes modulo13 for all n>=0 exactly when i=3 modulo4."
  ],
  "reviews": [],
  "evidencePackage": "Written modular-form arguments, exact cusp cancellations, complete Sturm checks, normal and optimized replay and semantic negative controls.",
  "openProblems": [],
  "mathObjects": [],
  "relatedWorks": [
    {
      "citation": "Wei (2026), New Ramanujan-type congruences for overpartitions modulo 11 and 13: source conjectures and starting forms.",
      "url": "https://arxiv.org/abs/2603.08510v1",
      "doi": "10.48550/arXiv.2603.08510"
    },
    {
      "citation": "Ryan, Sirolli, Villegas-Morales and Zheng (2024), Explicit families of congruences for the overpartition function: square-prime predecessors.",
      "url": "https://doi.org/10.1007/s11139-024-00953-z",
      "doi": "10.1007/s11139-024-00953-z"
    },
    {
      "citation": "Aydin and Inam (2023), On the Hecke eigenforms of half-integral weight and Dedekind-eta products: known auxiliary eigenform.",
      "url": "https://arxiv.org/abs/2301.08461",
      "doi": "10.48550/arXiv.2301.08461"
    },
    {
      "citation": "Kong and Teo (2023), An elementary proof of the transformation formula for the Dedekind eta function.",
      "url": "https://arxiv.org/abs/2302.03280",
      "doi": "10.48550/arXiv.2302.03280"
    }
  ],
  "claimAssurance": null,
  "operatingModel": {
    "version": "1.0",
    "workId": "ep-work:overpartition-congruences-and-towers",
    "attemptIds": [
      "ep-attempt:overpartition-congruences-and-towers-publication"
    ],
    "aims": [
      "science"
    ],
    "artifactRoles": [
      "research-output",
      "evidence-assessment",
      "communication"
    ],
    "lineageId": null,
    "accelerationPrimitives": [
      "certificate-first",
      "structural-compression",
      "adversarial-controls",
      "assurance-vector",
      "agent-readable-research-object"
    ],
    "decisionObject": {
      "type": "certificate",
      "description": "Exact finite modular-form certificates for specified overpartition congruences.",
      "scope": "Only the stated prime, class and Legendre restrictions; overlapping base results counted once."
    },
    "bottleneckTargeted": [
      "assurance",
      "publication"
    ],
    "semanticBridge": {
      "state": "explicit",
      "description": "Written dissections and modularity/cusp arguments justify complete finite Sturm closures; exact eigenvectors propagate support to all tower levels.",
      "remainingRisks": [
        "No proof-assistant verification.",
        "One symbolic cusp engine, inspected and replayed, not independently reimplemented.",
        "Priority and significance remain bounded assessments."
      ]
    },
    "humanJudgmentGates": [
      "External specialist scrutiny remains open; no human research work inferred."
    ],
    "parentLinks": [],
    "assuranceTarget": {
      "dimensions": [
        "specialistReview",
        "independentReimplementation"
      ],
      "nextAction": "Independently implement the symbolic cusp expansion and inspect the source-to-modular-form bridge.",
      "claimCeiling": "Unrefereed computer-assisted proof collection. Internal replay and implementation diversity do not establish formal verification, unaffiliated reproduction, external peer review or broad significance."
    },
    "impactClaims": [
      {
        "id": "overpartition-congruences-and-towers-no-impact",
        "aim": "science",
        "outcome": "Inspectable specialised congruence candidates",
        "setting": "Producer-coordinated mathematics",
        "status": "NO_IMPACT_EVIDENCE",
        "designClass": "none",
        "comparator": "None.",
        "estimand": "No discovery acceleration or applied benefit measured.",
        "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:overpartition-congruences-and-towers-publication",
        "status": "result-ready",
        "resultClass": "positive",
        "metrics": {
          "schemaVersion": "1.0",
          "measurementScope": "assurance-through-publication",
          "scopeBoundary": "Site-ledger registration onward; earlier preparation is left-censored.",
          "forecast": {
            "frozenAt": "2026-10-12T14:06:56.765Z",
            "procedureClass": "full-candidate",
            "targetOutcome": "Immutable research publication and canonical site readback",
            "expectedActiveMinutes": 90,
            "plausibleLowMinutes": 60,
            "plausibleHighMinutes": 150,
            "expectedUnattendedWaitMinutes": 30,
            "referenceClass": {
              "label": "Remaining full-candidate publication",
              "sampleSize": 0,
              "basis": "Procedural forecast, not measured benchmark"
            },
            "fermiComponents": [
              {
                "component": "Provider publication and asset readback",
                "count": 1,
                "lowMinutesPerUnit": 10,
                "centralMinutesPerUnit": 20,
                "highMinutesPerUnit": 35,
                "basis": "Small archive; provider latency remains variable."
              },
              {
                "component": "Media, page and browser QA",
                "count": 1,
                "lowMinutesPerUnit": 20,
                "centralMinutesPerUnit": 30,
                "highMinutesPerUnit": 50,
                "basis": "New release and exact banner."
              },
              {
                "component": "Both guarded A/B and C/D deployment cycles and closeout",
                "count": 1,
                "lowMinutesPerUnit": 30,
                "centralMinutesPerUnit": 40,
                "highMinutesPerUnit": 65,
                "basis": "Required CI, preservation and canonical readback."
              }
            ],
            "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
      }
    ]
  }
}