{
  "schemaVersion": "1.6",
  "slug": "delayed-cascade-recovery",
  "title": "Recovering a dense planted set below square-root size from one SI cascade",
  "shortTitle": "A hidden cluster in one cascade",
  "url": "https://evidencepress.org/releases/delayed-cascade-recovery/",
  "oneLine": "A written-proof candidate recovers a hidden dense set from infection times in a specified random-graph model, while its small pilot records twelve failures.",
  "abstract": "A widest rapid-window estimator consistently detects and approximately recovers a planted dense set of size n^alpha for 1/3<alpha<1 when background mean degree is log² n. A strengthened theorem permits known d=np with d/log n tending to infinity and arbitrary s≤n whenever nd(log n)²/s³+d(log n)²/s tends to zero. The recorded sixteen-run pilot returned empty sets throughout; no practical finite-size performance is established.",
  "datePublished": "2026-10-11",
  "dateModified": "2026-10-11",
  "version": "1.1.0-candidate",
  "doi": "10.5281/zenodo.23298826",
  "doiUrl": "https://doi.org/10.5281/zenodo.23298826",
  "conceptDoi": "10.5281/zenodo.23298825",
  "pdfUrl": "https://zenodo.org/records/23298826/files/delayed-cascade-recovery-v1.1.0-candidate.pdf",
  "altPdfUrl": "https://github.com/ipitchford/delayed-cascade-recovery/releases/download/v1.1.0-candidate/delayed-cascade-recovery-v1.1.0-candidate.pdf",
  "altPdfLabel": null,
  "zenodoUrl": "https://zenodo.org/records/23298826",
  "repoUrl": "https://github.com/ipitchford/delayed-cascade-recovery",
  "releaseUrl": "https://github.com/ipitchford/delayed-cascade-recovery/releases/tag/v1.1.0-candidate",
  "markdownUrl": "https://evidencepress.org/releases/delayed-cascade-recovery/index.md",
  "bibtexUrl": "https://evidencepress.org/releases/delayed-cascade-recovery/cite.bib",
  "audioUrl": "https://evidencepress.org/assets/audio/delayed-cascade-recovery.mp3",
  "imageUrl": "https://evidencepress.org/assets/og/delayed-cascade-recovery.png?v=defd80eacc",
  "coverArtUrl": "https://evidencepress.org/assets/art/delayed-cascade-recovery.svg?v=e5c1ee7c15",
  "media": [
    {
      "type": "audio",
      "url": "https://evidencepress.org/assets/audio/delayed-cascade-recovery.mp3",
      "name": "Audio briefing — A hidden cluster in one cascade",
      "description": "Synthetic explanation, not additional scientific evidence.",
      "transcriptUrl": "https://evidencepress.org/assets/audio/delayed-cascade-recovery.txt"
    }
  ],
  "authors": [
    "Anonymous"
  ],
  "license": "CC0-1.0",
  "status": "unrefereed-candidate",
  "verification": {
    "peerReviewed": false,
    "independentlyReproduced": false,
    "formallyVerified": false,
    "internallyReplayed": true,
    "detail": "Unrefereed written-proof candidate with fresh internal finite-code replay. No formal verification, unaffiliated reproduction or external peer review established; the negative pilot demonstrates no useful finite-size power."
  },
  "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/23298826",
      "note": "Public research assets match the frozen package; availability does not establish correctness."
    },
    {
      "dimension": "internalReplay",
      "label": "Internal replay",
      "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?",
      "state": "passed",
      "note": "Seven finite tests passed in normal and optimized Python with semantic negative controls, plus byte-identical replay of all sixteen recorded pilot outcomes in normal Python. These coordinated internal checks do not prove the asymptotic theorem.",
      "evidenceUrl": "https://github.com/ipitchford/delayed-cascade-recovery/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": "This assurance dimension is not established by the coordinated internal checks or publication."
    },
    {
      "dimension": "independentReimplementation",
      "label": "Independent reimplementation",
      "question": "Has someone else reached the result from an independent implementation?",
      "state": "not-assessed",
      "note": "This assurance dimension is not established by the coordinated internal checks or publication."
    },
    {
      "dimension": "formalVerification",
      "label": "Formal verification",
      "question": "Is a formalised statement machine-checked, and over which trusted base?",
      "state": "not-assessed",
      "note": "This assurance dimension is not established by the coordinated internal checks or publication."
    },
    {
      "dimension": "specialistReview",
      "label": "Specialist review",
      "question": "Has a domain specialist assessed the argument?",
      "state": "not-assessed",
      "note": "This assurance dimension is not established by the coordinated internal checks or publication."
    },
    {
      "dimension": "editorialPeerReview",
      "label": "Editorial peer review",
      "question": "Has a journal or venue run peer review to a decision?",
      "state": "not-assessed",
      "note": "This assurance dimension is not established by the coordinated internal checks 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/delayed-cascade-recovery/blob/v1.1.0-candidate/ENVIRONMENT.txt",
      "note": "Code, inputs, adverse results and environment are retained; 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 written-proof candidate with fresh internal finite-code replay. No formal verification, unaffiliated reproduction or external peer review established; the negative pilot demonstrates no useful finite-size power."
  },
  "attributionBoundary": null,
  "problem": {
    "name": "Recovery of a planted dense set from a single network cascade",
    "url": "https://arxiv.org/abs/2610.08766v1"
  },
  "orderedProductAverage": null,
  "corrections": [],
  "publicCorrections": [],
  "publicCorrectionIndexes": null,
  "pageStructureVersion": "2.0",
  "pageStructureVariant": "canonical-theorem",
  "pageStructureWaivers": [],
  "recordMaturity": "current",
  "metadataProvenance": "Supplied manuscript and review, preserved negative pilot and bounded internal general-background proof extension. Earlier research clocks unknown.",
  "grandfatheredAtSchemaVersion": null,
  "keywords": [
    "SI cascade",
    "planted dense subgraph",
    "statistical recovery",
    "counting processes",
    "negative pilot"
  ],
  "keyResults": [
    "Consistent relative recovery below square-root size in the specified known-background model.",
    "General sufficient condition nd(log n)²/s³+d(log n)²/s→0 for d/log n→∞.",
    "All twelve planted pilot runs failed; eight face a deterministic minimum-width obstruction."
  ],
  "reviews": [],
  "evidencePackage": "Written probabilistic proof with internal extension audit; seven finite diagnostic tests passed in normal and optimized Python, plus byte-identical replay of all sixteen preserved pilot outcomes in normal Python. All twelve planted pilot cases failed.",
  "openProblems": [],
  "mathObjects": [],
  "relatedWorks": [
    {
      "citation": "Dreveton, Mürmann and Thiran (2026), Estimation and Recovery of a Planted Dense Subgraph from a Single Network Cascade, v1: first-entry and growth comparisons; sharper error in the overlap and nuisance-parameter estimation.",
      "url": "https://arxiv.org/abs/2610.08766v1",
      "doi": "10.48550/arXiv.2610.08766"
    },
    {
      "citation": "Brandenberger, Mossel and Sridhar (2025), Detecting abrupt changes in point processes: Fundamental limits and applications.",
      "url": "https://arxiv.org/abs/2501.08392v1",
      "doi": "10.48550/arXiv.2501.08392"
    },
    {
      "citation": "Prokhorenkova, Tikhonov and Litvak (2022), When less is more: Systematic analysis of cascade-based community detection.",
      "url": "https://doi.org/10.1145/3494563",
      "doi": "10.1145/3494563"
    }
  ],
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    "lineageId": null,
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    "decisionObject": {
      "type": "bound",
      "description": "Sufficient conditions for relative recovery of a hidden dense set from one SI cascade.",
      "scope": "Independent-edge model, fixed internal density, known background and rate-one clocks, complete observations."
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    "bottleneckTargeted": [
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      "publication"
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    "semanticBridge": {
      "state": "explicit",
      "description": "Observable rapid windows are controlled simultaneously before the widest is selected; a latent planted burst supplies a witness.",
      "remainingRisks": [
        "Written proof is not formally verified.",
        "Negative pilot establishes no useful finite-size power.",
        "No optimal threshold or unknown-rate theorem."
      ]
    },
    "humanJudgmentGates": [
      "External scrutiny of the probabilistic proof and relevance of the observation model remains open."
    ],
    "parentLinks": [],
    "assuranceTarget": {
      "dimensions": [
        "independentRerun",
        "specialistReview"
      ],
      "nextAction": "Audit the asymptotic proof and reproduce the preserved pilot outside the producer workflow.",
      "claimCeiling": "Unrefereed written-proof candidate with fresh internal finite-code replay. No formal verification, unaffiliated reproduction or external peer review established; the negative pilot demonstrates no useful finite-size power."
    },
    "impactClaims": [
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        "aim": "science",
        "outcome": "Relative recovery in a specified single-cascade model",
        "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,
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    "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": [
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        "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": "2026-10-11T13:27:18Z",
            "procedureClass": "full-candidate",
            "targetOutcome": "Immutable research publication and canonical site readback",
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            "plausibleLowMinutes": 120,
            "plausibleHighMinutes": 210,
            "expectedUnattendedWaitMinutes": 30,
            "referenceClass": {
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              "basis": "Prospective procedural estimate, not a measured benchmark."
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                "basis": "Mandatory remaining publication stages; no assurance gate is waived for time"
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            "probabilityPositiveSignal": 0.9,
            "probabilityTargetClosure": 0.8,
            "probabilityHorizonMinutes": 480,
            "assumptions": [
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            "reforecastTriggers": [
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}