{
  "schemaVersion": "1.3",
  "slug": "finite-sample-affine-diversification",
  "title": "Finite-Sample Signal Uncertainty and Sharp Partial Identification of Diversification Histories",
  "shortTitle": "Finite-sample affine diversification",
  "url": "https://evidencepress.org/releases/finite-sample-affine-diversification/",
  "oneLine": "A reconstructed tree can fit many speciation-and-extinction histories. Under a fixed-stem model, this candidate turns that ambiguity into rigorous finite-sample decisions—showing which conclusions survive every compatible history and when plug-in estimates or finite CRABS clouds are too confident.",
  "abstract": "One reconstructed timetree can be compatible with many different histories of speciation and extinction, so a single fitted curve or finite random cloud can appear decisive when other histories supported by the same tree reverse the conclusion. This anonymous, unrefereed successor candidate supplies a finite-sample safeguard under an exact fixed-stem, stem-survival, homogeneous time-varying birth-death model. Exact geometric tip-count inversion and a Dvoretzky--Kiefer--Wolfowitz--Massart node-age band yield an at-least-nominal simultaneous confidence set for the entire pulled scale F. The method propagates that set through an affine cumulative-loss representation and asks whether a turnover-cap conclusion survives across every compatible signal and history. Its answer is deliberately three-valued: certified incompatible, compatible throughout the band, or unresolved. In a frozen synthetic example with 22 tips, the 95 percent band gives F(T) in [5.31, 1749.48], rules out a registered cap of 0.70 under the stated normalized constraint, and withdraws an interior plug-in compatible call to unresolved. A 20,000-replicate sanity check reports 96.755 percent joint component coverage; the theorem, not the simulation, supplies the guarantee. A separate frozen affine--CRABS benchmark found that all 240 returned primary clouds missed at least one sharp endpoint, with 60 additional structural censors. This shows that the finite clouds did not certify the sharp limits in the registered cases. Exact certification changed 532 of 3,840 clustered statuses, or 13.854 percent, below the preregistered 20 percent H4 gate, so the benchmark identifies a concrete failure mode without establishing broad CRABS utility. Producer-side local and public Linux replay pass. No topology or dating coverage, model-misspecification coverage, fossil observation model, empirical validation, broad CRABS utility, unaffiliated reproduction, external specialist review, formal verification, editorial peer review, priority determination, or demonstrated field impact is claimed.",
  "datePublished": "2026-08-21",
  "dateModified": "2026-08-21",
  "version": "0.3.0-candidate-r2",
  "doi": "10.5281/zenodo.22041054",
  "doiUrl": "https://doi.org/10.5281/zenodo.22041054",
  "conceptDoi": "10.5281/zenodo.21851318",
  "pdfUrl": "https://github.com/ipitchford/affine-diversification-fibres/releases/download/v0.3.0-candidate-r2/finite-sample-affine-diversification-0.3.0-candidate-r2.pdf",
  "altPdfUrl": "https://zenodo.org/records/22041054/files/finite-sample-affine-diversification-0.3.0-candidate-r2.pdf?download=1",
  "altPdfLabel": null,
  "zenodoUrl": "https://zenodo.org/records/22041054",
  "repoUrl": "https://github.com/ipitchford/affine-diversification-fibres",
  "releaseUrl": "https://github.com/ipitchford/affine-diversification-fibres/releases/tag/v0.3.0-candidate-r2",
  "markdownUrl": "https://evidencepress.org/releases/finite-sample-affine-diversification/index.md",
  "bibtexUrl": "https://evidencepress.org/releases/finite-sample-affine-diversification/cite.bib",
  "audioUrl": "https://evidencepress.org/assets/audio/finite-sample-affine-diversification.mp3?v=b380744762",
  "imageUrl": "https://evidencepress.org/assets/og/finite-sample-affine-diversification.png",
  "coverArtUrl": "https://evidencepress.org/assets/art/finite-sample-affine-diversification.svg",
  "media": [
    {
      "type": "audio",
      "url": "https://evidencepress.org/assets/audio/finite-sample-affine-diversification.mp3",
      "name": "Audio briefing — finite-sample affine diversification",
      "description": "Plain-English OpenAI API synthetic-voice summary of the fixed-stem signal band, affine three-valued decisions, failed CRABS H4 gate and assurance boundary; a communication aid, not additional scientific evidence.",
      "transcriptUrl": "https://evidencepress.org/assets/audio/finite-sample-affine-diversification.txt"
    }
  ],
  "authors": [
    "Anonymous"
  ],
  "license": "CC0-1.0",
  "status": "unrefereed-candidate",
  "verification": {
    "peerReviewed": false,
    "independentlyReproduced": false,
    "formallyVerified": false,
    "internallyReplayed": true,
    "detail": "Anonymous, unrefereed theorem-and-method candidate published with notes. The fixed-stem finite-sample signal band, affine propagation and three-valued decision statements are presented within their exact conditional model. Producer-side local and public Linux replay, independent numerical checks, simulation, negative controls, sealed-ledger reconciliation and release byte checks pass. The preregistered H4 broad-utility gate failed at 532 of 3,840 changed statuses. No topology or dating uncertainty, lineage heterogeneity, model misspecification, fossil observation process, empirical validation, unaffiliated rerun, independent reimplementation, proof-assistant formalization, external reconstructed-process specialist review, editorial peer review, exhaustive novelty or priority assessment, or demonstrated field impact is claimed."
  },
  "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://doi.org/10.5281/zenodo.22041054",
      "note": "The exact five-file candidate payload is public through an immutable GitHub prerelease and Zenodo version DOI with matching hashes. 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": "Producer-controlled GitHub Actions passed the frozen historical replay, Route A successor verifier and pinned Linux-container smoke job on the tagged payload.",
      "evidenceUrl": "https://github.com/ipitchford/affine-diversification-fibres/actions/runs/32458618950"
    },
    {
      "dimension": "independentRerun",
      "label": "Independent rerun",
      "question": "Has someone else run the supplied implementation and obtained the stated result?",
      "state": "not-assessed",
      "note": "No unaffiliated party has reported rerunning the immutable successor package."
    },
    {
      "dimension": "independentReimplementation",
      "label": "Independent reimplementation",
      "question": "Has someone else reached the result from an independent implementation?",
      "state": "not-assessed",
      "note": "The separate envelope oracle and simulations were produced within the same research programme and are fault-diversity controls, not unaffiliated reimplementation."
    },
    {
      "dimension": "formalVerification",
      "label": "Formal verification",
      "question": "Is a formalised statement machine-checked, and over which trusted base?",
      "state": "not-assessed",
      "note": "No fixed-stem probability theorem, DKW propagation result, affine-fibre theorem or finite certificate has been formalized in a proof assistant."
    },
    {
      "dimension": "specialistReview",
      "label": "Specialist review",
      "question": "Has a domain specialist assessed the argument?",
      "state": "not-assessed",
      "note": "The retained substantive and confirmation reviews are internal model-assisted records. No identified external reconstructed-process specialist has signed off."
    },
    {
      "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 comparable venue has conducted editorial peer review to a decision."
    },
    {
      "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/affine-diversification-fibres/blob/v0.3.0-candidate-r2/environment.json",
      "note": "The macOS environment, dependency lock and container base digest are recorded, and producer-controlled Linux CI passes. No unaffiliated environment recreation has been reported."
    }
  ],
  "provenance": {
    "aiGenerated": true,
    "aiAssisted": true,
    "generatedBy": [
      "AI systems under human direction",
      "OpenAI Codex"
    ],
    "humanRole": "The user set the objective, authorized staged continuation, selected Route A and authorized publication. Ian Pitchford acts as repository maintainer and publisher. The scholarly creator is cited as Anonymous.",
    "disclosure": "The AI system performed derivation, implementation, simulation, ledger analysis, literature work, drafting, review, revision and release engineering within one producer-coordinated workflow. Internal implementation diversity, model-assisted review and public CI are not unaffiliated reproduction or external specialist review."
  },
  "problem": {
    "name": "Partial identification within phylogenetic birth-death congruence classes",
    "url": "https://doi.org/10.1038/s41586-020-2176-1"
  },
  "orderedProductAverage": null,
  "corrections": [
    {
      "date": "2026-08-21",
      "scope": "presentation",
      "summary": "Revised the standfirst, abstract and opening plain-English summary to make the positive finite-sample signal-to-decision contribution clear before presenting the failed H4 broad-utility gate.",
      "detail": "The revised page explains that the method distinguishes conclusions that survive uncertainty from plug-in conclusions that must be withdrawn, and presents the CRABS endpoint diagnostic separately from its measured decision impact. The paper, DOI package, numerical results, failed H4 gate and assurance status are unchanged."
    }
  ],
  "keywords": [
    "phylogenetics",
    "birth-death process",
    "partial identification",
    "pulled diversification rate",
    "simultaneous confidence band",
    "sharp bounds",
    "turnover cap",
    "CRABS",
    "negative result",
    "reproducible research",
    "unrefereed candidate"
  ],
  "keyResults": [
    "Under the exact fixed-stem, stem-survival, homogeneous time-varying law, exact geometric tip-count inversion and a conditional DKW--Massart node-age band give an at-least-nominal simultaneous confidence set for the pulled scale F.",
    "Propagating that signal set through the affine cumulative-loss fibre yields a confidence-containing union of conditional identified sets and three-valued turnover-cap decisions: certified incompatible, compatible throughout the band, or unresolved.",
    "In the frozen 22-tip synthetic example, the 95 percent band gives F(T) in [5.31, 1749.48], certifies a cap of 0.70 as incompatible under the stated normalized constraint, and withdraws an interior plug-in compatible call to unresolved.",
    "The 20,000-replicate sanity check reports 98.685 percent count coverage, 98.035 percent node-age coverage and 96.755 percent joint component coverage, above the stated 95 percent nominal lower bound; the analytic theorem supplies the guarantee.",
    "All 240 returned primary CRABS clouds missed at least one sharp endpoint beyond tolerance, with 60 additional structural censors, but exact certification changed only 532 of 3,840 clustered statuses, below the preregistered 20 percent H4 utility gate.",
    "The failed H4 gate prohibits claims that the method is broadly superior, essential, or a must-have complement to CRABS."
  ],
  "reviews": [],
  "evidencePackage": "A 23-page anonymous unrefereed candidate paper with accessible Markdown; exact geometric inversion, conditional DKW--Massart bands and affine decision code; 21 deterministic tests under ordinary and optimized Python; 720 implementation-diverse linear-programming endpoints across 180 feasible cases; a 160,000-replicate branching-process simulation; five detected semantic negative controls; a 20,000-replicate fixed-stem coverage sanity check; a frozen 1,100-cell affine--CRABS experiment with 1,900 sealed result and sidecar hashes; exact H2/H4 transition tables; a structured recognition search; component-level licence and provenance records; a 5,033-entry successor manifest; public GitHub Actions historical, successor and pinned-container jobs; and exact GitHub/Zenodo asset readback. This establishes scoped producer-side evidence and public availability, not independent theorem verification, biological validity, broad comparative utility or field impact.",
  "openProblems": [
    "Obtain a focused external process-theory review of the exact fixed-stem descendant-count law, node-age factorization, conditioning conventions and simultaneous-coverage argument.",
    "Reimplement the fixed-stem band and affine propagation independently in another open-source stack, starting from the immutable public package rather than producer intermediates.",
    "Extend the uncertainty analysis to topology and node-age estimation, smoothing, model selection and model misspecification without silently differentiating a nondifferentiable confidence band.",
    "Add an explicit fossil preservation, observation and taxonomic-scale model before treating fossil restrictions as empirical inference.",
    "Design a new preregistered comparison that explains when exact certification changes decisions, rather than reusing the failed H4 broad-utility claim.",
    "Develop crown-conditioned, random-origin, lineage-dependent and trait-dependent counterparts as separate newly gated research objects.",
    "Conduct a broader multilingual and specialist priority review and an independent component-rights audit."
  ],
  "relatedWorks": [
    {
      "citation": "Anonymous. (2026). Conditional Sharp Partial Identification of Diversification Histories: Affine Measure Geometry, Event Congruence and Certified Extremes (Version 0.2.1-candidate). Zenodo.",
      "url": "https://doi.org/10.5281/zenodo.21851319"
    },
    {
      "citation": "Louca, S., and Pennell, M. W. (2020). Extant timetrees are consistent with a myriad of diversification histories. Nature, 580, 502-505.",
      "url": "https://doi.org/10.1038/s41586-020-2176-1"
    },
    {
      "citation": "Höhna, S., Kopperud, B. T., and Magee, A. F. (2022). CRABS: Congruent rate analyses in birth-death scenarios. Methods in Ecology and Evolution, 13, 2709-2718.",
      "url": "https://doi.org/10.1111/2041-210X.13997"
    },
    {
      "citation": "Andréoletti, J., and Morlon, H. (2023). Exploring congruent diversification histories with flexibility and parsimony. Methods in Ecology and Evolution.",
      "url": "https://doi.org/10.1111/2041-210X.14240"
    },
    {
      "citation": "Massart, P. (1990). The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality. The Annals of Probability, 18(3), 1269-1283.",
      "url": "https://doi.org/10.1214/aop/1176990746"
    },
    {
      "citation": "Manski, C. F. (2003). Partial Identification of Probability Distributions. Springer.",
      "url": "https://doi.org/10.1007/b97478"
    }
  ],
  "operatingModel": {
    "version": "1.0",
    "workId": "ep-work:finite-sample-affine-diversification",
    "attemptIds": [
      "ep-attempt:finite-sample-affine-diversification"
    ],
    "aims": [
      "science"
    ],
    "artifactRoles": [
      "research-output",
      "evidence-assessment",
      "method-demonstration",
      "communication"
    ],
    "lineageId": "affine-diversification-programme",
    "accelerationPrimitives": [
      "structural-compression",
      "adversarial-controls",
      "research-lineage-reuse",
      "productive-failure",
      "identification-gate",
      "partial-identification",
      "certified-decision-margin",
      "assurance-vector",
      "agent-readable-research-object"
    ],
    "decisionObject": {
      "type": "identified-set",
      "description": "An exact fixed-stem confidence set for the pulled scale, propagated through an affine cumulative-loss fibre to three-valued turnover-cap decisions.",
      "scope": "Exact node ages under the declared homogeneous time-varying fixed-stem and stem-survival model; excludes topology, dating, smoothing, misspecification, fossil observation and broad CRABS utility."
    },
    "bottleneckTargeted": [
      "discovery",
      "assurance",
      "publication"
    ],
    "semanticBridge": {
      "state": "explicit",
      "description": "The observed tip count and unordered node ages are mapped through their exact conditional laws to a confidence set for F, then through the affine cumulative-loss coordinate to conditional histories, target bounds and three-valued decisions. The separate CRABS ledger is mapped only to its registered H2 and H4 questions.",
      "remainingRisks": [
        "No unaffiliated reconstructed-process specialist has validated the fixed-stem probability and conditioning bridge.",
        "The confidence set does not include topology, dating, smoothing, model-selection or misspecification uncertainty.",
        "The CRABS comparison is bounded to its frozen grid and failed its broad-utility threshold.",
        "Fossil and taxonomic-scale constraints lack an observation model."
      ]
    },
    "humanJudgmentGates": [
      "Assess the fixed-stem probability object and conditioning conventions as mathematics rather than inferring truth from simulation or CI.",
      "Keep exact-signal affine sharpness separate from finite-sample coverage and from biological model adequacy.",
      "Do not differentiate the F band to claim derivative or pulled-rate coverage without a separately justified smoothness procedure.",
      "Retain the failed H4 gate and prohibit must-have, essential-complement, replacement or broad-superiority language about CRABS.",
      "Require a new release decision before claiming external specialist endorsement, independent reproduction, empirical validation, priority or impact.",
      "Confirm Anonymous scholarly attribution, component licences and public-release authority."
    ],
    "parentLinks": [
      {
        "relation": "extends-result",
        "workId": null,
        "legacyReleaseSlug": "affine-diversification-fibres",
        "externalUrl": null,
        "inheritedClaim": "The predecessor established the conditional affine cumulative-loss coordinate, sharp fixed-signal bounds, finite infeasibility certificates and an exact endpoint-sampling diagnostic.",
        "inheritedAssuranceCeiling": "The predecessor is an anonymous unrefereed producer-side candidate; reusing its framework does not independently confirm it, and the successor adds rather than retroactively supplies finite-sample uncertainty to that archived version."
      }
    ],
    "assuranceTarget": {
      "dimensions": [
        "independentRerun",
        "independentReimplementation",
        "formalVerification",
        "specialistReview",
        "dataEnvironmentReproducibility",
        "semanticValidation",
        "noveltyAssessment",
        "priorityAssessment"
      ],
      "nextAction": "Obtain focused unaffiliated process-theory review and an independently authored fixed-stem/affine implementation, then extend the observation boundary to topology, dating and model misspecification before any empirical claim.",
      "claimCeiling": "A producer-side unrefereed theorem and method candidate for exact fixed-stem finite-sample pulled-scale uncertainty and conditional affine decisions, plus a bounded CRABS benchmark with a failed H4 gate; not empirical validation, broad CRABS utility, independent reproduction, formal verification, external specialist or editorial peer review, absolute priority, or demonstrated research impact."
    },
    "impactClaims": [
      {
        "id": "affine-finite-sample-science-no-impact",
        "aim": "science",
        "outcome": "More reliable uncertainty-aware decisions within diversification congruence classes",
        "setting": "Research using homogeneous time-varying fixed-stem reconstructed birth-death models and bounded comparisons with congruent-history samplers",
        "status": "NO_IMPACT_EVIDENCE",
        "designClass": "none",
        "comparator": "No matched conventional research, theorem-review or publication workflow was registered.",
        "estimand": "No effect on discovery time, proof quality, error rate, review effort, scientific decisions, method uptake, citation or field outcomes was estimated.",
        "evidenceRefs": [],
        "registeredDesignRef": null,
        "independentAssessment": null
      }
    ]
  }
}