{ "schemaVersion": "1.2", "slug": "affine-diversification-fibres", "title": "Conditional Sharp Partial Identification of Diversification Histories: Affine Measure Geometry, Event Congruence and Certified Extremes", "shortTitle": "Conditional sharp partial identification of diversification histories", "url": "https://evidencepress.org/releases/affine-diversification-fibres/", "oneLine": "For a fixed pulled speciation signal and explicit model restrictions, an affine measure coordinate turns alternative birth-death histories into a tractable feasible set with sharp bounds, incompatibility certificates, and a precise account of why finite random searches can miss extremes.", "abstract": "Extant timetrees can identify a pulled diversification signal without separately identifying time-varying speciation and extinction. This anonymous theorem-led candidate represents a stated class of homogeneous birth-death histories by a cumulative-loss measure beneath an explicit survival barrier. Reciprocal speciation is affine in that measure, and the absolutely continuous density relative to pulled scale is the turnover ratio. Under precisely stated fixed-stem conditioning conventions, finitely many independent deterministic survival events preserve the complete reconstructed-tree law. For every finite turnover cap, the candidate derives sharp pointwise projections, including a phase transition at cap one. Finite interval constraints yield explicit extremal trajectories, pairwise incompatibility witnesses, a positive-survival test, and the minimum compatible turnover cap. An exact endpoint-sampling law shows why a finite random cloud is not an extremum certificate. A public mammal curve is used only for deterministic plug-in sensitivity: there is no simultaneous uncertainty band, fossil observation model, crown-conditioned theorem, posterior-equivalence claim, or matched performance result against CRABS.", "datePublished": "2026-08-08", "dateModified": "2026-08-08", "version": "0.2.1-candidate", "doi": "10.5281/zenodo.21851319", "doiUrl": "https://doi.org/10.5281/zenodo.21851319", "conceptDoi": "10.5281/zenodo.21851318", "pdfUrl": "https://github.com/ipitchford/affine-diversification-fibres/releases/download/v0.2.1-candidate/manuscript.pdf", "altPdfUrl": "https://raw.githubusercontent.com/ipitchford/affine-diversification-fibres/v0.2.1-candidate/manuscript.pdf", "zenodoUrl": "https://zenodo.org/records/21851319", "repoUrl": "https://github.com/ipitchford/affine-diversification-fibres", "releaseUrl": "https://github.com/ipitchford/affine-diversification-fibres/releases/tag/v0.2.1-candidate", "markdownUrl": "https://evidencepress.org/releases/affine-diversification-fibres/index.md", "bibtexUrl": "https://evidencepress.org/releases/affine-diversification-fibres/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/affine-diversification-fibres.mp3", "imageUrl": "https://evidencepress.org/assets/og/affine-diversification-fibres.png", "coverArtUrl": "https://evidencepress.org/assets/art/affine-diversification-fibres.svg", "media": [], "authors": [ "Anonymous agentic research candidate" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Anonymous, unrefereed theorem-led candidate. Internal replay, scoped independent numerical implementations, direct simulation, mutation controls, citation checking, data-extraction checking, and pinned-container recreation pass. The load-bearing fixed-stem finite-event theorem has not been audited by an external stochastic-process specialist. Independent external replay, proof-assistant formalization, systematic novelty or priority review, editorial peer review, simultaneous uncertainty propagation for the pulled signal, a validated fossil observation model, crown or random-origin conditioning, and an actual matched CRABS comparison are not assessed. Sharpness is only over the stated conditional model class." }, "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/21851319", "note": "The exact candidate archive is public under a specific-version DOI and CC0 for original content." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "Producer-side normal and optimized scratch replay and pinned-container recreation pass.", "evidenceUrl": "https://github.com/ipitchford/affine-diversification-fibres/releases/download/v0.2.1-candidate/REPLAY_RECEIPT.json" }, { "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 running the supplied package." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "The package contains a separately written numerical checker, but it was produced inside the same research workflow and is not an 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 formalization is supplied." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "External stochastic-process and macroevolution specialists have not audited the theorems." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "The candidate has not undergone journal or venue peer review." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "passed", "evidenceUrl": "https://github.com/ipitchford/affine-diversification-fibres/blob/v0.2.1-candidate/environment.json", "note": "The release pins package hashes, dependencies, and the container base-image digest; upstream extraction was hash- and value-checked. This does not rerun or validate the upstream biological fit." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "OpenAI GPT-5.6 Pro" ], "humanRole": "Research objective, supplied candidate and review, and publication authorization; the scholarly creator is cited as Anonymous agentic research candidate.", "disclosure": "The AI system audited prior art and claims, developed mathematical extensions and proofs, wrote and revised the manuscript and code, ran computational and document checks, and prepared the release. System agreement and producer-side replay are not independent verification." }, "problem": { "name": "Partial identification within phylogenetic birth-death congruence classes", "url": "https://doi.org/10.1038/s41586-020-2176-1" }, "corrections": [], "keywords": [ "partial identification", "phylogenetics", "birth-death process", "non-identifiability", "pulled speciation rate", "sharp bounds", "turnover cap", "survival events", "infinite-dimensional linear programming", "reproducible research", "agentic research", "unrefereed candidate" ], "keyResults": [ "Conditional on a fixed positive pulled speciation signal, continuously differentiable compatible histories are represented bijectively by nondecreasing cumulative-loss functions below an explicit survival barrier; reciprocal speciation is affine in this coordinate.", "For absolutely continuous histories with a finite turnover cap c, the paper gives sharp pointwise speciation projections for every c >= 0. At c > 1 the upper endpoint becomes infinite beyond a calculable pulled scale, whereas the common c <= 1 restriction excludes continuous negative net diversification.", "Finite interval constraints admit explicit least and greatest feasible cumulative-loss trajectories, pairwise infeasibility witnesses, an exact positive-survival test, and the minimum compatible turnover cap.", "Under the manuscript's fixed-stem survival and fixed-tip-count conventions, finitely many independent deterministic survival events change survival probabilities but preserve the conditional positive descendant-count law and complete reconstructed-tree law.", "For the paper's transparent endpoint sampler, exact finite-dimensional probabilities quantify why random trajectory clouds can fail factorially to certify a sharp endpoint." ], "reviews": [], "evidencePackage": "A 16-page anonymous candidate paper in PDF, LaTeX, and accessible Markdown; a reference Python implementation with 17 deterministic tests; 720 independent linear-programming endpoint comparisons across 180 random cases; a 160,000-replicate finite-event branching simulation; five detected negative controls; seven machine-readable figures; a pinned Python 3.13.5 container digest; normal and optimized scratch replay; SHA-256 manifest, replay receipt, claim-evidence map, provenance and source records; and an integrity audit covering 18 citations and exact upstream-data extraction. These are producer-side and scoped computational checks, not external theorem verification.", "openProblems": [ "Obtain an external specialist proof audit of the finite-event descendant-count and fixed-stem reconstructed-tree law, including every conditioning and event convention.", "Conduct a broader recognition and priority search across books, theses, adjacent mathematical fields, software documentation, and non-English literature.", "Construct a simultaneous uncertainty set for the pulled speciation signal and propagate it through the conditional sharp identified sets.", "Add an explicit fossil preservation, observation, and taxonomic-scale model before treating fossil restrictions as empirical inference.", "Run a preregistered matched comparison against CRABS or an equivalent implementation under identical signal, cap, constraint, and numerical conventions.", "Derive and verify crown-conditioned and random-origin counterparts of the finite-event results.", "Recreate the environment and replay the package independently, without relying on the producer's prepared environment or intermediate outputs." ], "relatedWorks": [ { "citation": "Louca, S., & 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": "Lambert, A., & Stadler, T. (2013). Birth-death models and coalescent point processes: The shape and probability of reconstructed phylogenies. Theoretical Population Biology, 90, 113-128.", "url": "https://doi.org/10.1016/j.tpb.2013.10.002" }, { "citation": "Höhna, S., Kopperud, B. T., & 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., & 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": "Legried, B., & Terhorst, J. (2022). A class of identifiable phylogenetic birth-death models. Proceedings of the National Academy of Sciences, 119(35), e2119513119.", "url": "https://doi.org/10.1073/pnas.2119513119" }, { "citation": "Manski, C. F. (2003). Partial Identification of Probability Distributions. Springer.", "url": "https://doi.org/10.1007/b97478" } ] }