{"paper":{"title":"Viability Space Decomposition: A geometric partition of survival outcomes in single- and multi-agent systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Viability space decomposition partitions state space into regions of qualitatively similar survival outcomes using mortality, ordering, and collapse manifolds.","cross_cats":["math.DS"],"primary_cat":"q-bio.QM","authors_text":"Connor McShaffrey, Randall D. Beer","submitted_at":"2026-05-16T02:09:14Z","abstract_excerpt":"What determines whether an organism or collective will survive under particular conditions? This question is asked across the life sciences when determining adaptive fit, developing efficacious treatments for diseases, and assessing the risks posed by ecological shifts. To aid their investigations, researchers employ models of agents which must respect particular constraints to remain alive. By constraining the dynamics of these agents to bounded viability regions, these models form a class of extended dynamical systems where transient dynamics can lead to death, making traditional attractors "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Viability space decomposition reveals how several new classes of manifolds (mortality, ordering, and collapse) permit a complete decomposition of state space into regions of qualitatively similar survival outcomes: a viability portrait.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the introduced manifolds can be identified and used to achieve a complete decomposition for the class of viability-constrained ODE models without model-specific limitations that would leave some survival outcomes unclassified.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Viability space decomposition decomposes state space in viability-constrained dynamical systems into qualitatively similar survival regions via mortality, ordering, and collapse manifolds, demonstrated on subcellular, cellular, and coupled-cell models.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Viability space decomposition partitions state space into regions of qualitatively similar survival outcomes using mortality, ordering, and collapse manifolds.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"534e95c23c303e386f794561e61031909ada1c12ad18942c8f58cec7347d8136"},"source":{"id":"2605.16753","kind":"arxiv","version":1},"verdict":{"id":"4780ac41-891c-4cf2-80f8-933c7fe03297","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:50:40.914193Z","strongest_claim":"Viability space decomposition reveals how several new classes of manifolds (mortality, ordering, and collapse) permit a complete decomposition of state space into regions of qualitatively similar survival outcomes: a viability portrait.","one_line_summary":"Viability space decomposition decomposes state space in viability-constrained dynamical systems into qualitatively similar survival regions via mortality, ordering, and collapse manifolds, demonstrated on subcellular, cellular, and coupled-cell models.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the introduced manifolds can be identified and used to achieve a complete decomposition for the class of viability-constrained ODE models without model-specific limitations that would leave some survival outcomes unclassified.","pith_extraction_headline":"Viability space decomposition partitions state space into regions of qualitatively similar survival outcomes using mortality, ordering, and collapse manifolds."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16753/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:19.101525Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:01:13.586924Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.324958Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.456054Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"b460a2ed1548e2212359f2f03ac9b92042323fa38fbdeb5a87ee41ab5c2b2db6"},"references":{"count":60,"sample":[{"doi":"","year":null,"title":"This makes the set of molecules autocatalytic","work_id":"da8e73ad-d9cc-404c-bb6a-d169e3107973","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Numerical exploration To approximate the possible existential outcomes in the single-cell physiology, we uniformly sample a million initial conditions in the range [Mi] ∈ [0, 20]. 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Zooming in closer around o and sampling another 160,000 initial con- ditions for improved resolutio","work_id":"c94361b2-aa02-465f-a74c-4b019b660e5b","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":60,"snapshot_sha256":"2c65fa48f50cacb61bd74ec45c5b86e1105b4dda4bdf83cd5c0176a8ac3a07f4","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"e135fe325b410968f070ae3b06ea1b6cc556ba3615aa623bdc143802bec58093"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}