{"paper":{"title":"Resident fitness computation in linear time and other algorithmic aspects of interacting trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Resident fitness for n interacting trajectories is computable in O(n) time.","cross_cats":["math.PR"],"primary_cat":"cs.DS","authors_text":"Andr\\'as T\\'obi\\'as, Katalin Friedl, Vikt\\'oria Nemkin","submitted_at":"2025-02-17T08:48:29Z","abstract_excerpt":"Systems of interacting trajectories were recently studied in~\\cite{HGSTW24}. Such a system of $[0,1]$-valued piecewise linear trajectories arises as a scaling limit of the system of logarithmic subpopulation sizes in a population-genetic model (more precisely, a Moran model) with mutation and selection. By definition, the resident fitness is initially 0 and afterwards it increases by the ultimate slope of each trajectory that reaches height 1.\n  We show that although the interaction of $n$ trajectories may yield $\\Omega(n^2)$ slope changes in total, the resident fitness function can be compute"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Although the interaction of n trajectories may yield Ω(n²) slope changes in total, the resident fitness function can be computed algorithmically in O(n) time.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The system consists of [0,1]-valued piecewise linear trajectories whose interactions are captured by the continued lines representation, and resident fitness is defined precisely as the cumulative sum of ultimate slopes of trajectories reaching height 1; this representation must allow direct computation without enumerating all slope changes.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Resident fitness in systems of n interacting [0,1]-valued piecewise linear trajectories can be computed in O(n) time.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Resident fitness for n interacting trajectories is computable in O(n) time.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"35449959e631f87f62330297ea9b8db5ea7665d9cb2d1bfb9f54a4fecab65a9c"},"source":{"id":"2502.11561","kind":"arxiv","version":4},"verdict":{"id":"658c84d1-ccda-4990-b048-2e30289bdf1f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-23T03:09:35.250103Z","strongest_claim":"Although the interaction of n trajectories may yield Ω(n²) slope changes in total, the resident fitness function can be computed algorithmically in O(n) time.","one_line_summary":"Resident fitness in systems of n interacting [0,1]-valued piecewise linear trajectories can be computed in O(n) time.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The system consists of [0,1]-valued piecewise linear trajectories whose interactions are captured by the continued lines representation, and resident fitness is defined precisely as the cumulative sum of ultimate slopes of trajectories reaching height 1; this representation must allow direct computation without enumerating all slope changes.","pith_extraction_headline":"Resident fitness for n interacting trajectories is computable in O(n) time."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.11561/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}