{"paper":{"title":"Continuous-state branching processes with L\\'evy-Khintchine drift-interaction: Laplace duality and Fellerian extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Lévy-Khintchine drift in continuous-state branching processes induces a Laplace duality that exchanges branching and interaction mechanisms.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cl\\'ement Foucart, F\\'elix Rebotier","submitted_at":"2026-05-07T16:09:14Z","abstract_excerpt":"We investigate the class of continuous-state branching processes with interaction driven by a L\\'evy-Khintchine type drift (CBDI). These $[0,\\infty]$-valued processes capture both dynamics of branching and density-dependence, allowing for cooperation at low population sizes and competition at high densities. Although the interaction breaks the branching property, the L\\'evy--Khintchine form of the drift induces a Laplace duality. This duality expresses the Laplace transform of a CBDI process in terms of that of another CBDI process, in which the branching and drift-interaction mechanisms are e"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The Lévy-Khintchine form of the drift induces a Laplace duality expressing the Laplace transform of a CBDI process in terms of that of another CBDI process in which the branching and drift-interaction mechanisms are exchanged. The process stopped upon hitting 0 or ∞ is uniquely characterized in law by these mechanisms.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the interaction is of Lévy-Khintchine type drift, allowing the duality to hold, and that the process can be extended Fellerianly when drift is non-Lipschitz and sufficiently strong at boundaries.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"CBDI processes admit Laplace duality swapping branching and drift-interaction, enabling unique characterization and Fellerian extensions that determine entrance, exit, or regular boundary behaviors at 0 and infinity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Lévy-Khintchine drift in continuous-state branching processes induces a Laplace duality that exchanges branching and interaction mechanisms.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"09db0ff35669e116a7e241375e3ae46140702f660b37a74afea0d31fb0c8a542"},"source":{"id":"2605.06488","kind":"arxiv","version":2},"verdict":{"id":"4a4d0713-bea5-43ac-bf47-ea076ef1cfb7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T06:04:50.756638Z","strongest_claim":"The Lévy-Khintchine form of the drift induces a Laplace duality expressing the Laplace transform of a CBDI process in terms of that of another CBDI process in which the branching and drift-interaction mechanisms are exchanged. The process stopped upon hitting 0 or ∞ is uniquely characterized in law by these mechanisms.","one_line_summary":"CBDI processes admit Laplace duality swapping branching and drift-interaction, enabling unique characterization and Fellerian extensions that determine entrance, exit, or regular boundary behaviors at 0 and infinity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the interaction is of Lévy-Khintchine type drift, allowing the duality to hold, and that the process can be extended Fellerianly when drift is non-Lipschitz and sufficiently strong at boundaries.","pith_extraction_headline":"Lévy-Khintchine drift in continuous-state branching processes induces a Laplace duality that exchanges branching and interaction mechanisms."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.06488/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T12:22:03.903770Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T07:41:10.049269Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T18:31:18.834904Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T12:37:57.881090Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ca2da1a6b5d61b516c74c864fb438b467061673e32a0adb5a94e8bb1b97dcf22"},"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"}