{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3SRAQYBH7IRAVXS7A4ZHE34KMH","short_pith_number":"pith:3SRAQYBH","schema_version":"1.0","canonical_sha256":"dca2086027fa220ade5f0732726f8a61f5248ebd7dc39632cd9b4762b00c366e","source":{"kind":"arxiv","id":"1304.1342","version":1},"attestation_state":"computed","paper":{"title":"On Exceptional Times for generalized Fleming-Viot Processes with Mutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Julien Berestycki, Leif Doering, Leonid Mytnik, Lorenzo Zambotti","submitted_at":"2013-04-04T12:14:13Z","abstract_excerpt":"If $\\mathbf Y$ is a standard Fleming-Viot process with constant mutation rate (in the infinitely many sites model) then it is well known that for each $t>0$ the measure $\\mathbf Y_t$ is purely atomic with infinitely many atoms. However, Schmuland proved that there is a critical value for the mutation rate under which almost surely there are exceptional times at which $\\mathbf Y$ is a finite sum of weighted Dirac masses. In the present work we discuss the existence of such exceptional times for the generalized Fleming-Viot processes. In the case of Beta-Fleming-Viot processes with index $\\alpha"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1304.1342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-04T12:14:13Z","cross_cats_sorted":[],"title_canon_sha256":"bbe600a84cd121a8b01e041291b0c7fa311c054878d98570728b81d925ae8a03","abstract_canon_sha256":"36c81ad38d7be346012b97ed3ac635fb7527118a580d7cc0244e7c3ed1b400fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:03.701225Z","signature_b64":"11zVYk7qI1OtZ4vYIqOAhkb3zbUe6doZWp7K8HtpokXh0xvY5s+3Sy3N5zBCFoMgZd+e8NmIzrAj3eGEk9tZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dca2086027fa220ade5f0732726f8a61f5248ebd7dc39632cd9b4762b00c366e","last_reissued_at":"2026-05-18T03:29:03.700586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:03.700586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Exceptional Times for generalized Fleming-Viot Processes with Mutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Julien Berestycki, Leif Doering, Leonid Mytnik, Lorenzo Zambotti","submitted_at":"2013-04-04T12:14:13Z","abstract_excerpt":"If $\\mathbf Y$ is a standard Fleming-Viot process with constant mutation rate (in the infinitely many sites model) then it is well known that for each $t>0$ the measure $\\mathbf Y_t$ is purely atomic with infinitely many atoms. However, Schmuland proved that there is a critical value for the mutation rate under which almost surely there are exceptional times at which $\\mathbf Y$ is a finite sum of weighted Dirac masses. In the present work we discuss the existence of such exceptional times for the generalized Fleming-Viot processes. In the case of Beta-Fleming-Viot processes with index $\\alpha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1342","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1304.1342","created_at":"2026-05-18T03:29:03.700709+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.1342v1","created_at":"2026-05-18T03:29:03.700709+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1342","created_at":"2026-05-18T03:29:03.700709+00:00"},{"alias_kind":"pith_short_12","alias_value":"3SRAQYBH7IRA","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3SRAQYBH7IRAVXS7","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3SRAQYBH","created_at":"2026-05-18T12:27:32.513160+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3SRAQYBH7IRAVXS7A4ZHE34KMH","json":"https://pith.science/pith/3SRAQYBH7IRAVXS7A4ZHE34KMH.json","graph_json":"https://pith.science/api/pith-number/3SRAQYBH7IRAVXS7A4ZHE34KMH/graph.json","events_json":"https://pith.science/api/pith-number/3SRAQYBH7IRAVXS7A4ZHE34KMH/events.json","paper":"https://pith.science/paper/3SRAQYBH"},"agent_actions":{"view_html":"https://pith.science/pith/3SRAQYBH7IRAVXS7A4ZHE34KMH","download_json":"https://pith.science/pith/3SRAQYBH7IRAVXS7A4ZHE34KMH.json","view_paper":"https://pith.science/paper/3SRAQYBH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.1342&json=true","fetch_graph":"https://pith.science/api/pith-number/3SRAQYBH7IRAVXS7A4ZHE34KMH/graph.json","fetch_events":"https://pith.science/api/pith-number/3SRAQYBH7IRAVXS7A4ZHE34KMH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3SRAQYBH7IRAVXS7A4ZHE34KMH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3SRAQYBH7IRAVXS7A4ZHE34KMH/action/storage_attestation","attest_author":"https://pith.science/pith/3SRAQYBH7IRAVXS7A4ZHE34KMH/action/author_attestation","sign_citation":"https://pith.science/pith/3SRAQYBH7IRAVXS7A4ZHE34KMH/action/citation_signature","submit_replication":"https://pith.science/pith/3SRAQYBH7IRAVXS7A4ZHE34KMH/action/replication_record"}},"created_at":"2026-05-18T03:29:03.700709+00:00","updated_at":"2026-05-18T03:29:03.700709+00:00"}