{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:W3NWMMJ3Q4AFQV276QG5N4OL5Z","short_pith_number":"pith:W3NWMMJ3","schema_version":"1.0","canonical_sha256":"b6db66313b870058575ff40dd6f1cbee7de31a8e69d7a49c41462cc223dae00d","source":{"kind":"arxiv","id":"0911.1973","version":3},"attestation_state":"computed","paper":{"title":"Limit theorems for Markov processes indexed by continuous time Galton--Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Delmas, Laurence Marsalle, Viet Chi Tran, Vincent Bansaye","submitted_at":"2009-11-10T19:17:40Z","abstract_excerpt":"We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton--Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring locations depend on the position of the mother and the number of offspring. We prove a law of large numbers for the empirical measure of individuals alive at time t. This relies on a probabilistic interpretation of its intensity by mean of an auxiliary process. The latter has the same generator as the Markov process along the branches plus additional jumps, ass"},"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":"0911.1973","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-11-10T19:17:40Z","cross_cats_sorted":[],"title_canon_sha256":"b2c93cab3946a3efe7fcf7c95d6fca30044d3e0cc4f88f297a41876a22deb06c","abstract_canon_sha256":"bf32ea3e4d91915cd56e7204f26f6b0aa0220881e5d42e7ccb3c8ba1972f1f31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:12.192258Z","signature_b64":"FXW2ZuNaSZMNEkkd0ZWNpd4KM4A09ULX4j67zzHuMmpWgIBmlkHwI1aiUmKNxpjU/SHA/CqjC159Je6YHoJGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6db66313b870058575ff40dd6f1cbee7de31a8e69d7a49c41462cc223dae00d","last_reissued_at":"2026-05-18T04:02:12.191456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:12.191456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit theorems for Markov processes indexed by continuous time Galton--Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Delmas, Laurence Marsalle, Viet Chi Tran, Vincent Bansaye","submitted_at":"2009-11-10T19:17:40Z","abstract_excerpt":"We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton--Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring locations depend on the position of the mother and the number of offspring. We prove a law of large numbers for the empirical measure of individuals alive at time t. This relies on a probabilistic interpretation of its intensity by mean of an auxiliary process. The latter has the same generator as the Markov process along the branches plus additional jumps, ass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1973","kind":"arxiv","version":3},"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":"0911.1973","created_at":"2026-05-18T04:02:12.191584+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.1973v3","created_at":"2026-05-18T04:02:12.191584+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1973","created_at":"2026-05-18T04:02:12.191584+00:00"},{"alias_kind":"pith_short_12","alias_value":"W3NWMMJ3Q4AF","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"W3NWMMJ3Q4AFQV27","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"W3NWMMJ3","created_at":"2026-05-18T12:26:02.257875+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/W3NWMMJ3Q4AFQV276QG5N4OL5Z","json":"https://pith.science/pith/W3NWMMJ3Q4AFQV276QG5N4OL5Z.json","graph_json":"https://pith.science/api/pith-number/W3NWMMJ3Q4AFQV276QG5N4OL5Z/graph.json","events_json":"https://pith.science/api/pith-number/W3NWMMJ3Q4AFQV276QG5N4OL5Z/events.json","paper":"https://pith.science/paper/W3NWMMJ3"},"agent_actions":{"view_html":"https://pith.science/pith/W3NWMMJ3Q4AFQV276QG5N4OL5Z","download_json":"https://pith.science/pith/W3NWMMJ3Q4AFQV276QG5N4OL5Z.json","view_paper":"https://pith.science/paper/W3NWMMJ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.1973&json=true","fetch_graph":"https://pith.science/api/pith-number/W3NWMMJ3Q4AFQV276QG5N4OL5Z/graph.json","fetch_events":"https://pith.science/api/pith-number/W3NWMMJ3Q4AFQV276QG5N4OL5Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W3NWMMJ3Q4AFQV276QG5N4OL5Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W3NWMMJ3Q4AFQV276QG5N4OL5Z/action/storage_attestation","attest_author":"https://pith.science/pith/W3NWMMJ3Q4AFQV276QG5N4OL5Z/action/author_attestation","sign_citation":"https://pith.science/pith/W3NWMMJ3Q4AFQV276QG5N4OL5Z/action/citation_signature","submit_replication":"https://pith.science/pith/W3NWMMJ3Q4AFQV276QG5N4OL5Z/action/replication_record"}},"created_at":"2026-05-18T04:02:12.191584+00:00","updated_at":"2026-05-18T04:02:12.191584+00:00"}