{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:44NQISROFUXNUOL4GOASB3TJPB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a0dd193c6b0716e4d5f7c1531c851daea5eb2cbb50675aac3e1f30088b8f58d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-02-13T18:34:05Z","title_canon_sha256":"f9a8c01c37f805c975a6dcdb171c91fa9d41fcdf6425ae9980da21b372a77b8e"},"schema_version":"1.0","source":{"id":"1202.2811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2811","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2811v1","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2811","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"pith_short_12","alias_value":"44NQISROFUXN","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"44NQISROFUXNUOL4","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"44NQISRO","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:1ce2ca36b260145e1bb57358c72d5ec73bdf7a36df0a6e415eb92b1d4b5de80d","target":"graph","created_at":"2026-05-18T03:51:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Branching random walks are key to the description of several physical and biological systems, such as neutron multiplication, genetics and population dynamics. For a broad class of such processes, in this Letter we derive the discrete Feynman-Kac equations for the probability and the moments of the number of visits $n_V$ of the walker to a given region $V$ in the phase space. Feynman-Kac formulas for the residence times of Markovian processes are recovered in the diffusion limit.","authors_text":"Alain Mazzolo, Andrea Zoia, Eric Dumonteil","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-02-13T18:34:05Z","title":"Discrete Feynman-Kac formulas for branching random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2811","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:433994cd0c60514103cf50944636e06cd698d76ca5ae01555f888779abc98b3e","target":"record","created_at":"2026-05-18T03:51:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a0dd193c6b0716e4d5f7c1531c851daea5eb2cbb50675aac3e1f30088b8f58d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-02-13T18:34:05Z","title_canon_sha256":"f9a8c01c37f805c975a6dcdb171c91fa9d41fcdf6425ae9980da21b372a77b8e"},"schema_version":"1.0","source":{"id":"1202.2811","kind":"arxiv","version":1}},"canonical_sha256":"e71b044a2e2d2eda397c338120ee69787ad0c250f8c86eb684e5f7123c2fdf02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e71b044a2e2d2eda397c338120ee69787ad0c250f8c86eb684e5f7123c2fdf02","first_computed_at":"2026-05-18T03:51:35.495124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:35.495124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CokZwALG5+E0mHidY11wuQ415zokQO+aiHqJS7eaHyq1rNHf+g73f6AL9h8iPs58RPOQqbRZooH5WJYO3YfHCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:35.495652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:433994cd0c60514103cf50944636e06cd698d76ca5ae01555f888779abc98b3e","sha256:1ce2ca36b260145e1bb57358c72d5ec73bdf7a36df0a6e415eb92b1d4b5de80d"],"state_sha256":"7b06243b88ee2bb85e82befeff6f07edefc86ce2c3349373a2c52c51e43db40f"}