{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7DR2GJZU5OBEDUXMW3GCJHMMZP","short_pith_number":"pith:7DR2GJZU","schema_version":"1.0","canonical_sha256":"f8e3a32734eb8241d2ecb6cc249d8ccbfe5e1fc6e92b471387a340885a892cbb","source":{"kind":"arxiv","id":"1512.05431","version":4},"attestation_state":"computed","paper":{"title":"A Path Integral Approach to Age Dependent Branching Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-bio.PE"],"primary_cat":"physics.bio-ph","authors_text":"Chris D Greenman","submitted_at":"2015-12-17T01:16:38Z","abstract_excerpt":"Age dependent population dynamics are frequently modeled with generalizations of the classic McKendrick-von Foerster equation. These are deterministic systems, and a stochastic generalization was recently reported in [1,2]. Here we develop a fully stochastic theory for age-structured populations via quantum field theoretical Doi-Peliti techniques. This results in a path integral formulation where birth and death events correspond to cubic and quadratic interaction terms. This formalism allows us to efficiently recapitulate the results in [1,2], exemplifying the utility of Doi-Peliti methods. F"},"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":"1512.05431","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2015-12-17T01:16:38Z","cross_cats_sorted":["math.PR","q-bio.PE"],"title_canon_sha256":"043da1f381a0ae1e8bde7fae9838002ab4ad6bae581fe35a487eca2a80a6bb95","abstract_canon_sha256":"15bba0a45687fc695fab641b12a35a52ceca0bb21b8b5ba1fd8c803ac8b41ea7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:44.207240Z","signature_b64":"OBl/2E5t96cF719fOHi/+RqMF2JAMj6EBpho/hQago9Szz+sPpecIHcZ2c0d74CdrMqjiuW6ePjcnO8N+il4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8e3a32734eb8241d2ecb6cc249d8ccbfe5e1fc6e92b471387a340885a892cbb","last_reissued_at":"2026-05-18T00:57:44.206865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:44.206865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Path Integral Approach to Age Dependent Branching Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-bio.PE"],"primary_cat":"physics.bio-ph","authors_text":"Chris D Greenman","submitted_at":"2015-12-17T01:16:38Z","abstract_excerpt":"Age dependent population dynamics are frequently modeled with generalizations of the classic McKendrick-von Foerster equation. These are deterministic systems, and a stochastic generalization was recently reported in [1,2]. Here we develop a fully stochastic theory for age-structured populations via quantum field theoretical Doi-Peliti techniques. This results in a path integral formulation where birth and death events correspond to cubic and quadratic interaction terms. This formalism allows us to efficiently recapitulate the results in [1,2], exemplifying the utility of Doi-Peliti methods. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05431","kind":"arxiv","version":4},"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":"1512.05431","created_at":"2026-05-18T00:57:44.206925+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.05431v4","created_at":"2026-05-18T00:57:44.206925+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05431","created_at":"2026-05-18T00:57:44.206925+00:00"},{"alias_kind":"pith_short_12","alias_value":"7DR2GJZU5OBE","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"7DR2GJZU5OBEDUXM","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"7DR2GJZU","created_at":"2026-05-18T12:29:07.941421+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/7DR2GJZU5OBEDUXMW3GCJHMMZP","json":"https://pith.science/pith/7DR2GJZU5OBEDUXMW3GCJHMMZP.json","graph_json":"https://pith.science/api/pith-number/7DR2GJZU5OBEDUXMW3GCJHMMZP/graph.json","events_json":"https://pith.science/api/pith-number/7DR2GJZU5OBEDUXMW3GCJHMMZP/events.json","paper":"https://pith.science/paper/7DR2GJZU"},"agent_actions":{"view_html":"https://pith.science/pith/7DR2GJZU5OBEDUXMW3GCJHMMZP","download_json":"https://pith.science/pith/7DR2GJZU5OBEDUXMW3GCJHMMZP.json","view_paper":"https://pith.science/paper/7DR2GJZU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.05431&json=true","fetch_graph":"https://pith.science/api/pith-number/7DR2GJZU5OBEDUXMW3GCJHMMZP/graph.json","fetch_events":"https://pith.science/api/pith-number/7DR2GJZU5OBEDUXMW3GCJHMMZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7DR2GJZU5OBEDUXMW3GCJHMMZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7DR2GJZU5OBEDUXMW3GCJHMMZP/action/storage_attestation","attest_author":"https://pith.science/pith/7DR2GJZU5OBEDUXMW3GCJHMMZP/action/author_attestation","sign_citation":"https://pith.science/pith/7DR2GJZU5OBEDUXMW3GCJHMMZP/action/citation_signature","submit_replication":"https://pith.science/pith/7DR2GJZU5OBEDUXMW3GCJHMMZP/action/replication_record"}},"created_at":"2026-05-18T00:57:44.206925+00:00","updated_at":"2026-05-18T00:57:44.206925+00:00"}