{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:FA2OKTU3B2M7LMDIJUME7AGKCK","short_pith_number":"pith:FA2OKTU3","schema_version":"1.0","canonical_sha256":"2834e54e9b0e99f5b0684d184f80ca128a066f3c8dcf2b79fd1817786844544a","source":{"kind":"arxiv","id":"2606.11511","version":1},"attestation_state":"computed","paper":{"title":"Convergence of a Critical Multitype Bellman--Harris Process with One Infinite-Mean Lifetime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Prates Machado Fabio, Ram\\'irez-Gonz\\'alez J.H.","submitted_at":"2026-06-09T23:14:59Z","abstract_excerpt":"We study a critical multitype Bellman--Harris branching particle system in $\\mathbb R^N$ with a finite type space $\\mathbb K=\\{1,\\dots,K\\}$. Particles of type $i$ move according to a symmetric $\\alpha_i$-stable process and reproduce according to a critical offspring law whose mean matrix is irreducible and stochastic. The lifetime distribution of type $1$ is assumed to have infinite mean with regularly varying tail $$\n  1-F_1(t)\\sim c_1t^{-\\gamma},\\, 0<\\gamma<1, $$ whereas the remaining lifetime distributions satisfy polynomial upper-tail bounds\n  $$\n  \\overline F_i(t)\\le C t^{-\\eta_i},\\, i=2,"},"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":"2606.11511","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-09T23:14:59Z","cross_cats_sorted":[],"title_canon_sha256":"71cfb5325b16729d7dd4b3e38f6707ad5d28e28b79cb3f2611859808cae4ac64","abstract_canon_sha256":"248275a1868bfba5e442fe5a5d9cbe67af703407cd55102977a01acb6db1f50a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:09:53.359765Z","signature_b64":"7Q4rYhpwR7cnSwbGZYDpgZoj1ZBh0Ab8zyZBBYeTkyeHtdc9Mn5BGB0CHGAWTdy6WIqhyVireS5qvIh0kUouCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2834e54e9b0e99f5b0684d184f80ca128a066f3c8dcf2b79fd1817786844544a","last_reissued_at":"2026-06-11T01:09:53.358895Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:09:53.358895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of a Critical Multitype Bellman--Harris Process with One Infinite-Mean Lifetime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Prates Machado Fabio, Ram\\'irez-Gonz\\'alez J.H.","submitted_at":"2026-06-09T23:14:59Z","abstract_excerpt":"We study a critical multitype Bellman--Harris branching particle system in $\\mathbb R^N$ with a finite type space $\\mathbb K=\\{1,\\dots,K\\}$. Particles of type $i$ move according to a symmetric $\\alpha_i$-stable process and reproduce according to a critical offspring law whose mean matrix is irreducible and stochastic. The lifetime distribution of type $1$ is assumed to have infinite mean with regularly varying tail $$\n  1-F_1(t)\\sim c_1t^{-\\gamma},\\, 0<\\gamma<1, $$ whereas the remaining lifetime distributions satisfy polynomial upper-tail bounds\n  $$\n  \\overline F_i(t)\\le C t^{-\\eta_i},\\, i=2,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11511","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11511/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.11511","created_at":"2026-06-11T01:09:53.359032+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.11511v1","created_at":"2026-06-11T01:09:53.359032+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11511","created_at":"2026-06-11T01:09:53.359032+00:00"},{"alias_kind":"pith_short_12","alias_value":"FA2OKTU3B2M7","created_at":"2026-06-11T01:09:53.359032+00:00"},{"alias_kind":"pith_short_16","alias_value":"FA2OKTU3B2M7LMDI","created_at":"2026-06-11T01:09:53.359032+00:00"},{"alias_kind":"pith_short_8","alias_value":"FA2OKTU3","created_at":"2026-06-11T01:09:53.359032+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/FA2OKTU3B2M7LMDIJUME7AGKCK","json":"https://pith.science/pith/FA2OKTU3B2M7LMDIJUME7AGKCK.json","graph_json":"https://pith.science/api/pith-number/FA2OKTU3B2M7LMDIJUME7AGKCK/graph.json","events_json":"https://pith.science/api/pith-number/FA2OKTU3B2M7LMDIJUME7AGKCK/events.json","paper":"https://pith.science/paper/FA2OKTU3"},"agent_actions":{"view_html":"https://pith.science/pith/FA2OKTU3B2M7LMDIJUME7AGKCK","download_json":"https://pith.science/pith/FA2OKTU3B2M7LMDIJUME7AGKCK.json","view_paper":"https://pith.science/paper/FA2OKTU3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.11511&json=true","fetch_graph":"https://pith.science/api/pith-number/FA2OKTU3B2M7LMDIJUME7AGKCK/graph.json","fetch_events":"https://pith.science/api/pith-number/FA2OKTU3B2M7LMDIJUME7AGKCK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FA2OKTU3B2M7LMDIJUME7AGKCK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FA2OKTU3B2M7LMDIJUME7AGKCK/action/storage_attestation","attest_author":"https://pith.science/pith/FA2OKTU3B2M7LMDIJUME7AGKCK/action/author_attestation","sign_citation":"https://pith.science/pith/FA2OKTU3B2M7LMDIJUME7AGKCK/action/citation_signature","submit_replication":"https://pith.science/pith/FA2OKTU3B2M7LMDIJUME7AGKCK/action/replication_record"}},"created_at":"2026-06-11T01:09:53.359032+00:00","updated_at":"2026-06-11T01:09:53.359032+00:00"}