{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5ZAY7S5ZDYOZPBTQWXP2JZ6ESW","short_pith_number":"pith:5ZAY7S5Z","schema_version":"1.0","canonical_sha256":"ee418fcbb91e1d978670b5dfa4e7c495bb2d1217c853a72024ba8d4551d21076","source":{"kind":"arxiv","id":"1609.00823","version":2},"attestation_state":"computed","paper":{"title":"Multi-type Galton-Watson processes with affinity-dependent selection applied to antibody affinity maturation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gilles Wainrib, Irene Balelli, Vuk Mili\\v{s}i\\'c","submitted_at":"2016-09-03T12:37:53Z","abstract_excerpt":"We analyze the interactions between division, mutation and selection in a simplified evolutionary model, assuming that the population observed can be classified into fitness levels. The construction of our mathematical framework is motivated by the modeling of antibody affinity maturation of B-cells in Germinal Centers during an immune response. This is a key process in adaptive immunity leading to the production of high affinity antibodies against a presented antigen. Our aim is to understand how the different biological parameters affect the system's functionality. We identify the existence "},"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":"1609.00823","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-03T12:37:53Z","cross_cats_sorted":[],"title_canon_sha256":"6d056031e39a0ee34490bc3155cbea5ab56fe92a96d8cf34e32a5030e6ab6c1c","abstract_canon_sha256":"9a592607363ff55c059a4fffe3de2c77b74240008f6eff8fd3582bd7dc0282b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:51.997878Z","signature_b64":"7hkuGcp6iPHMnCGP6L8iO6EgfeNlw6MdKh7orIQ3SOyqiLGQY3WzlxmPUbwNuPekfSeTeIKc8BycoeLkRv6gAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee418fcbb91e1d978670b5dfa4e7c495bb2d1217c853a72024ba8d4551d21076","last_reissued_at":"2026-05-18T00:26:51.997213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:51.997213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-type Galton-Watson processes with affinity-dependent selection applied to antibody affinity maturation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gilles Wainrib, Irene Balelli, Vuk Mili\\v{s}i\\'c","submitted_at":"2016-09-03T12:37:53Z","abstract_excerpt":"We analyze the interactions between division, mutation and selection in a simplified evolutionary model, assuming that the population observed can be classified into fitness levels. The construction of our mathematical framework is motivated by the modeling of antibody affinity maturation of B-cells in Germinal Centers during an immune response. This is a key process in adaptive immunity leading to the production of high affinity antibodies against a presented antigen. Our aim is to understand how the different biological parameters affect the system's functionality. We identify the existence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00823","kind":"arxiv","version":2},"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":"1609.00823","created_at":"2026-05-18T00:26:51.997308+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.00823v2","created_at":"2026-05-18T00:26:51.997308+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00823","created_at":"2026-05-18T00:26:51.997308+00:00"},{"alias_kind":"pith_short_12","alias_value":"5ZAY7S5ZDYOZ","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5ZAY7S5ZDYOZPBTQ","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5ZAY7S5Z","created_at":"2026-05-18T12:30:01.593930+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/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW","json":"https://pith.science/pith/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW.json","graph_json":"https://pith.science/api/pith-number/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW/graph.json","events_json":"https://pith.science/api/pith-number/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW/events.json","paper":"https://pith.science/paper/5ZAY7S5Z"},"agent_actions":{"view_html":"https://pith.science/pith/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW","download_json":"https://pith.science/pith/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW.json","view_paper":"https://pith.science/paper/5ZAY7S5Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.00823&json=true","fetch_graph":"https://pith.science/api/pith-number/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW/graph.json","fetch_events":"https://pith.science/api/pith-number/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW/action/storage_attestation","attest_author":"https://pith.science/pith/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW/action/author_attestation","sign_citation":"https://pith.science/pith/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW/action/citation_signature","submit_replication":"https://pith.science/pith/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW/action/replication_record"}},"created_at":"2026-05-18T00:26:51.997308+00:00","updated_at":"2026-05-18T00:26:51.997308+00:00"}