{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IEECZUUPWK33L2DNGEHOB7XOLW","short_pith_number":"pith:IEECZUUP","schema_version":"1.0","canonical_sha256":"41082cd28fb2b7b5e86d310ee0feee5d9822cc44d1d4463f571171f0c6170620","source":{"kind":"arxiv","id":"1601.02516","version":3},"attestation_state":"computed","paper":{"title":"On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Coralie Fritsch (CMAP, Fabien Campillo (MATHNEURO, IECL, IMAG), Nicolas Champagnat (IECL, TOSCA)","submitted_at":"2016-01-11T16:36:00Z","abstract_excerpt":"We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of the model. We study the variations of the survival probability of the stochastic model, using a generation by generation approach. Then, making use of the link between the survival probability and the principal eigenvalue established in a previous work, we deduce the variations of the eigenvalue with respect to the parameter of the model."},"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":"1601.02516","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-11T16:36:00Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"bf03cf099da133579dc6c86584d6ba6390b77ed51847db87c55de09bc1b75440","abstract_canon_sha256":"c9485f657a08fa88cb2c2fffe93add3a5176b791e93bce531772ed8142016d91"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:23.649024Z","signature_b64":"0TVM+TbqmhOBvKefwPSumC7cZfo5XoLuZ0ppGQ+kai4W7s9P+U0QDhVYS8bv1dxO6wDYvQnyylT5Isx06dd7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41082cd28fb2b7b5e86d310ee0feee5d9822cc44d1d4463f571171f0c6170620","last_reissued_at":"2026-05-18T00:52:23.648272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:23.648272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Coralie Fritsch (CMAP, Fabien Campillo (MATHNEURO, IECL, IMAG), Nicolas Champagnat (IECL, TOSCA)","submitted_at":"2016-01-11T16:36:00Z","abstract_excerpt":"We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of the model. We study the variations of the survival probability of the stochastic model, using a generation by generation approach. Then, making use of the link between the survival probability and the principal eigenvalue established in a previous work, we deduce the variations of the eigenvalue with respect to the parameter of the model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02516","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":"1601.02516","created_at":"2026-05-18T00:52:23.648390+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.02516v3","created_at":"2026-05-18T00:52:23.648390+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02516","created_at":"2026-05-18T00:52:23.648390+00:00"},{"alias_kind":"pith_short_12","alias_value":"IEECZUUPWK33","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IEECZUUPWK33L2DN","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IEECZUUP","created_at":"2026-05-18T12:30:22.444734+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/IEECZUUPWK33L2DNGEHOB7XOLW","json":"https://pith.science/pith/IEECZUUPWK33L2DNGEHOB7XOLW.json","graph_json":"https://pith.science/api/pith-number/IEECZUUPWK33L2DNGEHOB7XOLW/graph.json","events_json":"https://pith.science/api/pith-number/IEECZUUPWK33L2DNGEHOB7XOLW/events.json","paper":"https://pith.science/paper/IEECZUUP"},"agent_actions":{"view_html":"https://pith.science/pith/IEECZUUPWK33L2DNGEHOB7XOLW","download_json":"https://pith.science/pith/IEECZUUPWK33L2DNGEHOB7XOLW.json","view_paper":"https://pith.science/paper/IEECZUUP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.02516&json=true","fetch_graph":"https://pith.science/api/pith-number/IEECZUUPWK33L2DNGEHOB7XOLW/graph.json","fetch_events":"https://pith.science/api/pith-number/IEECZUUPWK33L2DNGEHOB7XOLW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IEECZUUPWK33L2DNGEHOB7XOLW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IEECZUUPWK33L2DNGEHOB7XOLW/action/storage_attestation","attest_author":"https://pith.science/pith/IEECZUUPWK33L2DNGEHOB7XOLW/action/author_attestation","sign_citation":"https://pith.science/pith/IEECZUUPWK33L2DNGEHOB7XOLW/action/citation_signature","submit_replication":"https://pith.science/pith/IEECZUUPWK33L2DNGEHOB7XOLW/action/replication_record"}},"created_at":"2026-05-18T00:52:23.648390+00:00","updated_at":"2026-05-18T00:52:23.648390+00:00"}