{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BMEJN76JVADZMLYJ77F5OXZ6Z6","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":"da2c1625e0da007d97b037bb99043aa99281f205837dfb0f0a1b8dea7a3d5433","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-08T17:44:33Z","title_canon_sha256":"5e7a235eec0b46291d70685fd8e8e88792113dec39abff2932729332bcac38d6"},"schema_version":"1.0","source":{"id":"1505.02109","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02109","created_at":"2026-05-18T00:36:44Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02109v4","created_at":"2026-05-18T00:36:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02109","created_at":"2026-05-18T00:36:44Z"},{"alias_kind":"pith_short_12","alias_value":"BMEJN76JVADZ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BMEJN76JVADZMLYJ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BMEJN76J","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:3469ced0da5736c5eff105c2f82a6e4c01edb2407d4d1223ad2b64f5eedbe5ca","target":"graph","created_at":"2026-05-18T00:36:44Z","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":"In this paper we analyse the genetic evolution of a diploid hermaphroditic population, which is modelled by a three-type nonlinear birth-and-death process with competition and Mendelian reproduction. In a recent paper, Collet et al., 2013 have shown that, on the mutation time-scale, the process converges to the Trait-Substitution Sequence of adaptive dynamics, stepping from one homozygotic state to another with higher fitness. We prove that, under the assumption that a dominant allele is also the fittest one, the recessive allele survives for a time of order at least K^{1/4-a}, where K is the ","authors_text":"Anton Bovier, Rebecca Neukirch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-08T17:44:33Z","title":"Survival of a recessive allele in a Mendelian diploid model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02109","kind":"arxiv","version":4},"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:c86a9729f89c15fee41a8421cf6b8a280dca53b5ef64a8e7c56aa06f9713a4b0","target":"record","created_at":"2026-05-18T00:36:44Z","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":"da2c1625e0da007d97b037bb99043aa99281f205837dfb0f0a1b8dea7a3d5433","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-08T17:44:33Z","title_canon_sha256":"5e7a235eec0b46291d70685fd8e8e88792113dec39abff2932729332bcac38d6"},"schema_version":"1.0","source":{"id":"1505.02109","kind":"arxiv","version":4}},"canonical_sha256":"0b0896ffc9a807962f09ffcbd75f3ecfba661235cec4c6dcb061efee04ba89ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b0896ffc9a807962f09ffcbd75f3ecfba661235cec4c6dcb061efee04ba89ea","first_computed_at":"2026-05-18T00:36:44.012286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:44.012286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y2hesFjTfaMr9jCqffEyoDcywAxqPRJY7gkyvtFuqM66o/2MjZWNi/fTdeoIU+n9v2lEZtAWdSoEAUUEnH5wCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:44.012855Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02109","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c86a9729f89c15fee41a8421cf6b8a280dca53b5ef64a8e7c56aa06f9713a4b0","sha256:3469ced0da5736c5eff105c2f82a6e4c01edb2407d4d1223ad2b64f5eedbe5ca"],"state_sha256":"f11a0f78e9f686919dc0e7b7b5ff70bd9d96e3029ac861b4c9683a304783abe5"}