{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MPVPEJF7VLLNOKZT4GWM5FFDGF","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":"46b116804950ea1567f7f17b296d74629660cc953fdb16ab21aec74cf7d714b8","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-17T14:21:43Z","title_canon_sha256":"a87806d41146ba1a4e61e1224362315d7ff47d2d274ded3618afbf8d216700f8"},"schema_version":"1.0","source":{"id":"1411.4488","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4488","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4488v4","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4488","created_at":"2026-05-18T01:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"MPVPEJF7VLLN","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MPVPEJF7VLLNOKZT","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MPVPEJF7","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:a0c77612325cf49ddf14ea09fc0346f40384cc27a40e028da867d4b21239dfb3","target":"graph","created_at":"2026-05-18T01:11:41Z","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":"We study a classical multitype Galton--Watson process with mutation and selection. The individuals are sequences of fixed length over a finite alphabet. On the sharp peak fitness landscape together with independent mutations per locus, we show that, as the length of the sequences goes to $\\infty$ and the mutation probability goes to 0, the asymptotic relative frequency of the sequences differing on $k$ digits from the master sequence approaches $$(\\sigma e^{-a}-1)\\frac{a^k}{k!}\\sum_{i\\geq1}\\frac{i^k}{\\sigma^i}\\,,$$ where $\\sigma$ is the selective advantage of the master sequence and $a$ is the","authors_text":"Joseba Dalmau","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-17T14:21:43Z","title":"The distribution of the quasispecies for a Galton--Watson process on the sharp peak landscape"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4488","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:f5cbb7120d5b57448ae8b9d4dec7912c905eddb96e09e07b01417a90e9416baf","target":"record","created_at":"2026-05-18T01:11:41Z","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":"46b116804950ea1567f7f17b296d74629660cc953fdb16ab21aec74cf7d714b8","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-17T14:21:43Z","title_canon_sha256":"a87806d41146ba1a4e61e1224362315d7ff47d2d274ded3618afbf8d216700f8"},"schema_version":"1.0","source":{"id":"1411.4488","kind":"arxiv","version":4}},"canonical_sha256":"63eaf224bfaad6d72b33e1acce94a3315b6335362a5784ba3c30f230adc78ea2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63eaf224bfaad6d72b33e1acce94a3315b6335362a5784ba3c30f230adc78ea2","first_computed_at":"2026-05-18T01:11:41.440773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:41.440773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hIyUFxzyTMlaK3Or0EqgtOlXoFBBeY3le3Y6GsKgT73tSkr2Q9Av+FohKskAS+V78vnqs1a5lQ5tOsrMd+UXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:41.441105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4488","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5cbb7120d5b57448ae8b9d4dec7912c905eddb96e09e07b01417a90e9416baf","sha256:a0c77612325cf49ddf14ea09fc0346f40384cc27a40e028da867d4b21239dfb3"],"state_sha256":"42660ba451f64724d7dc703de3fc7586d8c2d532f5fcaff72ddb008ea2855975"}