{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EL25PSWY55FKFGKEQXHFEDRUE4","short_pith_number":"pith:EL25PSWY","schema_version":"1.0","canonical_sha256":"22f5d7cad8ef4aa2994485ce520e342716ae7b3b1426803292336991f67ba199","source":{"kind":"arxiv","id":"1804.02293","version":4},"attestation_state":"computed","paper":{"title":"Phase Transitions of the Moran Process and Algorithmic Consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.SI","math.CO","q-bio.PE"],"primary_cat":"math.PR","authors_text":"David Richerby, John Lapinskas, Leslie Ann Goldberg","submitted_at":"2018-04-06T14:23:15Z","abstract_excerpt":"The Moran process is a random process that models the spread of genetic mutations through graphs. If the graph is connected, the process eventually reaches \"fixation\", where every vertex is a mutant, or \"extinction\", where no vertex is a mutant.\n  Our main result is an almost-tight bound on expected absorption time. For all epsilon > 0, we show that the expected absorption time on an n-vertex graph is o(n^(3+epsilon)). In fact, we show that it is at most n^3 * exp(O((log log n)^3)) and that there is a family of graphs where it is Omega(n^3). In the course of proving our main result, we also es"},"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":"1804.02293","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-06T14:23:15Z","cross_cats_sorted":["cs.DM","cs.SI","math.CO","q-bio.PE"],"title_canon_sha256":"0c4b0a8452ab8ff7ffafc92410f8fdf79f0e7d1ef6c7007330a8b2bf2ccb420c","abstract_canon_sha256":"f3a937a6de0593755e96108dd035f1f80c423da2a132aa7ae6e80233d0c3c22f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:41.859104Z","signature_b64":"pShV9VuuMsraHRBsS4GK6YCc/kowo0J6rEYraXrk5B/c3BaydWZItFbyH0bc7KqPO9DJbSH2/ZlPemOqNY9oBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22f5d7cad8ef4aa2994485ce520e342716ae7b3b1426803292336991f67ba199","last_reissued_at":"2026-05-17T23:40:41.858597Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:41.858597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase Transitions of the Moran Process and Algorithmic Consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.SI","math.CO","q-bio.PE"],"primary_cat":"math.PR","authors_text":"David Richerby, John Lapinskas, Leslie Ann Goldberg","submitted_at":"2018-04-06T14:23:15Z","abstract_excerpt":"The Moran process is a random process that models the spread of genetic mutations through graphs. If the graph is connected, the process eventually reaches \"fixation\", where every vertex is a mutant, or \"extinction\", where no vertex is a mutant.\n  Our main result is an almost-tight bound on expected absorption time. For all epsilon > 0, we show that the expected absorption time on an n-vertex graph is o(n^(3+epsilon)). In fact, we show that it is at most n^3 * exp(O((log log n)^3)) and that there is a family of graphs where it is Omega(n^3). In the course of proving our main result, we also es"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02293","kind":"arxiv","version":4},"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":"1804.02293","created_at":"2026-05-17T23:40:41.858684+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.02293v4","created_at":"2026-05-17T23:40:41.858684+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.02293","created_at":"2026-05-17T23:40:41.858684+00:00"},{"alias_kind":"pith_short_12","alias_value":"EL25PSWY55FK","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EL25PSWY55FKFGKE","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EL25PSWY","created_at":"2026-05-18T12:32:22.470017+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/EL25PSWY55FKFGKEQXHFEDRUE4","json":"https://pith.science/pith/EL25PSWY55FKFGKEQXHFEDRUE4.json","graph_json":"https://pith.science/api/pith-number/EL25PSWY55FKFGKEQXHFEDRUE4/graph.json","events_json":"https://pith.science/api/pith-number/EL25PSWY55FKFGKEQXHFEDRUE4/events.json","paper":"https://pith.science/paper/EL25PSWY"},"agent_actions":{"view_html":"https://pith.science/pith/EL25PSWY55FKFGKEQXHFEDRUE4","download_json":"https://pith.science/pith/EL25PSWY55FKFGKEQXHFEDRUE4.json","view_paper":"https://pith.science/paper/EL25PSWY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.02293&json=true","fetch_graph":"https://pith.science/api/pith-number/EL25PSWY55FKFGKEQXHFEDRUE4/graph.json","fetch_events":"https://pith.science/api/pith-number/EL25PSWY55FKFGKEQXHFEDRUE4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EL25PSWY55FKFGKEQXHFEDRUE4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EL25PSWY55FKFGKEQXHFEDRUE4/action/storage_attestation","attest_author":"https://pith.science/pith/EL25PSWY55FKFGKEQXHFEDRUE4/action/author_attestation","sign_citation":"https://pith.science/pith/EL25PSWY55FKFGKEQXHFEDRUE4/action/citation_signature","submit_replication":"https://pith.science/pith/EL25PSWY55FKFGKEQXHFEDRUE4/action/replication_record"}},"created_at":"2026-05-17T23:40:41.858684+00:00","updated_at":"2026-05-17T23:40:41.858684+00:00"}