{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:KPUFZMILTGVYDNKT3MSYGX4ZAZ","short_pith_number":"pith:KPUFZMIL","schema_version":"1.0","canonical_sha256":"53e85cb10b99ab81b553db25835f99067d19b2880e9b96bb2a829ddbe9f5fabc","source":{"kind":"arxiv","id":"1210.4798","version":4},"attestation_state":"computed","paper":{"title":"On the existence of accessible paths in various models of fitness landscapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","q-bio.QM"],"primary_cat":"math.PR","authors_text":"Anders Martinsson, Peter Hegarty","submitted_at":"2012-10-17T17:16:05Z","abstract_excerpt":"We present rigorous mathematical analyses of a number of well-known mathematical models for genetic mutations. In these models, the genome is represented by a vertex of the $n$-dimensional binary hypercube, for some $n$, a mutation involves the flipping of a single bit, and each vertex is assigned a real number, called its fitness, according to some rules. Our main concern is with the issue of existence of (selectively) accessible paths; that is, monotonic paths in the hypercube along which fitness is always increasing. Our main results resolve open questions about three such models, which in "},"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":"1210.4798","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-17T17:16:05Z","cross_cats_sorted":["math.CO","q-bio.QM"],"title_canon_sha256":"a9dc862599e94f17e2af2eda8833669ccdc0508e2483229a4c50308dfbd55dd2","abstract_canon_sha256":"8ee6dc8ed9b2706abb72ba98cc63d44d5f3a1dbe1859612d82b00cb59580461a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:48.697293Z","signature_b64":"KRO/n2bnaqTxwUIr1315ePVO5klmpPBWRQp4kqdC7exaqRP8mT/WJ4evfX5E8g+qNeLUo0KcgpqNV9ebAGGFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53e85cb10b99ab81b553db25835f99067d19b2880e9b96bb2a829ddbe9f5fabc","last_reissued_at":"2026-05-18T02:51:48.696822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:48.696822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the existence of accessible paths in various models of fitness landscapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","q-bio.QM"],"primary_cat":"math.PR","authors_text":"Anders Martinsson, Peter Hegarty","submitted_at":"2012-10-17T17:16:05Z","abstract_excerpt":"We present rigorous mathematical analyses of a number of well-known mathematical models for genetic mutations. In these models, the genome is represented by a vertex of the $n$-dimensional binary hypercube, for some $n$, a mutation involves the flipping of a single bit, and each vertex is assigned a real number, called its fitness, according to some rules. Our main concern is with the issue of existence of (selectively) accessible paths; that is, monotonic paths in the hypercube along which fitness is always increasing. Our main results resolve open questions about three such models, which in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4798","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":"1210.4798","created_at":"2026-05-18T02:51:48.696898+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.4798v4","created_at":"2026-05-18T02:51:48.696898+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4798","created_at":"2026-05-18T02:51:48.696898+00:00"},{"alias_kind":"pith_short_12","alias_value":"KPUFZMILTGVY","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"KPUFZMILTGVYDNKT","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"KPUFZMIL","created_at":"2026-05-18T12:27:11.947152+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/KPUFZMILTGVYDNKT3MSYGX4ZAZ","json":"https://pith.science/pith/KPUFZMILTGVYDNKT3MSYGX4ZAZ.json","graph_json":"https://pith.science/api/pith-number/KPUFZMILTGVYDNKT3MSYGX4ZAZ/graph.json","events_json":"https://pith.science/api/pith-number/KPUFZMILTGVYDNKT3MSYGX4ZAZ/events.json","paper":"https://pith.science/paper/KPUFZMIL"},"agent_actions":{"view_html":"https://pith.science/pith/KPUFZMILTGVYDNKT3MSYGX4ZAZ","download_json":"https://pith.science/pith/KPUFZMILTGVYDNKT3MSYGX4ZAZ.json","view_paper":"https://pith.science/paper/KPUFZMIL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.4798&json=true","fetch_graph":"https://pith.science/api/pith-number/KPUFZMILTGVYDNKT3MSYGX4ZAZ/graph.json","fetch_events":"https://pith.science/api/pith-number/KPUFZMILTGVYDNKT3MSYGX4ZAZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KPUFZMILTGVYDNKT3MSYGX4ZAZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KPUFZMILTGVYDNKT3MSYGX4ZAZ/action/storage_attestation","attest_author":"https://pith.science/pith/KPUFZMILTGVYDNKT3MSYGX4ZAZ/action/author_attestation","sign_citation":"https://pith.science/pith/KPUFZMILTGVYDNKT3MSYGX4ZAZ/action/citation_signature","submit_replication":"https://pith.science/pith/KPUFZMILTGVYDNKT3MSYGX4ZAZ/action/replication_record"}},"created_at":"2026-05-18T02:51:48.696898+00:00","updated_at":"2026-05-18T02:51:48.696898+00:00"}