{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:AU5AVRRKEJ62QZKURCBWLRCOVB","short_pith_number":"pith:AU5AVRRK","schema_version":"1.0","canonical_sha256":"053a0ac62a227da86554888365c44ea85e9d3049f995403915c80a83c1fc4303","source":{"kind":"arxiv","id":"1303.0026","version":3},"attestation_state":"computed","paper":{"title":"When Hamilton circuits generate the cycle space of a random graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter C. Heinig","submitted_at":"2013-02-28T21:40:24Z","abstract_excerpt":"If eps > 0 and p >= n^{-1/2 + eps}, in a binomial random graph G(n,p) a.a.s. the set of cycles which can be constructed as a symmetric difference of Hamilton circuits is as large as parity by itself permits (all cycles if n is odd, all even cycles if n is even). Moreover, every p which ensures the above property a.a.s. must necessarily be such that for any constant c>0, eventually p >= (log n + 2 log log n + c)/n. So, whatever the smallest sufficient p for an a.a.s. Hamilton-generated cycle space might be, it does not coincide with the threshold for hamiltonicity of G(n,p)."},"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":"1303.0026","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-28T21:40:24Z","cross_cats_sorted":[],"title_canon_sha256":"2896229cd25fd0304655610f3f126bf447eaa08541e23f0967e659cfae7e2e5a","abstract_canon_sha256":"e3b12417789b192d591319e196739773a3bd24831d926b583b6141828e455cea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:51.145835Z","signature_b64":"qbKij+NptVuxSckE2RiqZd9CMJDh+UFYpjA08HqOGPCPEnfNUeNjwxN3NzNupeZSxYKRyyxXtkcVmnfCEFucAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"053a0ac62a227da86554888365c44ea85e9d3049f995403915c80a83c1fc4303","last_reissued_at":"2026-05-18T03:16:51.145287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:51.145287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When Hamilton circuits generate the cycle space of a random graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter C. Heinig","submitted_at":"2013-02-28T21:40:24Z","abstract_excerpt":"If eps > 0 and p >= n^{-1/2 + eps}, in a binomial random graph G(n,p) a.a.s. the set of cycles which can be constructed as a symmetric difference of Hamilton circuits is as large as parity by itself permits (all cycles if n is odd, all even cycles if n is even). Moreover, every p which ensures the above property a.a.s. must necessarily be such that for any constant c>0, eventually p >= (log n + 2 log log n + c)/n. So, whatever the smallest sufficient p for an a.a.s. Hamilton-generated cycle space might be, it does not coincide with the threshold for hamiltonicity of G(n,p)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0026","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":"1303.0026","created_at":"2026-05-18T03:16:51.145382+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.0026v3","created_at":"2026-05-18T03:16:51.145382+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0026","created_at":"2026-05-18T03:16:51.145382+00:00"},{"alias_kind":"pith_short_12","alias_value":"AU5AVRRKEJ62","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"AU5AVRRKEJ62QZKU","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"AU5AVRRK","created_at":"2026-05-18T12:27:38.830355+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.05835","citing_title":"On graphs whose cycle space is spanned by their Hamilton cycles","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AU5AVRRKEJ62QZKURCBWLRCOVB","json":"https://pith.science/pith/AU5AVRRKEJ62QZKURCBWLRCOVB.json","graph_json":"https://pith.science/api/pith-number/AU5AVRRKEJ62QZKURCBWLRCOVB/graph.json","events_json":"https://pith.science/api/pith-number/AU5AVRRKEJ62QZKURCBWLRCOVB/events.json","paper":"https://pith.science/paper/AU5AVRRK"},"agent_actions":{"view_html":"https://pith.science/pith/AU5AVRRKEJ62QZKURCBWLRCOVB","download_json":"https://pith.science/pith/AU5AVRRKEJ62QZKURCBWLRCOVB.json","view_paper":"https://pith.science/paper/AU5AVRRK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.0026&json=true","fetch_graph":"https://pith.science/api/pith-number/AU5AVRRKEJ62QZKURCBWLRCOVB/graph.json","fetch_events":"https://pith.science/api/pith-number/AU5AVRRKEJ62QZKURCBWLRCOVB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AU5AVRRKEJ62QZKURCBWLRCOVB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AU5AVRRKEJ62QZKURCBWLRCOVB/action/storage_attestation","attest_author":"https://pith.science/pith/AU5AVRRKEJ62QZKURCBWLRCOVB/action/author_attestation","sign_citation":"https://pith.science/pith/AU5AVRRKEJ62QZKURCBWLRCOVB/action/citation_signature","submit_replication":"https://pith.science/pith/AU5AVRRKEJ62QZKURCBWLRCOVB/action/replication_record"}},"created_at":"2026-05-18T03:16:51.145382+00:00","updated_at":"2026-05-18T03:16:51.145382+00:00"}