{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XZJTGWTQPZP6T3WLYAAP7TWGAA","short_pith_number":"pith:XZJTGWTQ","schema_version":"1.0","canonical_sha256":"be53335a707e5fe9eecbc000ffcec600053407d9739fe4eafca0a0dff8a2c779","source":{"kind":"arxiv","id":"1701.08506","version":1},"attestation_state":"computed","paper":{"title":"On Hamilton Decompositions of Infinite Circulant Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Barbara Maenhaut, Bridget Webb, Darryn Bryant, Sarada Herke","submitted_at":"2017-01-30T07:46:49Z","abstract_excerpt":"The natural infinite analogue of a (finite) Hamilton cycle is a two-way-infinite Hamilton path (connected spanning 2-valent subgraph). Although it is known that every connected $2k$-valent infinite circulant graph has a two-way-infinite Hamilton path, there exist many such graphs that do not have a decomposition into $k$ edge-disjoint two-way-infinite Hamilton paths. This contrasts with the finite case where it is conjectured that every $2k$-valent connected circulant graph has a decomposition into $k$ edge-disjoint Hamilton cycles. We settle the problem of decomposing $2k$-valent infinite cir"},"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":"1701.08506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-30T07:46:49Z","cross_cats_sorted":[],"title_canon_sha256":"e6a4d91afe1ff0fb1ca396e1cebd6243a24a762e041c77dce1c5c5a5c8c69c37","abstract_canon_sha256":"686b7bb7d5e8dc6f0df8a963239730b171d7e4285a24901c0f9e242addd4fd19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:53.893279Z","signature_b64":"8mfZXhZAKUxADyqDWMNySUEosOup5lJSgDrIGF/BL00TH2OloYY20/PuslM0jccXIXwxCB7XEGhowhzEVQaSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be53335a707e5fe9eecbc000ffcec600053407d9739fe4eafca0a0dff8a2c779","last_reissued_at":"2026-05-18T00:51:53.892653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:53.892653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Hamilton Decompositions of Infinite Circulant Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Barbara Maenhaut, Bridget Webb, Darryn Bryant, Sarada Herke","submitted_at":"2017-01-30T07:46:49Z","abstract_excerpt":"The natural infinite analogue of a (finite) Hamilton cycle is a two-way-infinite Hamilton path (connected spanning 2-valent subgraph). Although it is known that every connected $2k$-valent infinite circulant graph has a two-way-infinite Hamilton path, there exist many such graphs that do not have a decomposition into $k$ edge-disjoint two-way-infinite Hamilton paths. This contrasts with the finite case where it is conjectured that every $2k$-valent connected circulant graph has a decomposition into $k$ edge-disjoint Hamilton cycles. We settle the problem of decomposing $2k$-valent infinite cir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08506","kind":"arxiv","version":1},"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":"1701.08506","created_at":"2026-05-18T00:51:53.892766+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.08506v1","created_at":"2026-05-18T00:51:53.892766+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08506","created_at":"2026-05-18T00:51:53.892766+00:00"},{"alias_kind":"pith_short_12","alias_value":"XZJTGWTQPZP6","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XZJTGWTQPZP6T3WL","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XZJTGWTQ","created_at":"2026-05-18T12:31:56.362134+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/XZJTGWTQPZP6T3WLYAAP7TWGAA","json":"https://pith.science/pith/XZJTGWTQPZP6T3WLYAAP7TWGAA.json","graph_json":"https://pith.science/api/pith-number/XZJTGWTQPZP6T3WLYAAP7TWGAA/graph.json","events_json":"https://pith.science/api/pith-number/XZJTGWTQPZP6T3WLYAAP7TWGAA/events.json","paper":"https://pith.science/paper/XZJTGWTQ"},"agent_actions":{"view_html":"https://pith.science/pith/XZJTGWTQPZP6T3WLYAAP7TWGAA","download_json":"https://pith.science/pith/XZJTGWTQPZP6T3WLYAAP7TWGAA.json","view_paper":"https://pith.science/paper/XZJTGWTQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.08506&json=true","fetch_graph":"https://pith.science/api/pith-number/XZJTGWTQPZP6T3WLYAAP7TWGAA/graph.json","fetch_events":"https://pith.science/api/pith-number/XZJTGWTQPZP6T3WLYAAP7TWGAA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XZJTGWTQPZP6T3WLYAAP7TWGAA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XZJTGWTQPZP6T3WLYAAP7TWGAA/action/storage_attestation","attest_author":"https://pith.science/pith/XZJTGWTQPZP6T3WLYAAP7TWGAA/action/author_attestation","sign_citation":"https://pith.science/pith/XZJTGWTQPZP6T3WLYAAP7TWGAA/action/citation_signature","submit_replication":"https://pith.science/pith/XZJTGWTQPZP6T3WLYAAP7TWGAA/action/replication_record"}},"created_at":"2026-05-18T00:51:53.892766+00:00","updated_at":"2026-05-18T00:51:53.892766+00:00"}