{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XZJTGWTQPZP6T3WLYAAP7TWGAA","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":"686b7bb7d5e8dc6f0df8a963239730b171d7e4285a24901c0f9e242addd4fd19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-30T07:46:49Z","title_canon_sha256":"e6a4d91afe1ff0fb1ca396e1cebd6243a24a762e041c77dce1c5c5a5c8c69c37"},"schema_version":"1.0","source":{"id":"1701.08506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08506","created_at":"2026-05-18T00:51:53Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08506v1","created_at":"2026-05-18T00:51:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08506","created_at":"2026-05-18T00:51:53Z"},{"alias_kind":"pith_short_12","alias_value":"XZJTGWTQPZP6","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XZJTGWTQPZP6T3WL","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XZJTGWTQ","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:025f58e12e0458c5097f59a187adf580e22bebe7bf40d0cbcd13333bc5c4446f","target":"graph","created_at":"2026-05-18T00:51:53Z","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":"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","authors_text":"Barbara Maenhaut, Bridget Webb, Darryn Bryant, Sarada Herke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-30T07:46:49Z","title":"On Hamilton Decompositions of Infinite Circulant Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08506","kind":"arxiv","version":1},"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":"sha256:62b380d3c3be31528f9cf0d3af36d96676a332dd2227e5de7395cabbf340360d","target":"record","created_at":"2026-05-18T00:51:53Z","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":"686b7bb7d5e8dc6f0df8a963239730b171d7e4285a24901c0f9e242addd4fd19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-30T07:46:49Z","title_canon_sha256":"e6a4d91afe1ff0fb1ca396e1cebd6243a24a762e041c77dce1c5c5a5c8c69c37"},"schema_version":"1.0","source":{"id":"1701.08506","kind":"arxiv","version":1}},"canonical_sha256":"be53335a707e5fe9eecbc000ffcec600053407d9739fe4eafca0a0dff8a2c779","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be53335a707e5fe9eecbc000ffcec600053407d9739fe4eafca0a0dff8a2c779","first_computed_at":"2026-05-18T00:51:53.892653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:53.892653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8mfZXhZAKUxADyqDWMNySUEosOup5lJSgDrIGF/BL00TH2OloYY20/PuslM0jccXIXwxCB7XEGhowhzEVQaSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:53.893279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62b380d3c3be31528f9cf0d3af36d96676a332dd2227e5de7395cabbf340360d","sha256:025f58e12e0458c5097f59a187adf580e22bebe7bf40d0cbcd13333bc5c4446f"],"state_sha256":"cde0cb9c476cab55be572d95285b3185bd67bba64c18150627e306fc9a3df258"}