{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:C3KPWME3537TS4GM5T6YAYU2P2","short_pith_number":"pith:C3KPWME3","canonical_record":{"source":{"id":"1209.0096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-01T14:32:39Z","cross_cats_sorted":[],"title_canon_sha256":"5fad428d6b2fb8efed05503f36c3823c13ac2ab7c98607313f43d3310faa93ac","abstract_canon_sha256":"86407e7a1478171435b4393ef59cc6867b19d15cb756db2a40a11d815243295f"},"schema_version":"1.0"},"canonical_sha256":"16d4fb309beeff3970ccecfd80629a7e9195f5cc0c5ba2d98f05120c7617ad93","source":{"kind":"arxiv","id":"1209.0096","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0096","created_at":"2026-05-18T03:41:12Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0096v1","created_at":"2026-05-18T03:41:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0096","created_at":"2026-05-18T03:41:12Z"},{"alias_kind":"pith_short_12","alias_value":"C3KPWME3537T","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C3KPWME3537TS4GM","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C3KPWME3","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:C3KPWME3537TS4GM5T6YAYU2P2","target":"record","payload":{"canonical_record":{"source":{"id":"1209.0096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-01T14:32:39Z","cross_cats_sorted":[],"title_canon_sha256":"5fad428d6b2fb8efed05503f36c3823c13ac2ab7c98607313f43d3310faa93ac","abstract_canon_sha256":"86407e7a1478171435b4393ef59cc6867b19d15cb756db2a40a11d815243295f"},"schema_version":"1.0"},"canonical_sha256":"16d4fb309beeff3970ccecfd80629a7e9195f5cc0c5ba2d98f05120c7617ad93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:12.260789Z","signature_b64":"d/HdsU7a4qPKCRiXwjbwjx9YIzHbMTt4l6kf4K2KW1W3e9NAPxGT9Q0drabKlzGAm6wuehodlJ5SDz6fmmxkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16d4fb309beeff3970ccecfd80629a7e9195f5cc0c5ba2d98f05120c7617ad93","last_reissued_at":"2026-05-18T03:41:12.260118Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:12.260118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.0096","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:41:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OdwJHSxj0lZ7+D8QOLVO6MlOfTP/XaGoG6O+SM+6sXXGTL1cEW0JIqWzzJjM4gCZGHjv9mNU65EZxIRNrNvQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T01:14:21.365845Z"},"content_sha256":"6af12476da584bba5a8899d62994c1c0c9366591e0d2db83c57aff1e305a618d","schema_version":"1.0","event_id":"sha256:6af12476da584bba5a8899d62994c1c0c9366591e0d2db83c57aff1e305a618d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:C3KPWME3537TS4GM5T6YAYU2P2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on 5-cycle double covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arthur Hoffmann-Ostenhof","submitted_at":"2012-09-01T14:32:39Z","abstract_excerpt":"The strong cycle double cover conjecture states that for every circuit $C$ of a bridgeless cubic graph $G$, there is a cycle double cover of $G$ which contains $C$. We conjecture that there is even a 5-cycle double cover $S$ of $G$ which contains $C$, i.e. $C$ is a subgraph of one of the five 2-regular subgraphs of $S$. We prove a necessary and sufficient condition for a 2-regular subgraph to be contained in a 5-cycle double cover of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0096","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:41:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eLo3E0aDpTeoKv6osDAeq/e1jeQm6cw5eN0HE+KUmPDu357HGyKbT5VmP8H226CAeEsV+duYVAET15Qeg3TyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T01:14:21.366187Z"},"content_sha256":"1ba8076ae00cf3e20408d42e09354c4a53cbd1a9ed42d049d903fd8212588d00","schema_version":"1.0","event_id":"sha256:1ba8076ae00cf3e20408d42e09354c4a53cbd1a9ed42d049d903fd8212588d00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3KPWME3537TS4GM5T6YAYU2P2/bundle.json","state_url":"https://pith.science/pith/C3KPWME3537TS4GM5T6YAYU2P2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3KPWME3537TS4GM5T6YAYU2P2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T01:14:21Z","links":{"resolver":"https://pith.science/pith/C3KPWME3537TS4GM5T6YAYU2P2","bundle":"https://pith.science/pith/C3KPWME3537TS4GM5T6YAYU2P2/bundle.json","state":"https://pith.science/pith/C3KPWME3537TS4GM5T6YAYU2P2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3KPWME3537TS4GM5T6YAYU2P2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:C3KPWME3537TS4GM5T6YAYU2P2","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":"86407e7a1478171435b4393ef59cc6867b19d15cb756db2a40a11d815243295f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-01T14:32:39Z","title_canon_sha256":"5fad428d6b2fb8efed05503f36c3823c13ac2ab7c98607313f43d3310faa93ac"},"schema_version":"1.0","source":{"id":"1209.0096","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0096","created_at":"2026-05-18T03:41:12Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0096v1","created_at":"2026-05-18T03:41:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0096","created_at":"2026-05-18T03:41:12Z"},{"alias_kind":"pith_short_12","alias_value":"C3KPWME3537T","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C3KPWME3537TS4GM","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C3KPWME3","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:1ba8076ae00cf3e20408d42e09354c4a53cbd1a9ed42d049d903fd8212588d00","target":"graph","created_at":"2026-05-18T03:41:12Z","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 strong cycle double cover conjecture states that for every circuit $C$ of a bridgeless cubic graph $G$, there is a cycle double cover of $G$ which contains $C$. We conjecture that there is even a 5-cycle double cover $S$ of $G$ which contains $C$, i.e. $C$ is a subgraph of one of the five 2-regular subgraphs of $S$. We prove a necessary and sufficient condition for a 2-regular subgraph to be contained in a 5-cycle double cover of $G$.","authors_text":"Arthur Hoffmann-Ostenhof","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-01T14:32:39Z","title":"A note on 5-cycle double covers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0096","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":"sha256:6af12476da584bba5a8899d62994c1c0c9366591e0d2db83c57aff1e305a618d","target":"record","created_at":"2026-05-18T03:41:12Z","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":"86407e7a1478171435b4393ef59cc6867b19d15cb756db2a40a11d815243295f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-01T14:32:39Z","title_canon_sha256":"5fad428d6b2fb8efed05503f36c3823c13ac2ab7c98607313f43d3310faa93ac"},"schema_version":"1.0","source":{"id":"1209.0096","kind":"arxiv","version":1}},"canonical_sha256":"16d4fb309beeff3970ccecfd80629a7e9195f5cc0c5ba2d98f05120c7617ad93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16d4fb309beeff3970ccecfd80629a7e9195f5cc0c5ba2d98f05120c7617ad93","first_computed_at":"2026-05-18T03:41:12.260118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:12.260118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d/HdsU7a4qPKCRiXwjbwjx9YIzHbMTt4l6kf4K2KW1W3e9NAPxGT9Q0drabKlzGAm6wuehodlJ5SDz6fmmxkBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:12.260789Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0096","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6af12476da584bba5a8899d62994c1c0c9366591e0d2db83c57aff1e305a618d","sha256:1ba8076ae00cf3e20408d42e09354c4a53cbd1a9ed42d049d903fd8212588d00"],"state_sha256":"b9182686ac114f694fd39cbea7356d071609581fa8eb68924bdfead5f23ce83d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qfjyx2FE1o05rNjGeFFbsn/jzi8VeP7SlkE4wNk03xsWD5vuuYWnaHa6tHAg98cnU55a6zxkqLq7dsHxuzQPAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T01:14:21.368353Z","bundle_sha256":"8991bc1476f84aa3b5055c87ff0610f2ab2b6550c87c30007e7f8685db3d7a2c"}}