{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7MIG5KH23DTHWWHYJADDJ6KOD4","short_pith_number":"pith:7MIG5KH2","canonical_record":{"source":{"id":"1110.3198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-14T13:15:56Z","cross_cats_sorted":[],"title_canon_sha256":"b9eac0014148f1657c749b0dd544f8fd00362a4df9e02c23ed39d538534fe9ce","abstract_canon_sha256":"bc3f88a4cc8f4ac2549f073c80707fbff83c4827321970c3298dae7197aac503"},"schema_version":"1.0"},"canonical_sha256":"fb106ea8fad8e67b58f8480634f94e1f0b4e3a6fee8ca9e35805da5887d76360","source":{"kind":"arxiv","id":"1110.3198","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3198","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3198v1","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3198","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"7MIG5KH23DTH","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7MIG5KH23DTHWWHY","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7MIG5KH2","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7MIG5KH23DTHWWHYJADDJ6KOD4","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-14T13:15:56Z","cross_cats_sorted":[],"title_canon_sha256":"b9eac0014148f1657c749b0dd544f8fd00362a4df9e02c23ed39d538534fe9ce","abstract_canon_sha256":"bc3f88a4cc8f4ac2549f073c80707fbff83c4827321970c3298dae7197aac503"},"schema_version":"1.0"},"canonical_sha256":"fb106ea8fad8e67b58f8480634f94e1f0b4e3a6fee8ca9e35805da5887d76360","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:57.781497Z","signature_b64":"t4Kc+q3g9wlab3iXyfYD334YWpMk+hQAE5bjfcESalZcmliQG5tOasNjiWe0tgxUZxFFeJUcyruFJhM1v02eBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb106ea8fad8e67b58f8480634f94e1f0b4e3a6fee8ca9e35805da5887d76360","last_reissued_at":"2026-05-18T04:10:57.780835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:57.780835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3198","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":"2026-05-18T04:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pri8NFgmW1t87X6cs1L0+XH5pLNqUwLYG7x6T+oemlo39WtR9/D+f2G/82kHKfCUDiq90cvq5bpXoD9+4KWhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:02:48.003674Z"},"content_sha256":"8bd32598c207745b2bb9bd5080fe16259c2a0e016749a8a9927734146f402c5a","schema_version":"1.0","event_id":"sha256:8bd32598c207745b2bb9bd5080fe16259c2a0e016749a8a9927734146f402c5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7MIG5KH23DTHWWHYJADDJ6KOD4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Note on parity factors of regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu","submitted_at":"2011-10-14T13:15:56Z","abstract_excerpt":"In this paper, we obtain a sufficient condition for the existence of parity factors in a regular graph in terms of edge-connectivity. Moreover, we also show that our condition is sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3198","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":"2026-05-18T04:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H7vfMuB2RHxLzGBQuYZWQReEizSYQw+RTcsgImYqfX5fBuxuQaUnmZFajKqvDbd3y+lYLAeDy7oXj7d2ehVrAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:02:48.004014Z"},"content_sha256":"3b7ec487347c7a0a8a8df98a6a0bb3aa72748b89c2e0bbdd195e3e25a92f6672","schema_version":"1.0","event_id":"sha256:3b7ec487347c7a0a8a8df98a6a0bb3aa72748b89c2e0bbdd195e3e25a92f6672"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7MIG5KH23DTHWWHYJADDJ6KOD4/bundle.json","state_url":"https://pith.science/pith/7MIG5KH23DTHWWHYJADDJ6KOD4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7MIG5KH23DTHWWHYJADDJ6KOD4/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":"2026-06-19T23:02:48Z","links":{"resolver":"https://pith.science/pith/7MIG5KH23DTHWWHYJADDJ6KOD4","bundle":"https://pith.science/pith/7MIG5KH23DTHWWHYJADDJ6KOD4/bundle.json","state":"https://pith.science/pith/7MIG5KH23DTHWWHYJADDJ6KOD4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7MIG5KH23DTHWWHYJADDJ6KOD4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7MIG5KH23DTHWWHYJADDJ6KOD4","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":"bc3f88a4cc8f4ac2549f073c80707fbff83c4827321970c3298dae7197aac503","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-14T13:15:56Z","title_canon_sha256":"b9eac0014148f1657c749b0dd544f8fd00362a4df9e02c23ed39d538534fe9ce"},"schema_version":"1.0","source":{"id":"1110.3198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3198","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3198v1","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3198","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"7MIG5KH23DTH","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7MIG5KH23DTHWWHY","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7MIG5KH2","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:3b7ec487347c7a0a8a8df98a6a0bb3aa72748b89c2e0bbdd195e3e25a92f6672","target":"graph","created_at":"2026-05-18T04:10:57Z","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":"In this paper, we obtain a sufficient condition for the existence of parity factors in a regular graph in terms of edge-connectivity. Moreover, we also show that our condition is sharp.","authors_text":"Hongliang Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-14T13:15:56Z","title":"Note on parity factors of regular graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3198","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":"sha256:8bd32598c207745b2bb9bd5080fe16259c2a0e016749a8a9927734146f402c5a","target":"record","created_at":"2026-05-18T04:10:57Z","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":"bc3f88a4cc8f4ac2549f073c80707fbff83c4827321970c3298dae7197aac503","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-14T13:15:56Z","title_canon_sha256":"b9eac0014148f1657c749b0dd544f8fd00362a4df9e02c23ed39d538534fe9ce"},"schema_version":"1.0","source":{"id":"1110.3198","kind":"arxiv","version":1}},"canonical_sha256":"fb106ea8fad8e67b58f8480634f94e1f0b4e3a6fee8ca9e35805da5887d76360","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb106ea8fad8e67b58f8480634f94e1f0b4e3a6fee8ca9e35805da5887d76360","first_computed_at":"2026-05-18T04:10:57.780835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:57.780835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t4Kc+q3g9wlab3iXyfYD334YWpMk+hQAE5bjfcESalZcmliQG5tOasNjiWe0tgxUZxFFeJUcyruFJhM1v02eBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:57.781497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bd32598c207745b2bb9bd5080fe16259c2a0e016749a8a9927734146f402c5a","sha256:3b7ec487347c7a0a8a8df98a6a0bb3aa72748b89c2e0bbdd195e3e25a92f6672"],"state_sha256":"380dfee4ed87411f63fc8ab0d9d3421ad2bd882808ad95d6fbb070ec690ae76d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UXEPdsWvP06ZUTgAqx8687VWoDzf85ztplTchMX0JTqkqdF1HXLws681c7oZyLHMP8BKeTJ38gMMYEN3eSSvCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-19T23:02:48.005911Z","bundle_sha256":"9d886b852190aaf07675551439b3b901f49c2b41258957429e9bde2d6a1653cd"}}