{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:FT6TOQJPE47QNLZAFCBQ46WFMT","short_pith_number":"pith:FT6TOQJP","canonical_record":{"source":{"id":"2212.08315","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-16T07:38:30Z","cross_cats_sorted":[],"title_canon_sha256":"ae36edb8bb9cba60c7ef0416195998abca94c34310164ea8ee304309b93dde1a","abstract_canon_sha256":"efb902febe41e52fa8d219f097bbb06140bd0bade5b1b997460d629bc5f5543b"},"schema_version":"1.0"},"canonical_sha256":"2cfd37412f273f06af2028830e7ac564eed9b36a8b892980b744d25980f926d5","source":{"kind":"arxiv","id":"2212.08315","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.08315","created_at":"2026-07-05T05:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"2212.08315v2","created_at":"2026-07-05T05:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.08315","created_at":"2026-07-05T05:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"FT6TOQJPE47Q","created_at":"2026-07-05T05:43:18Z"},{"alias_kind":"pith_short_16","alias_value":"FT6TOQJPE47QNLZA","created_at":"2026-07-05T05:43:18Z"},{"alias_kind":"pith_short_8","alias_value":"FT6TOQJP","created_at":"2026-07-05T05:43:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:FT6TOQJPE47QNLZAFCBQ46WFMT","target":"record","payload":{"canonical_record":{"source":{"id":"2212.08315","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-16T07:38:30Z","cross_cats_sorted":[],"title_canon_sha256":"ae36edb8bb9cba60c7ef0416195998abca94c34310164ea8ee304309b93dde1a","abstract_canon_sha256":"efb902febe41e52fa8d219f097bbb06140bd0bade5b1b997460d629bc5f5543b"},"schema_version":"1.0"},"canonical_sha256":"2cfd37412f273f06af2028830e7ac564eed9b36a8b892980b744d25980f926d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:43:18.247683Z","signature_b64":"pnhkb0Av72uswyqcyxwEYnSYWLOyd4FCMee0BgoV+51XjXHuKxdTke/P8aLjbIGDaX46G1TTEsRj6i6BnGszCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cfd37412f273f06af2028830e7ac564eed9b36a8b892980b744d25980f926d5","last_reissued_at":"2026-07-05T05:43:18.247277Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:43:18.247277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.08315","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uT1Z6NmKatlNDJLRg12TNCqwe5M4aLMcjQZK0896ljZZ+UqCRYePZ2YGmz+Q9WaBE/vJ32/rjX6rplunfLDGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T03:33:39.613186Z"},"content_sha256":"fcd3558f30783fde31abff23b6b705d2dd8cad18e12c8d5ab6fa0a8dcd6a05b2","schema_version":"1.0","event_id":"sha256:fcd3558f30783fde31abff23b6b705d2dd8cad18e12c8d5ab6fa0a8dcd6a05b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:FT6TOQJPE47QNLZAFCBQ46WFMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compatible Powers of Hamilton Cycles in Dense Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Donglei Yang, Jie Hu, Xiaohan Cheng","submitted_at":"2022-12-16T07:38:30Z","abstract_excerpt":"Motivated by the concept of transition system investigated by Kotzig in 1968, Krivelevich, Lee and Sudakov proposed a more general notion of incompatibility system to formulate the robustness of Hamiltonicity of Dirac graphs. Given a graph $G=(V,E)$, an {\\em incompatibility system} $\\mathcal{F}$ over $G$ is a family $\\mathcal{F}=\\{F_v\\}_{v\\in V}$ such that for every $v\\in V$, $F_v$ is a family of edge pairs in $\\{\\{e,e'\\}: e\\ne e'\\in E, e\\cap e'=\\{v\\}\\}$. An incompatibility system $\\mathcal{F}$ is \\emph{$\\Delta$-bounded} if for every vertex $v$ and every edge $e$ incident with $v$, there are a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.08315","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.08315/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lnFx5z7gYo0ckvsDZnKWvjRuc/zoHdOF+PmFptfaliVxe7dPU2jA/l3jMT5RE7bdca3T/3t6hmxYp3y4miWODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T03:33:39.613692Z"},"content_sha256":"31da7a3c5733b068b6074f1d02bd7de8acc48aa5b460497ee60699943dc746f9","schema_version":"1.0","event_id":"sha256:31da7a3c5733b068b6074f1d02bd7de8acc48aa5b460497ee60699943dc746f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FT6TOQJPE47QNLZAFCBQ46WFMT/bundle.json","state_url":"https://pith.science/pith/FT6TOQJPE47QNLZAFCBQ46WFMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FT6TOQJPE47QNLZAFCBQ46WFMT/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":"2026-08-07T03:33:39Z","links":{"resolver":"https://pith.science/pith/FT6TOQJPE47QNLZAFCBQ46WFMT","bundle":"https://pith.science/pith/FT6TOQJPE47QNLZAFCBQ46WFMT/bundle.json","state":"https://pith.science/pith/FT6TOQJPE47QNLZAFCBQ46WFMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FT6TOQJPE47QNLZAFCBQ46WFMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:FT6TOQJPE47QNLZAFCBQ46WFMT","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":"efb902febe41e52fa8d219f097bbb06140bd0bade5b1b997460d629bc5f5543b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-16T07:38:30Z","title_canon_sha256":"ae36edb8bb9cba60c7ef0416195998abca94c34310164ea8ee304309b93dde1a"},"schema_version":"1.0","source":{"id":"2212.08315","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.08315","created_at":"2026-07-05T05:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"2212.08315v2","created_at":"2026-07-05T05:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.08315","created_at":"2026-07-05T05:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"FT6TOQJPE47Q","created_at":"2026-07-05T05:43:18Z"},{"alias_kind":"pith_short_16","alias_value":"FT6TOQJPE47QNLZA","created_at":"2026-07-05T05:43:18Z"},{"alias_kind":"pith_short_8","alias_value":"FT6TOQJP","created_at":"2026-07-05T05:43:18Z"}],"graph_snapshots":[{"event_id":"sha256:31da7a3c5733b068b6074f1d02bd7de8acc48aa5b460497ee60699943dc746f9","target":"graph","created_at":"2026-07-05T05:43:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2212.08315/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the concept of transition system investigated by Kotzig in 1968, Krivelevich, Lee and Sudakov proposed a more general notion of incompatibility system to formulate the robustness of Hamiltonicity of Dirac graphs. Given a graph $G=(V,E)$, an {\\em incompatibility system} $\\mathcal{F}$ over $G$ is a family $\\mathcal{F}=\\{F_v\\}_{v\\in V}$ such that for every $v\\in V$, $F_v$ is a family of edge pairs in $\\{\\{e,e'\\}: e\\ne e'\\in E, e\\cap e'=\\{v\\}\\}$. An incompatibility system $\\mathcal{F}$ is \\emph{$\\Delta$-bounded} if for every vertex $v$ and every edge $e$ incident with $v$, there are a","authors_text":"Donglei Yang, Jie Hu, Xiaohan Cheng","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-16T07:38:30Z","title":"Compatible Powers of Hamilton Cycles in Dense Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.08315","kind":"arxiv","version":2},"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:fcd3558f30783fde31abff23b6b705d2dd8cad18e12c8d5ab6fa0a8dcd6a05b2","target":"record","created_at":"2026-07-05T05:43:18Z","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":"efb902febe41e52fa8d219f097bbb06140bd0bade5b1b997460d629bc5f5543b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-16T07:38:30Z","title_canon_sha256":"ae36edb8bb9cba60c7ef0416195998abca94c34310164ea8ee304309b93dde1a"},"schema_version":"1.0","source":{"id":"2212.08315","kind":"arxiv","version":2}},"canonical_sha256":"2cfd37412f273f06af2028830e7ac564eed9b36a8b892980b744d25980f926d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cfd37412f273f06af2028830e7ac564eed9b36a8b892980b744d25980f926d5","first_computed_at":"2026-07-05T05:43:18.247277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:43:18.247277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pnhkb0Av72uswyqcyxwEYnSYWLOyd4FCMee0BgoV+51XjXHuKxdTke/P8aLjbIGDaX46G1TTEsRj6i6BnGszCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:43:18.247683Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.08315","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcd3558f30783fde31abff23b6b705d2dd8cad18e12c8d5ab6fa0a8dcd6a05b2","sha256:31da7a3c5733b068b6074f1d02bd7de8acc48aa5b460497ee60699943dc746f9"],"state_sha256":"55bfafbc563c9eceab7d2deb795a5124f7077d0d797ad1dab9ccb619f516ce14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZygKNIX+CjMMkNtFZygYU7Zk2JRzi07pIlpL8RhPHe+7BJPgmmKxqHsqwxxPGdimVv9tSCy/lCOkQUiQOYPlBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T03:33:39.617739Z","bundle_sha256":"60d96fbce6c1851a773a03429142e0eb0357ac37b20fa039288b456ca80615e3"}}