{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:RBFHDUH6BM73RHHWKS7HWSMGBM","short_pith_number":"pith:RBFHDUH6","canonical_record":{"source":{"id":"1206.5397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-23T14:34:04Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"3b60ae89de5231f78a5c3411db0dfbe4129ae2f65250fd02a095b0a125cddc50","abstract_canon_sha256":"f04d5f91042612fa148056f8f12cf03f69eff5cc67a9ec5d8e448a5131a0388a"},"schema_version":"1.0"},"canonical_sha256":"884a71d0fe0b3fb89cf654be7b49860b3a3594c68fc61e77ed8895286bcf2fe8","source":{"kind":"arxiv","id":"1206.5397","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5397","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5397v2","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5397","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"pith_short_12","alias_value":"RBFHDUH6BM73","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RBFHDUH6BM73RHHW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RBFHDUH6","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:RBFHDUH6BM73RHHWKS7HWSMGBM","target":"record","payload":{"canonical_record":{"source":{"id":"1206.5397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-23T14:34:04Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"3b60ae89de5231f78a5c3411db0dfbe4129ae2f65250fd02a095b0a125cddc50","abstract_canon_sha256":"f04d5f91042612fa148056f8f12cf03f69eff5cc67a9ec5d8e448a5131a0388a"},"schema_version":"1.0"},"canonical_sha256":"884a71d0fe0b3fb89cf654be7b49860b3a3594c68fc61e77ed8895286bcf2fe8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:41.238670Z","signature_b64":"w9B9MKMAJ2v5EkRgY4e2EPa+f5Mh/ZtoafWukzmXugHZCE4n5zBeaeN8FOn5E5vgJf7m5Nae/ybY90fypRdYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"884a71d0fe0b3fb89cf654be7b49860b3a3594c68fc61e77ed8895286bcf2fe8","last_reissued_at":"2026-05-18T03:37:41.238116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:41.238116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.5397","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":"2026-05-18T03:37:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pKWNMyZkbyimwmJIjggOSKcMVbSdHZftdAha1iQoj53gsvwSMSna+yeoy/2VNMbjYC8b2DAOrTkRDBWEh9B6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:24:37.807528Z"},"content_sha256":"df989ffb1787fe589b3c332f79b9e985f902973285d43c20bc6bf4d5a83674a7","schema_version":"1.0","event_id":"sha256:df989ffb1787fe589b3c332f79b9e985f902973285d43c20bc6bf4d5a83674a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:RBFHDUH6BM73RHHWKS7HWSMGBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Dirac-type Characterization of k-chordal Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"N. Sadagopan, N. S. Narayanaswamy, R. Krithika, Rogers Mathew","submitted_at":"2012-06-23T14:34:04Z","abstract_excerpt":"Characterization of k-chordal graphs based on the existence of a \"simplicial path\" was shown in [Chv{\\'a}tal et al. Note: Dirac-type characterizations of graphs without long chordless cycles. Discrete Mathematics, 256, 445-448, 2002]. We give a characterization of k-chordal graphs which is a generalization of the known characterization of chordal graphs due to [G. A. Dirac. On rigid circuit graphs. Abh. Math. Sem. Univ. Hamburg, 25, 71-76, 1961] that use notions of a \"simplicial vertex\" and a \"simplicial ordering\"."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5397","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":""},"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":"2026-05-18T03:37:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1bCx3XppOJ7RDWlSLv43MvFLQe6PdXn+EWHaY0VT9Ws6sBuk/H3iNRCRTUttVr0IVR3qxFsG05u3JoKcTsavBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:24:37.807883Z"},"content_sha256":"cc4b077265c17e9ef7d596e0e67d7f1da0c40eea9eba6650663091aed1b5f5d5","schema_version":"1.0","event_id":"sha256:cc4b077265c17e9ef7d596e0e67d7f1da0c40eea9eba6650663091aed1b5f5d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBFHDUH6BM73RHHWKS7HWSMGBM/bundle.json","state_url":"https://pith.science/pith/RBFHDUH6BM73RHHWKS7HWSMGBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBFHDUH6BM73RHHWKS7HWSMGBM/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":"2026-05-31T06:24:37Z","links":{"resolver":"https://pith.science/pith/RBFHDUH6BM73RHHWKS7HWSMGBM","bundle":"https://pith.science/pith/RBFHDUH6BM73RHHWKS7HWSMGBM/bundle.json","state":"https://pith.science/pith/RBFHDUH6BM73RHHWKS7HWSMGBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBFHDUH6BM73RHHWKS7HWSMGBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RBFHDUH6BM73RHHWKS7HWSMGBM","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":"f04d5f91042612fa148056f8f12cf03f69eff5cc67a9ec5d8e448a5131a0388a","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-23T14:34:04Z","title_canon_sha256":"3b60ae89de5231f78a5c3411db0dfbe4129ae2f65250fd02a095b0a125cddc50"},"schema_version":"1.0","source":{"id":"1206.5397","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5397","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5397v2","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5397","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"pith_short_12","alias_value":"RBFHDUH6BM73","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RBFHDUH6BM73RHHW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RBFHDUH6","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:cc4b077265c17e9ef7d596e0e67d7f1da0c40eea9eba6650663091aed1b5f5d5","target":"graph","created_at":"2026-05-18T03:37:41Z","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":"Characterization of k-chordal graphs based on the existence of a \"simplicial path\" was shown in [Chv{\\'a}tal et al. Note: Dirac-type characterizations of graphs without long chordless cycles. Discrete Mathematics, 256, 445-448, 2002]. We give a characterization of k-chordal graphs which is a generalization of the known characterization of chordal graphs due to [G. A. Dirac. On rigid circuit graphs. Abh. Math. Sem. Univ. Hamburg, 25, 71-76, 1961] that use notions of a \"simplicial vertex\" and a \"simplicial ordering\".","authors_text":"N. Sadagopan, N. S. Narayanaswamy, R. Krithika, Rogers Mathew","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-23T14:34:04Z","title":"A Dirac-type Characterization of k-chordal Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5397","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:df989ffb1787fe589b3c332f79b9e985f902973285d43c20bc6bf4d5a83674a7","target":"record","created_at":"2026-05-18T03:37:41Z","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":"f04d5f91042612fa148056f8f12cf03f69eff5cc67a9ec5d8e448a5131a0388a","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-23T14:34:04Z","title_canon_sha256":"3b60ae89de5231f78a5c3411db0dfbe4129ae2f65250fd02a095b0a125cddc50"},"schema_version":"1.0","source":{"id":"1206.5397","kind":"arxiv","version":2}},"canonical_sha256":"884a71d0fe0b3fb89cf654be7b49860b3a3594c68fc61e77ed8895286bcf2fe8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"884a71d0fe0b3fb89cf654be7b49860b3a3594c68fc61e77ed8895286bcf2fe8","first_computed_at":"2026-05-18T03:37:41.238116Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:41.238116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w9B9MKMAJ2v5EkRgY4e2EPa+f5Mh/ZtoafWukzmXugHZCE4n5zBeaeN8FOn5E5vgJf7m5Nae/ybY90fypRdYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:41.238670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5397","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df989ffb1787fe589b3c332f79b9e985f902973285d43c20bc6bf4d5a83674a7","sha256:cc4b077265c17e9ef7d596e0e67d7f1da0c40eea9eba6650663091aed1b5f5d5"],"state_sha256":"ed406f9388ab80c5ced65c2102426de2174a9e4accb1dff66722319a7019ba7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"auMbCc7v7deTtXXEIow5vP3cvdLCv1oy5W8Wea42Cxzo58795wl1lIjptaGkdX8fvV2CSfEuedLSZEdeVpB+AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:24:37.809868Z","bundle_sha256":"872efb96cb65b542f7260047637fc2589ca9730423b25fed292f9788b6a8c624"}}