{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NPJ2WLQ4N3FVHRV23HS5PRW5WP","short_pith_number":"pith:NPJ2WLQ4","canonical_record":{"source":{"id":"1208.5188","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-08-26T04:01:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c9d163e74f567295f985136e41f1258ed16179fe624c0aaeded4e1209a557f8c","abstract_canon_sha256":"63b29bde5de02c0a4fc0c8c219a94607075a4fb9d6539d958ba633acda666968"},"schema_version":"1.0"},"canonical_sha256":"6bd3ab2e1c6ecb53c6bad9e5d7c6ddb3ec7546a197ab2f5773dce8967c3ba0b8","source":{"kind":"arxiv","id":"1208.5188","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5188","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5188v2","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5188","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"NPJ2WLQ4N3FV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NPJ2WLQ4N3FVHRV2","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NPJ2WLQ4","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NPJ2WLQ4N3FVHRV23HS5PRW5WP","target":"record","payload":{"canonical_record":{"source":{"id":"1208.5188","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-08-26T04:01:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c9d163e74f567295f985136e41f1258ed16179fe624c0aaeded4e1209a557f8c","abstract_canon_sha256":"63b29bde5de02c0a4fc0c8c219a94607075a4fb9d6539d958ba633acda666968"},"schema_version":"1.0"},"canonical_sha256":"6bd3ab2e1c6ecb53c6bad9e5d7c6ddb3ec7546a197ab2f5773dce8967c3ba0b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:52.650992Z","signature_b64":"SWcfpmluU9pUGLaYwuXcqb6bp65YIaorqmyv9w/ip0NsUTNNEYnpJnEuKYDh87U+FOB31HJ/eQGYP/Svk6u4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bd3ab2e1c6ecb53c6bad9e5d7c6ddb3ec7546a197ab2f5773dce8967c3ba0b8","last_reissued_at":"2026-05-18T02:35:52.650547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:52.650547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.5188","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":"2026-05-18T02:35:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KGDpuTfMx8J7LR6u1Dvi9xaGBe05YmvMNths65VEPLhFs14d7ncj4SBvXrn/3/Y3+D08PfnnKQpL1NDchZisBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:58:14.676588Z"},"content_sha256":"fadfda3c9651e04bbac0e1fb393526033aa0a6e6e6be5de50e40545f34ec0256","schema_version":"1.0","event_id":"sha256:fadfda3c9651e04bbac0e1fb393526033aa0a6e6e6be5de50e40545f34ec0256"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NPJ2WLQ4N3FVHRV23HS5PRW5WP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A superlocal version of Reed's Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Andrew D. King, Katherine Edwards","submitted_at":"2012-08-26T04:01:31Z","abstract_excerpt":"Reed's well-known $\\omega$, $\\Delta$, $\\chi$ conjecture proposes that every graph satisfies $\\chi \\leq \\lceil \\frac 12(\\Delta+1+\\omega)\\rceil$. The second author formulated a {\\em local strengthening} of this conjecture that considers a bound supplied by the neighbourhood of a single vertex. Following the idea that the chromatic number cannot be greatly affected by any particular stable set of vertices, we propose a further strengthening that considers a bound supplied by the neighbourhoods of two adjacent vertices. We provide some fundamental evidence in support, namely that the stronger boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5188","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":"2026-05-18T02:35:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qsz8tT0GxkCRLYZ+Fv6SAn3mwhpb5qdTS4E6COyRQf/QSMQawhkewbT2s3Xov+pFkbRfGgOPl9wmTHa9JmDtAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:58:14.677308Z"},"content_sha256":"d90ce5e0b413ec79e856e22eaec82b22a8f0a12b47110bf9fc092cfd144bfac8","schema_version":"1.0","event_id":"sha256:d90ce5e0b413ec79e856e22eaec82b22a8f0a12b47110bf9fc092cfd144bfac8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NPJ2WLQ4N3FVHRV23HS5PRW5WP/bundle.json","state_url":"https://pith.science/pith/NPJ2WLQ4N3FVHRV23HS5PRW5WP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NPJ2WLQ4N3FVHRV23HS5PRW5WP/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":"2026-05-27T22:58:14Z","links":{"resolver":"https://pith.science/pith/NPJ2WLQ4N3FVHRV23HS5PRW5WP","bundle":"https://pith.science/pith/NPJ2WLQ4N3FVHRV23HS5PRW5WP/bundle.json","state":"https://pith.science/pith/NPJ2WLQ4N3FVHRV23HS5PRW5WP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NPJ2WLQ4N3FVHRV23HS5PRW5WP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NPJ2WLQ4N3FVHRV23HS5PRW5WP","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":"63b29bde5de02c0a4fc0c8c219a94607075a4fb9d6539d958ba633acda666968","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-08-26T04:01:31Z","title_canon_sha256":"c9d163e74f567295f985136e41f1258ed16179fe624c0aaeded4e1209a557f8c"},"schema_version":"1.0","source":{"id":"1208.5188","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5188","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5188v2","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5188","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"NPJ2WLQ4N3FV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NPJ2WLQ4N3FVHRV2","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NPJ2WLQ4","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:d90ce5e0b413ec79e856e22eaec82b22a8f0a12b47110bf9fc092cfd144bfac8","target":"graph","created_at":"2026-05-18T02:35:52Z","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":"Reed's well-known $\\omega$, $\\Delta$, $\\chi$ conjecture proposes that every graph satisfies $\\chi \\leq \\lceil \\frac 12(\\Delta+1+\\omega)\\rceil$. The second author formulated a {\\em local strengthening} of this conjecture that considers a bound supplied by the neighbourhood of a single vertex. Following the idea that the chromatic number cannot be greatly affected by any particular stable set of vertices, we propose a further strengthening that considers a bound supplied by the neighbourhoods of two adjacent vertices. We provide some fundamental evidence in support, namely that the stronger boun","authors_text":"Andrew D. King, Katherine Edwards","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-08-26T04:01:31Z","title":"A superlocal version of Reed's Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5188","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:fadfda3c9651e04bbac0e1fb393526033aa0a6e6e6be5de50e40545f34ec0256","target":"record","created_at":"2026-05-18T02:35:52Z","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":"63b29bde5de02c0a4fc0c8c219a94607075a4fb9d6539d958ba633acda666968","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-08-26T04:01:31Z","title_canon_sha256":"c9d163e74f567295f985136e41f1258ed16179fe624c0aaeded4e1209a557f8c"},"schema_version":"1.0","source":{"id":"1208.5188","kind":"arxiv","version":2}},"canonical_sha256":"6bd3ab2e1c6ecb53c6bad9e5d7c6ddb3ec7546a197ab2f5773dce8967c3ba0b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bd3ab2e1c6ecb53c6bad9e5d7c6ddb3ec7546a197ab2f5773dce8967c3ba0b8","first_computed_at":"2026-05-18T02:35:52.650547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:52.650547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SWcfpmluU9pUGLaYwuXcqb6bp65YIaorqmyv9w/ip0NsUTNNEYnpJnEuKYDh87U+FOB31HJ/eQGYP/Svk6u4Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:52.650992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5188","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fadfda3c9651e04bbac0e1fb393526033aa0a6e6e6be5de50e40545f34ec0256","sha256:d90ce5e0b413ec79e856e22eaec82b22a8f0a12b47110bf9fc092cfd144bfac8"],"state_sha256":"9fe676dfbd9c1187cd922b0d17fe8cd24b38479f7508c312cb0d6c1e29127746"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ll1wWaRRclJR0J4WtX5FjbUZky7XIQblTqSXD3W67+Q/m+JK/CTsZu0IzwAs4ZA85BiEllHWdpUnv/r2/AYcCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:58:14.680634Z","bundle_sha256":"524de7c0b590c73c15f035a7941dbe8fd6f76082b182dd6c730801714dc76fbd"}}