{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:W7EATIT4KWQARMVUBD2FJ47TRJ","short_pith_number":"pith:W7EATIT4","canonical_record":{"source":{"id":"1809.08140","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-21T14:16:46Z","cross_cats_sorted":["cs.DC","cs.DS"],"title_canon_sha256":"d3c14bdc6a50ddabf0790df0ac5d4a4c6a019f9d5dcbe28d0d6590c3b17e6178","abstract_canon_sha256":"581cb8ee2c2415e6de99e115fa0c59d566837891e737a65e35720f1cbcd35144"},"schema_version":"1.0"},"canonical_sha256":"b7c809a27c55a008b2b408f454f3f38a47a23467e22e36624d302bb4fe51a1f5","source":{"kind":"arxiv","id":"1809.08140","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08140","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08140v3","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08140","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"pith_short_12","alias_value":"W7EATIT4KWQA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"W7EATIT4KWQARMVU","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"W7EATIT4","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:W7EATIT4KWQARMVUBD2FJ47TRJ","target":"record","payload":{"canonical_record":{"source":{"id":"1809.08140","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-21T14:16:46Z","cross_cats_sorted":["cs.DC","cs.DS"],"title_canon_sha256":"d3c14bdc6a50ddabf0790df0ac5d4a4c6a019f9d5dcbe28d0d6590c3b17e6178","abstract_canon_sha256":"581cb8ee2c2415e6de99e115fa0c59d566837891e737a65e35720f1cbcd35144"},"schema_version":"1.0"},"canonical_sha256":"b7c809a27c55a008b2b408f454f3f38a47a23467e22e36624d302bb4fe51a1f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:38.372200Z","signature_b64":"Q9z4yic7yq8W4avgmJ+03Gr2YJOnp9Z2H/N1HinQd7Dct1p/j2QNfgKgAU+AkYDaQL4Vr+hFFDXzKPn+EUvQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7c809a27c55a008b2b408f454f3f38a47a23467e22e36624d302bb4fe51a1f5","last_reissued_at":"2026-05-17T23:55:38.371724Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:38.371724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.08140","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gsaK+v8e2nwKB61BksgmRq3hlRbvfkwv+sZ6G0NdKkJ4Hcf0XEGxUT1AGddYvHA69bVjRdGXV6n86n8XPFeVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:17:17.689943Z"},"content_sha256":"57a1bda39c0f8cdfc3e9baea5073b5912e0263d1f76a9a473624f3f6404a6a71","schema_version":"1.0","event_id":"sha256:57a1bda39c0f8cdfc3e9baea5073b5912e0263d1f76a9a473624f3f6404a6a71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:W7EATIT4KWQARMVUBD2FJ47TRJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributed coloring of graphs with an optimal number of colors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.DS"],"primary_cat":"math.CO","authors_text":"\\'Etienne Bamas, Louis Esperet","submitted_at":"2018-09-21T14:16:46Z","abstract_excerpt":"This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e.\\ with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so far has focused on coloring graphs of maximum degree $\\Delta$ with at most $\\Delta+1$ colors (or $\\Delta$ colors when some simple obstructions are forbidden). When $\\Delta$ is sufficiently large and $c\\ge \\Delta-k_\\Delta+1$, for some integer $k_\\Delta\\approx \\sqrt{\\Delta}-2$, we give a distributed algorithm that given a $c$-colorable graph $G$ of maximum degre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08140","kind":"arxiv","version":3},"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":"2026-05-17T23:55:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GG6nghrUCjA39omeKCUe3pnEezlW/Cll6eaxeK8tg8qkgHsQXQvpAZNJesDwWLRbVlyZ+ghAUQVjeuBGckMwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:17:17.690791Z"},"content_sha256":"062c0d5bff5cf2a7b99adaf8915781483c3026c389f0510c6d93c925eed167a5","schema_version":"1.0","event_id":"sha256:062c0d5bff5cf2a7b99adaf8915781483c3026c389f0510c6d93c925eed167a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W7EATIT4KWQARMVUBD2FJ47TRJ/bundle.json","state_url":"https://pith.science/pith/W7EATIT4KWQARMVUBD2FJ47TRJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W7EATIT4KWQARMVUBD2FJ47TRJ/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":"2026-06-11T17:17:17Z","links":{"resolver":"https://pith.science/pith/W7EATIT4KWQARMVUBD2FJ47TRJ","bundle":"https://pith.science/pith/W7EATIT4KWQARMVUBD2FJ47TRJ/bundle.json","state":"https://pith.science/pith/W7EATIT4KWQARMVUBD2FJ47TRJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W7EATIT4KWQARMVUBD2FJ47TRJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:W7EATIT4KWQARMVUBD2FJ47TRJ","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":"581cb8ee2c2415e6de99e115fa0c59d566837891e737a65e35720f1cbcd35144","cross_cats_sorted":["cs.DC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-21T14:16:46Z","title_canon_sha256":"d3c14bdc6a50ddabf0790df0ac5d4a4c6a019f9d5dcbe28d0d6590c3b17e6178"},"schema_version":"1.0","source":{"id":"1809.08140","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08140","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08140v3","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08140","created_at":"2026-05-17T23:55:38Z"},{"alias_kind":"pith_short_12","alias_value":"W7EATIT4KWQA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"W7EATIT4KWQARMVU","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"W7EATIT4","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:062c0d5bff5cf2a7b99adaf8915781483c3026c389f0510c6d93c925eed167a5","target":"graph","created_at":"2026-05-17T23:55:38Z","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":"This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e.\\ with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so far has focused on coloring graphs of maximum degree $\\Delta$ with at most $\\Delta+1$ colors (or $\\Delta$ colors when some simple obstructions are forbidden). When $\\Delta$ is sufficiently large and $c\\ge \\Delta-k_\\Delta+1$, for some integer $k_\\Delta\\approx \\sqrt{\\Delta}-2$, we give a distributed algorithm that given a $c$-colorable graph $G$ of maximum degre","authors_text":"\\'Etienne Bamas, Louis Esperet","cross_cats":["cs.DC","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-21T14:16:46Z","title":"Distributed coloring of graphs with an optimal number of colors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08140","kind":"arxiv","version":3},"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":"sha256:57a1bda39c0f8cdfc3e9baea5073b5912e0263d1f76a9a473624f3f6404a6a71","target":"record","created_at":"2026-05-17T23:55:38Z","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":"581cb8ee2c2415e6de99e115fa0c59d566837891e737a65e35720f1cbcd35144","cross_cats_sorted":["cs.DC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-21T14:16:46Z","title_canon_sha256":"d3c14bdc6a50ddabf0790df0ac5d4a4c6a019f9d5dcbe28d0d6590c3b17e6178"},"schema_version":"1.0","source":{"id":"1809.08140","kind":"arxiv","version":3}},"canonical_sha256":"b7c809a27c55a008b2b408f454f3f38a47a23467e22e36624d302bb4fe51a1f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7c809a27c55a008b2b408f454f3f38a47a23467e22e36624d302bb4fe51a1f5","first_computed_at":"2026-05-17T23:55:38.371724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:38.371724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q9z4yic7yq8W4avgmJ+03Gr2YJOnp9Z2H/N1HinQd7Dct1p/j2QNfgKgAU+AkYDaQL4Vr+hFFDXzKPn+EUvQDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:38.372200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08140","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57a1bda39c0f8cdfc3e9baea5073b5912e0263d1f76a9a473624f3f6404a6a71","sha256:062c0d5bff5cf2a7b99adaf8915781483c3026c389f0510c6d93c925eed167a5"],"state_sha256":"fae86abaa77b63ac937bf6637f1d025fca75ba9611fbf7a2ed45794cf1cabb40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aoGn7pKeCJU+7coQWYJ+zQDOxqa3Jl79qU95USSZEUFg8UINTgtcIiuX6YxBLRqFzPdmGZJONcYnvLQZdvuIDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T17:17:17.694718Z","bundle_sha256":"f916e89c13e16d912a82b3625b53b0e6fe37d9d5db331d5c65820ffd02425f8c"}}