{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JCFL6SXCJUZG6FEBOCI5UQWAVN","short_pith_number":"pith:JCFL6SXC","canonical_record":{"source":{"id":"1707.07581","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-24T14:43:58Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"4769a4f680c3048f0ae9c2a767cf4675136e599cb8c4960fce4a73e1f9976617","abstract_canon_sha256":"d0d5309376fddee14f2647ad9e507412041ee3b7d0831b84f5e5ea1974ddbb65"},"schema_version":"1.0"},"canonical_sha256":"488abf4ae24d326f14817091da42c0ab5e061df5ea297b04b2e8e6c85a9f9193","source":{"kind":"arxiv","id":"1707.07581","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07581","created_at":"2026-05-18T00:09:09Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07581v3","created_at":"2026-05-18T00:09:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07581","created_at":"2026-05-18T00:09:09Z"},{"alias_kind":"pith_short_12","alias_value":"JCFL6SXCJUZG","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"JCFL6SXCJUZG6FEB","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"JCFL6SXC","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JCFL6SXCJUZG6FEBOCI5UQWAVN","target":"record","payload":{"canonical_record":{"source":{"id":"1707.07581","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-24T14:43:58Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"4769a4f680c3048f0ae9c2a767cf4675136e599cb8c4960fce4a73e1f9976617","abstract_canon_sha256":"d0d5309376fddee14f2647ad9e507412041ee3b7d0831b84f5e5ea1974ddbb65"},"schema_version":"1.0"},"canonical_sha256":"488abf4ae24d326f14817091da42c0ab5e061df5ea297b04b2e8e6c85a9f9193","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:09.974513Z","signature_b64":"345soScIRxfhCMBQb0ur0DdL2avqUzt6l/0YX8cm5MolZyrlPzT+o6cMOGB5uej1le/Wt+3zj/dFTHPRKQxQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"488abf4ae24d326f14817091da42c0ab5e061df5ea297b04b2e8e6c85a9f9193","last_reissued_at":"2026-05-18T00:09:09.973802Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:09.973802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.07581","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":"2026-05-18T00:09:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PNt6fBqFhvw0TuaZlYbf2N6YJ/gCFxweHoiav2PKDPIOItV52yneLh8YjrsdPDlgeeiGWWKoTEQvpRFkTer0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:43:18.225758Z"},"content_sha256":"a6823f05eaec157de770181703b7d38d9e26840ca7c47fa803559fff6b3c112d","schema_version":"1.0","event_id":"sha256:a6823f05eaec157de770181703b7d38d9e26840ca7c47fa803559fff6b3c112d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JCFL6SXCJUZG6FEBOCI5UQWAVN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On minimal triangle-free 6-chromatic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jan Goedgebeur","submitted_at":"2017-07-24T14:43:58Z","abstract_excerpt":"A graph with chromatic number $k$ is called $k$-chromatic. Using computational methods, we show that the smallest triangle-free 6-chromatic graphs have at least 32 and at most 40 vertices.\n  We also determine the complete set of all triangle-free 5-chromatic graphs up to 24 vertices. This implies that Reed's conjecture holds for triangle-free graphs up to at least this order. We also establish that the smallest regular triangle-free 5-chromatic graphs have 24 vertices. Finally, we show that the smallest 5-chromatic graphs of girth at least 5 have at least 29 vertices and that the smallest 4-ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07581","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":"2026-05-18T00:09:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bw1LaIaIywmss96tc6s202N5niyv2ji4nUGYlwWsG6Mz3FVm04uXY+BB89RWpOebA/zMzx/DaSx4aJfbAbDpCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:43:18.226453Z"},"content_sha256":"bd347bab20260b60ed6e748056c9fa75c2951dd8126e4a2f73b51694c029e0ad","schema_version":"1.0","event_id":"sha256:bd347bab20260b60ed6e748056c9fa75c2951dd8126e4a2f73b51694c029e0ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JCFL6SXCJUZG6FEBOCI5UQWAVN/bundle.json","state_url":"https://pith.science/pith/JCFL6SXCJUZG6FEBOCI5UQWAVN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JCFL6SXCJUZG6FEBOCI5UQWAVN/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":"2026-05-31T08:43:18Z","links":{"resolver":"https://pith.science/pith/JCFL6SXCJUZG6FEBOCI5UQWAVN","bundle":"https://pith.science/pith/JCFL6SXCJUZG6FEBOCI5UQWAVN/bundle.json","state":"https://pith.science/pith/JCFL6SXCJUZG6FEBOCI5UQWAVN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JCFL6SXCJUZG6FEBOCI5UQWAVN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JCFL6SXCJUZG6FEBOCI5UQWAVN","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":"d0d5309376fddee14f2647ad9e507412041ee3b7d0831b84f5e5ea1974ddbb65","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-24T14:43:58Z","title_canon_sha256":"4769a4f680c3048f0ae9c2a767cf4675136e599cb8c4960fce4a73e1f9976617"},"schema_version":"1.0","source":{"id":"1707.07581","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07581","created_at":"2026-05-18T00:09:09Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07581v3","created_at":"2026-05-18T00:09:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07581","created_at":"2026-05-18T00:09:09Z"},{"alias_kind":"pith_short_12","alias_value":"JCFL6SXCJUZG","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"JCFL6SXCJUZG6FEB","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"JCFL6SXC","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:bd347bab20260b60ed6e748056c9fa75c2951dd8126e4a2f73b51694c029e0ad","target":"graph","created_at":"2026-05-18T00:09:09Z","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":"A graph with chromatic number $k$ is called $k$-chromatic. Using computational methods, we show that the smallest triangle-free 6-chromatic graphs have at least 32 and at most 40 vertices.\n  We also determine the complete set of all triangle-free 5-chromatic graphs up to 24 vertices. This implies that Reed's conjecture holds for triangle-free graphs up to at least this order. We also establish that the smallest regular triangle-free 5-chromatic graphs have 24 vertices. Finally, we show that the smallest 5-chromatic graphs of girth at least 5 have at least 29 vertices and that the smallest 4-ch","authors_text":"Jan Goedgebeur","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-24T14:43:58Z","title":"On minimal triangle-free 6-chromatic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07581","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:a6823f05eaec157de770181703b7d38d9e26840ca7c47fa803559fff6b3c112d","target":"record","created_at":"2026-05-18T00:09:09Z","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":"d0d5309376fddee14f2647ad9e507412041ee3b7d0831b84f5e5ea1974ddbb65","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-24T14:43:58Z","title_canon_sha256":"4769a4f680c3048f0ae9c2a767cf4675136e599cb8c4960fce4a73e1f9976617"},"schema_version":"1.0","source":{"id":"1707.07581","kind":"arxiv","version":3}},"canonical_sha256":"488abf4ae24d326f14817091da42c0ab5e061df5ea297b04b2e8e6c85a9f9193","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"488abf4ae24d326f14817091da42c0ab5e061df5ea297b04b2e8e6c85a9f9193","first_computed_at":"2026-05-18T00:09:09.973802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:09.973802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"345soScIRxfhCMBQb0ur0DdL2avqUzt6l/0YX8cm5MolZyrlPzT+o6cMOGB5uej1le/Wt+3zj/dFTHPRKQxQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:09.974513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07581","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6823f05eaec157de770181703b7d38d9e26840ca7c47fa803559fff6b3c112d","sha256:bd347bab20260b60ed6e748056c9fa75c2951dd8126e4a2f73b51694c029e0ad"],"state_sha256":"45931210b9e6925404242eab3fb8a7b66fd2ebf83c1bade37714fa6da42c7f7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xFaIeO5Mhjx8kGKwXFwd2wdLIR/3JquiYFiFroH7cPZrLZ+N3jkEqUhFVaYjgOwlEmeXnFkq8K14Lzyrt86gDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:43:18.231955Z","bundle_sha256":"0682dbd6b3ccbae149665d155adb3117b1ba09f9f0a355ddd0215fa5a6fe81d5"}}