{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:D3427LZG6SGOSCSRALVUAC6M4J","short_pith_number":"pith:D3427LZG","canonical_record":{"source":{"id":"2009.02611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-09-05T22:48:01Z","cross_cats_sorted":[],"title_canon_sha256":"0340dea1bf78e466157e85abfff3294d636b0ddd81bff6adbb08252f76abb1a7","abstract_canon_sha256":"b9d5cc3d87673411e7499810d3c8924aa746532dea58bb10b725c5c9d6d24c73"},"schema_version":"1.0"},"canonical_sha256":"1ef9afaf26f48ce90a5102eb400bcce264c9b1eed9e2e6d8d0929c25fea46d5f","source":{"kind":"arxiv","id":"2009.02611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.02611","created_at":"2026-07-05T01:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"2009.02611v1","created_at":"2026-07-05T01:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.02611","created_at":"2026-07-05T01:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"D3427LZG6SGO","created_at":"2026-07-05T01:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"D3427LZG6SGOSCSR","created_at":"2026-07-05T01:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"D3427LZG","created_at":"2026-07-05T01:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:D3427LZG6SGOSCSRALVUAC6M4J","target":"record","payload":{"canonical_record":{"source":{"id":"2009.02611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-09-05T22:48:01Z","cross_cats_sorted":[],"title_canon_sha256":"0340dea1bf78e466157e85abfff3294d636b0ddd81bff6adbb08252f76abb1a7","abstract_canon_sha256":"b9d5cc3d87673411e7499810d3c8924aa746532dea58bb10b725c5c9d6d24c73"},"schema_version":"1.0"},"canonical_sha256":"1ef9afaf26f48ce90a5102eb400bcce264c9b1eed9e2e6d8d0929c25fea46d5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:33:24.134999Z","signature_b64":"bQJBJ/CnwhmNHcm+usU4TsEYI5KE7w50oFfg157WoO0gec72ClrgCyF6FRJ4LeR7yzWpECaQsPmfv+awV6OXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ef9afaf26f48ce90a5102eb400bcce264c9b1eed9e2e6d8d0929c25fea46d5f","last_reissued_at":"2026-07-05T01:33:24.134600Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:33:24.134600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.02611","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:33:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6lHTk8Ixdl5qCWBItHZkFB7iPdpaJSbdQVMyOMjUhJhWSHK5WAzqtyTC5a9gsgBE8owLWU8ez3MqX3vTJTpODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T06:02:59.369220Z"},"content_sha256":"c5598f07e8723353fc3d3931b5c167ed06c3f671b70b4bb3480d6eb63279d145","schema_version":"1.0","event_id":"sha256:c5598f07e8723353fc3d3931b5c167ed06c3f671b70b4bb3480d6eb63279d145"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:D3427LZG6SGOSCSRALVUAC6M4J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the maximum diameter of $k$-colorable graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"\\'Eva Czabarka, Inne Singgih, L\\'aszl\\'o A. Sz\\'ekely","submitted_at":"2020-09-05T22:48:01Z","abstract_excerpt":"Erd\\H{o}s, Pach, Pollack and Tuza [J. Combin. Theory, B 47, (1989), 279-285] conjectured that the diameter of a $K_{2r}$-free connected graph of order $n$ and minimum degree $\\delta\\geq 2$ is at most $\\frac{2(r-1)(3r+2)}{(2r^2-1)}\\cdot \\frac{n}{\\delta} + O(1)$ for every $r\\ge 2$, if $\\delta$ is a multiple of $(r-1)(3r+2)$. For every $r>1$ and $\\delta\\ge 2(r-1)$, we create $K_{2r}$-free graphs with minimum degree $\\delta$ and diameter $\\frac{(6r-5)n}{(2r-1)\\delta+2r-3}+O(1)$, which are counterexamples to the conjecture for every $r>1$ and $\\delta>2(r-1)(3r+2)(2r-3)$. The rest of the paper prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.02611","kind":"arxiv","version":1},"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/2009.02611/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":"2026-07-05T01:33:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fuvICVoFSHBv3uaFi5kt1g7Qhqvy2ZGHrpAySXcHtCTbXITNc9MuEoiiyuZV/sboNgfeh659585Hdgu+a7Y2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T06:02:59.369900Z"},"content_sha256":"7ac38177b700b3a0a19e6fd4a1159bc3bf28a3f87b4b05d8e61e058b3e2b267a","schema_version":"1.0","event_id":"sha256:7ac38177b700b3a0a19e6fd4a1159bc3bf28a3f87b4b05d8e61e058b3e2b267a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D3427LZG6SGOSCSRALVUAC6M4J/bundle.json","state_url":"https://pith.science/pith/D3427LZG6SGOSCSRALVUAC6M4J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D3427LZG6SGOSCSRALVUAC6M4J/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":"2026-07-09T06:02:59Z","links":{"resolver":"https://pith.science/pith/D3427LZG6SGOSCSRALVUAC6M4J","bundle":"https://pith.science/pith/D3427LZG6SGOSCSRALVUAC6M4J/bundle.json","state":"https://pith.science/pith/D3427LZG6SGOSCSRALVUAC6M4J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D3427LZG6SGOSCSRALVUAC6M4J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:D3427LZG6SGOSCSRALVUAC6M4J","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":"b9d5cc3d87673411e7499810d3c8924aa746532dea58bb10b725c5c9d6d24c73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-09-05T22:48:01Z","title_canon_sha256":"0340dea1bf78e466157e85abfff3294d636b0ddd81bff6adbb08252f76abb1a7"},"schema_version":"1.0","source":{"id":"2009.02611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.02611","created_at":"2026-07-05T01:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"2009.02611v1","created_at":"2026-07-05T01:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.02611","created_at":"2026-07-05T01:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"D3427LZG6SGO","created_at":"2026-07-05T01:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"D3427LZG6SGOSCSR","created_at":"2026-07-05T01:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"D3427LZG","created_at":"2026-07-05T01:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:7ac38177b700b3a0a19e6fd4a1159bc3bf28a3f87b4b05d8e61e058b3e2b267a","target":"graph","created_at":"2026-07-05T01:33:24Z","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/2009.02611/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Erd\\H{o}s, Pach, Pollack and Tuza [J. Combin. Theory, B 47, (1989), 279-285] conjectured that the diameter of a $K_{2r}$-free connected graph of order $n$ and minimum degree $\\delta\\geq 2$ is at most $\\frac{2(r-1)(3r+2)}{(2r^2-1)}\\cdot \\frac{n}{\\delta} + O(1)$ for every $r\\ge 2$, if $\\delta$ is a multiple of $(r-1)(3r+2)$. For every $r>1$ and $\\delta\\ge 2(r-1)$, we create $K_{2r}$-free graphs with minimum degree $\\delta$ and diameter $\\frac{(6r-5)n}{(2r-1)\\delta+2r-3}+O(1)$, which are counterexamples to the conjecture for every $r>1$ and $\\delta>2(r-1)(3r+2)(2r-3)$. The rest of the paper prove","authors_text":"\\'Eva Czabarka, Inne Singgih, L\\'aszl\\'o A. Sz\\'ekely","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-09-05T22:48:01Z","title":"On the maximum diameter of $k$-colorable graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.02611","kind":"arxiv","version":1},"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:c5598f07e8723353fc3d3931b5c167ed06c3f671b70b4bb3480d6eb63279d145","target":"record","created_at":"2026-07-05T01:33:24Z","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":"b9d5cc3d87673411e7499810d3c8924aa746532dea58bb10b725c5c9d6d24c73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-09-05T22:48:01Z","title_canon_sha256":"0340dea1bf78e466157e85abfff3294d636b0ddd81bff6adbb08252f76abb1a7"},"schema_version":"1.0","source":{"id":"2009.02611","kind":"arxiv","version":1}},"canonical_sha256":"1ef9afaf26f48ce90a5102eb400bcce264c9b1eed9e2e6d8d0929c25fea46d5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ef9afaf26f48ce90a5102eb400bcce264c9b1eed9e2e6d8d0929c25fea46d5f","first_computed_at":"2026-07-05T01:33:24.134600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:33:24.134600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bQJBJ/CnwhmNHcm+usU4TsEYI5KE7w50oFfg157WoO0gec72ClrgCyF6FRJ4LeR7yzWpECaQsPmfv+awV6OXDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:33:24.134999Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.02611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5598f07e8723353fc3d3931b5c167ed06c3f671b70b4bb3480d6eb63279d145","sha256:7ac38177b700b3a0a19e6fd4a1159bc3bf28a3f87b4b05d8e61e058b3e2b267a"],"state_sha256":"fa8a7296da155ffc47c90572e72bfad3c7e1606f522ab018c1134632cd2ea16b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mXy0nZt/vD/+Z5PqAn2VjdxR+Gc9Ft0hINokECc5o9zia65U982EbRaVQrZuUoLUMdIwFhI/D1sEQM4vr/HECQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T06:02:59.373008Z","bundle_sha256":"c788a2fa946b674172af03313c0dfa228ca2c7103e1a8b8bf7c3a426bb8e6ee1"}}