{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:OVLJDIRVGDQCMEE3EQSWSPZAZW","short_pith_number":"pith:OVLJDIRV","canonical_record":{"source":{"id":"2006.09422","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-06-16T18:06:15Z","cross_cats_sorted":[],"title_canon_sha256":"a1ca004a338488b092c001959770d439bd05ec8436d4f808d7d539a130bb8c6d","abstract_canon_sha256":"e736b60e4d0ff42296da358bdc2cc6ae330e0c3022d3599dac473975f83d30e6"},"schema_version":"1.0"},"canonical_sha256":"755691a23530e026109b2425693f20cdbe1534f5f2a9797a6777e6b4c4354503","source":{"kind":"arxiv","id":"2006.09422","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.09422","created_at":"2026-07-05T08:58:38Z"},{"alias_kind":"arxiv_version","alias_value":"2006.09422v7","created_at":"2026-07-05T08:58:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.09422","created_at":"2026-07-05T08:58:38Z"},{"alias_kind":"pith_short_12","alias_value":"OVLJDIRVGDQC","created_at":"2026-07-05T08:58:38Z"},{"alias_kind":"pith_short_16","alias_value":"OVLJDIRVGDQCMEE3","created_at":"2026-07-05T08:58:38Z"},{"alias_kind":"pith_short_8","alias_value":"OVLJDIRV","created_at":"2026-07-05T08:58:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:OVLJDIRVGDQCMEE3EQSWSPZAZW","target":"record","payload":{"canonical_record":{"source":{"id":"2006.09422","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-06-16T18:06:15Z","cross_cats_sorted":[],"title_canon_sha256":"a1ca004a338488b092c001959770d439bd05ec8436d4f808d7d539a130bb8c6d","abstract_canon_sha256":"e736b60e4d0ff42296da358bdc2cc6ae330e0c3022d3599dac473975f83d30e6"},"schema_version":"1.0"},"canonical_sha256":"755691a23530e026109b2425693f20cdbe1534f5f2a9797a6777e6b4c4354503","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:58:38.390900Z","signature_b64":"4Nn+DMiJN+LfFtq6hmrVta3krV3h49ukfYo1pGMelHPbGTUVx1EEBDaK1h/Z6oeITKqfHELYAUtt+ijViIsyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"755691a23530e026109b2425693f20cdbe1534f5f2a9797a6777e6b4c4354503","last_reissued_at":"2026-07-05T08:58:38.390372Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:58:38.390372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.09422","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:58:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IJS46yDIIaFy6NcStmVOGliil1Kxk/DY5BKGEWlztoDhtGw8qbNm4cosos7Bd6OYXXILUuE2XHy+U4StPt0YAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T05:10:11.371636Z"},"content_sha256":"474b04ad41bd292cae01c64b9eeb3b98d75f7cf4d246fe69f31eca4b885f6274","schema_version":"1.0","event_id":"sha256:474b04ad41bd292cae01c64b9eeb3b98d75f7cf4d246fe69f31eca4b885f6274"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:OVLJDIRVGDQCMEE3EQSWSPZAZW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-bipartite k-common graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Kral, Fan Wei, Jan Volec, Jonathan A. Noel, Sergey Norin","submitted_at":"2020-06-16T18:06:15Z","abstract_excerpt":"A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K_n is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Stovicek and Thomason [Combinatorica 16 (1996), 123-141]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.09422","kind":"arxiv","version":7},"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/2006.09422/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":"2026-07-05T08:58:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RA4AElCEp71T5ewulAfiSLodqU15Awg+X6GQ0aKiaVBiRqZzL1kBwJO/9sp6+ZvAVUeDg42JQwG3xDf05Nn5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T05:10:11.372538Z"},"content_sha256":"ceccc21216f6d23b8b4ec1ff95bf476f9f2936edee6e7a848e84ba244813e6df","schema_version":"1.0","event_id":"sha256:ceccc21216f6d23b8b4ec1ff95bf476f9f2936edee6e7a848e84ba244813e6df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OVLJDIRVGDQCMEE3EQSWSPZAZW/bundle.json","state_url":"https://pith.science/pith/OVLJDIRVGDQCMEE3EQSWSPZAZW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OVLJDIRVGDQCMEE3EQSWSPZAZW/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":"2026-08-14T05:10:11Z","links":{"resolver":"https://pith.science/pith/OVLJDIRVGDQCMEE3EQSWSPZAZW","bundle":"https://pith.science/pith/OVLJDIRVGDQCMEE3EQSWSPZAZW/bundle.json","state":"https://pith.science/pith/OVLJDIRVGDQCMEE3EQSWSPZAZW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OVLJDIRVGDQCMEE3EQSWSPZAZW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:OVLJDIRVGDQCMEE3EQSWSPZAZW","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":"e736b60e4d0ff42296da358bdc2cc6ae330e0c3022d3599dac473975f83d30e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-06-16T18:06:15Z","title_canon_sha256":"a1ca004a338488b092c001959770d439bd05ec8436d4f808d7d539a130bb8c6d"},"schema_version":"1.0","source":{"id":"2006.09422","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.09422","created_at":"2026-07-05T08:58:38Z"},{"alias_kind":"arxiv_version","alias_value":"2006.09422v7","created_at":"2026-07-05T08:58:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.09422","created_at":"2026-07-05T08:58:38Z"},{"alias_kind":"pith_short_12","alias_value":"OVLJDIRVGDQC","created_at":"2026-07-05T08:58:38Z"},{"alias_kind":"pith_short_16","alias_value":"OVLJDIRVGDQCMEE3","created_at":"2026-07-05T08:58:38Z"},{"alias_kind":"pith_short_8","alias_value":"OVLJDIRV","created_at":"2026-07-05T08:58:38Z"}],"graph_snapshots":[{"event_id":"sha256:ceccc21216f6d23b8b4ec1ff95bf476f9f2936edee6e7a848e84ba244813e6df","target":"graph","created_at":"2026-07-05T08:58:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2006.09422/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K_n is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Stovicek and Thomason [Combinatorica 16 (1996), 123-141]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko.","authors_text":"Daniel Kral, Fan Wei, Jan Volec, Jonathan A. Noel, Sergey Norin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-06-16T18:06:15Z","title":"Non-bipartite k-common graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.09422","kind":"arxiv","version":7},"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":"sha256:474b04ad41bd292cae01c64b9eeb3b98d75f7cf4d246fe69f31eca4b885f6274","target":"record","created_at":"2026-07-05T08:58:38Z","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":"e736b60e4d0ff42296da358bdc2cc6ae330e0c3022d3599dac473975f83d30e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-06-16T18:06:15Z","title_canon_sha256":"a1ca004a338488b092c001959770d439bd05ec8436d4f808d7d539a130bb8c6d"},"schema_version":"1.0","source":{"id":"2006.09422","kind":"arxiv","version":7}},"canonical_sha256":"755691a23530e026109b2425693f20cdbe1534f5f2a9797a6777e6b4c4354503","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"755691a23530e026109b2425693f20cdbe1534f5f2a9797a6777e6b4c4354503","first_computed_at":"2026-07-05T08:58:38.390372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:58:38.390372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Nn+DMiJN+LfFtq6hmrVta3krV3h49ukfYo1pGMelHPbGTUVx1EEBDaK1h/Z6oeITKqfHELYAUtt+ijViIsyDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:58:38.390900Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.09422","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:474b04ad41bd292cae01c64b9eeb3b98d75f7cf4d246fe69f31eca4b885f6274","sha256:ceccc21216f6d23b8b4ec1ff95bf476f9f2936edee6e7a848e84ba244813e6df"],"state_sha256":"f905d74450cb046beb00614fa37db479fac8aed226598a2e6a090ac7275b6c1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3xSrsBT2XmKPFmES+Z40RNBexwCJLUSCOPXpc7Tnb1dBmM0jUrTlXVcjnUYJ2KEeC9PhCmn5O5HmfGa8we+xAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T05:10:11.379574Z","bundle_sha256":"138f58ae01786fc209c4ec40e55be4d0d02ecdc28c44226d410716d1fd29f702"}}