{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TP6XXMAKRDXZSYWEYL7ZH2WIRU","short_pith_number":"pith:TP6XXMAK","canonical_record":{"source":{"id":"1805.09394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-23T19:31:09Z","cross_cats_sorted":[],"title_canon_sha256":"ddf99e533b458221591cf8c8abeeac8742b0abe270762b66fb79cb208fd88018","abstract_canon_sha256":"3096ded4608d8d768266381b90a52b93c3b6f22d7c04b13a865d312e2bcb11ec"},"schema_version":"1.0"},"canonical_sha256":"9bfd7bb00a88ef9962c4c2ff93eac88d33b53d0c221795960a563ccb2cc32b0a","source":{"kind":"arxiv","id":"1805.09394","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09394","created_at":"2026-05-18T00:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09394v1","created_at":"2026-05-18T00:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09394","created_at":"2026-05-18T00:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"TP6XXMAKRDXZ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TP6XXMAKRDXZSYWE","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TP6XXMAK","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TP6XXMAKRDXZSYWEYL7ZH2WIRU","target":"record","payload":{"canonical_record":{"source":{"id":"1805.09394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-23T19:31:09Z","cross_cats_sorted":[],"title_canon_sha256":"ddf99e533b458221591cf8c8abeeac8742b0abe270762b66fb79cb208fd88018","abstract_canon_sha256":"3096ded4608d8d768266381b90a52b93c3b6f22d7c04b13a865d312e2bcb11ec"},"schema_version":"1.0"},"canonical_sha256":"9bfd7bb00a88ef9962c4c2ff93eac88d33b53d0c221795960a563ccb2cc32b0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:04.157377Z","signature_b64":"cIsfWxVJovrLgIhptnMj8z8PmeViTWaE36Cu9pBxzxcnXCBbVkeCZZGn07EMG7D7/ss4exifcTitHbpp9K2EBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bfd7bb00a88ef9962c4c2ff93eac88d33b53d0c221795960a563ccb2cc32b0a","last_reissued_at":"2026-05-18T00:15:04.156838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:04.156838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.09394","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":"2026-05-18T00:15:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rBLVsaogNDcgz/GN30bvE3xifd8G9IBRJw0ZnRvaiEcvgqXA7KHo1t8bJuIh5Tmx9IeW4WMEXrS9IuY38BF3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:48:08.056594Z"},"content_sha256":"2664dca5cc3341ad0fe10b62cea7249541c24986569a283753ed78c5b049b818","schema_version":"1.0","event_id":"sha256:2664dca5cc3341ad0fe10b62cea7249541c24986569a283753ed78c5b049b818"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TP6XXMAKRDXZSYWEYL7ZH2WIRU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coloring general Kneser graphs and hypergraphs via high-discrepancy hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Danila Cherkashin, Jozsef Balogh, Sergei Kiselev","submitted_at":"2018-05-23T19:31:09Z","abstract_excerpt":"We suggest a new method on coloring generalized Kneser graphs based on hypergraphs with high discrepancy and small number of edges. The main result is providing a proper coloring of K(n, n/2-t, s) in (4 + o(1))(s + t)^2 colors, which is produced by Hadamard matrices. Also, we show that for colorings by independent set of a natural type, this result is the best possible up to a multiplicative constant. Our method extends to Kneser hypergraphs as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09394","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":""},"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":"2026-05-18T00:15:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XOdC43t+hT+xfPIAuEiKOiqabKbRWIsDYTW6+DihkMq/HhZ7IxS0aQeiqhuPyB24rVHA5sOFT5SCC53BgHeDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:48:08.057311Z"},"content_sha256":"02c365f7f9d2fa15ac4c4256a6676c33635e0ac74fbf7424813bd42680ac0571","schema_version":"1.0","event_id":"sha256:02c365f7f9d2fa15ac4c4256a6676c33635e0ac74fbf7424813bd42680ac0571"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TP6XXMAKRDXZSYWEYL7ZH2WIRU/bundle.json","state_url":"https://pith.science/pith/TP6XXMAKRDXZSYWEYL7ZH2WIRU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TP6XXMAKRDXZSYWEYL7ZH2WIRU/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":"2026-06-09T07:48:08Z","links":{"resolver":"https://pith.science/pith/TP6XXMAKRDXZSYWEYL7ZH2WIRU","bundle":"https://pith.science/pith/TP6XXMAKRDXZSYWEYL7ZH2WIRU/bundle.json","state":"https://pith.science/pith/TP6XXMAKRDXZSYWEYL7ZH2WIRU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TP6XXMAKRDXZSYWEYL7ZH2WIRU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TP6XXMAKRDXZSYWEYL7ZH2WIRU","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":"3096ded4608d8d768266381b90a52b93c3b6f22d7c04b13a865d312e2bcb11ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-23T19:31:09Z","title_canon_sha256":"ddf99e533b458221591cf8c8abeeac8742b0abe270762b66fb79cb208fd88018"},"schema_version":"1.0","source":{"id":"1805.09394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09394","created_at":"2026-05-18T00:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09394v1","created_at":"2026-05-18T00:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09394","created_at":"2026-05-18T00:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"TP6XXMAKRDXZ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TP6XXMAKRDXZSYWE","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TP6XXMAK","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:02c365f7f9d2fa15ac4c4256a6676c33635e0ac74fbf7424813bd42680ac0571","target":"graph","created_at":"2026-05-18T00:15:04Z","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":"We suggest a new method on coloring generalized Kneser graphs based on hypergraphs with high discrepancy and small number of edges. The main result is providing a proper coloring of K(n, n/2-t, s) in (4 + o(1))(s + t)^2 colors, which is produced by Hadamard matrices. Also, we show that for colorings by independent set of a natural type, this result is the best possible up to a multiplicative constant. Our method extends to Kneser hypergraphs as well.","authors_text":"Danila Cherkashin, Jozsef Balogh, Sergei Kiselev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-23T19:31:09Z","title":"Coloring general Kneser graphs and hypergraphs via high-discrepancy hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09394","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":"sha256:2664dca5cc3341ad0fe10b62cea7249541c24986569a283753ed78c5b049b818","target":"record","created_at":"2026-05-18T00:15:04Z","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":"3096ded4608d8d768266381b90a52b93c3b6f22d7c04b13a865d312e2bcb11ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-23T19:31:09Z","title_canon_sha256":"ddf99e533b458221591cf8c8abeeac8742b0abe270762b66fb79cb208fd88018"},"schema_version":"1.0","source":{"id":"1805.09394","kind":"arxiv","version":1}},"canonical_sha256":"9bfd7bb00a88ef9962c4c2ff93eac88d33b53d0c221795960a563ccb2cc32b0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bfd7bb00a88ef9962c4c2ff93eac88d33b53d0c221795960a563ccb2cc32b0a","first_computed_at":"2026-05-18T00:15:04.156838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:04.156838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cIsfWxVJovrLgIhptnMj8z8PmeViTWaE36Cu9pBxzxcnXCBbVkeCZZGn07EMG7D7/ss4exifcTitHbpp9K2EBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:04.157377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.09394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2664dca5cc3341ad0fe10b62cea7249541c24986569a283753ed78c5b049b818","sha256:02c365f7f9d2fa15ac4c4256a6676c33635e0ac74fbf7424813bd42680ac0571"],"state_sha256":"db33076dfeaa69162ac1956d67d52c0dcbf59cf5115e1db9c10f2c39f93fb9e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eqRgB3HauWA3p5LqquVvk7lagder0MAchAupHNIiVSQuGOifDuXT53jHfl0MhFTtC3UTRmcppa3hf/6areolBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:48:08.061595Z","bundle_sha256":"f47e8946229b51acaf46af53f05406007dd69feabaad53157a13052a59968ab0"}}