{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GHBVKRPGSAKS6IHLKBN66FTDXM","short_pith_number":"pith:GHBVKRPG","canonical_record":{"source":{"id":"1603.05134","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-16T14:56:41Z","cross_cats_sorted":[],"title_canon_sha256":"bb960a39638f617b21b3487aa83d0d901246c542f836da7bd1798a3d20dc1492","abstract_canon_sha256":"a4b10351837960d50e6cad987737d059d6e82452f87963753cf832f3cb9f45fa"},"schema_version":"1.0"},"canonical_sha256":"31c35545e690152f20eb505bef1663bb1a4e3919a821ee99c6fdad04a39d5848","source":{"kind":"arxiv","id":"1603.05134","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05134","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05134v2","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05134","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"pith_short_12","alias_value":"GHBVKRPGSAKS","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GHBVKRPGSAKS6IHL","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GHBVKRPG","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GHBVKRPGSAKS6IHLKBN66FTDXM","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05134","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-16T14:56:41Z","cross_cats_sorted":[],"title_canon_sha256":"bb960a39638f617b21b3487aa83d0d901246c542f836da7bd1798a3d20dc1492","abstract_canon_sha256":"a4b10351837960d50e6cad987737d059d6e82452f87963753cf832f3cb9f45fa"},"schema_version":"1.0"},"canonical_sha256":"31c35545e690152f20eb505bef1663bb1a4e3919a821ee99c6fdad04a39d5848","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:44.328446Z","signature_b64":"okhun9wOaj4xPYEt5Y2f86v/giToHtH3RJjtoFdo9afReOnZh4ClGOoz/bBAzUEbVvH0wS+3Q7WbXt3f/UWcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31c35545e690152f20eb505bef1663bb1a4e3919a821ee99c6fdad04a39d5848","last_reissued_at":"2026-05-18T00:35:44.327795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:44.327795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05134","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pCHLpyPN4KWFZpFtCsDQMVBtRsVLugo3fCIFPtEFi2eGp9HpYmQx/6Nu4xyVwiMZG7Ssifyf98B7oh3KsySJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:50:43.095744Z"},"content_sha256":"f6d6eb9f12b1d6255ceeff7afb536b93c2d0316750167a4d088fdf174ccfe734","schema_version":"1.0","event_id":"sha256:f6d6eb9f12b1d6255ceeff7afb536b93c2d0316750167a4d088fdf174ccfe734"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GHBVKRPGSAKS6IHLKBN66FTDXM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The chromatic number of finite type-graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bill Kay, Christian Avart, Christian Reiher, Vojt\\v{e}ch R\\\"odl","submitted_at":"2016-03-16T14:56:41Z","abstract_excerpt":"By a finite type-graph we mean a graph whose set of vertices is the set of all $k$-subsets of $[n]=\\{1,2,\\ldots, n\\}$ for some integers $n\\ge k\\ge 1$, and in which two such sets are adjacent if and only if they realise a certain order type specified in advance. Examples of such graphs have been investigated in a great variety of contexts in the literature with particular attention being paid to their chromatic number. In recent joint work with Tomasz {\\L}uczak, two of the authors embarked on a systematic study of the chromatic numbers of such type-graphs, formulated a general conjecture determ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05134","kind":"arxiv","version":2},"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":"2026-05-18T00:35:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qo0m+kRcx/9TH7bgZGyVfukqFPN7fJdkJakGlKRrBFqToeMDOw7qXjMWuEpBkPWdha6e+yQaqlQRRyPSjPpvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:50:43.096414Z"},"content_sha256":"118781fbffe249c50853ef9e0995cf7b47277aa37ad379ed043a3ceffe57b4c9","schema_version":"1.0","event_id":"sha256:118781fbffe249c50853ef9e0995cf7b47277aa37ad379ed043a3ceffe57b4c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHBVKRPGSAKS6IHLKBN66FTDXM/bundle.json","state_url":"https://pith.science/pith/GHBVKRPGSAKS6IHLKBN66FTDXM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHBVKRPGSAKS6IHLKBN66FTDXM/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":"2026-06-09T03:50:43Z","links":{"resolver":"https://pith.science/pith/GHBVKRPGSAKS6IHLKBN66FTDXM","bundle":"https://pith.science/pith/GHBVKRPGSAKS6IHLKBN66FTDXM/bundle.json","state":"https://pith.science/pith/GHBVKRPGSAKS6IHLKBN66FTDXM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHBVKRPGSAKS6IHLKBN66FTDXM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GHBVKRPGSAKS6IHLKBN66FTDXM","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":"a4b10351837960d50e6cad987737d059d6e82452f87963753cf832f3cb9f45fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-16T14:56:41Z","title_canon_sha256":"bb960a39638f617b21b3487aa83d0d901246c542f836da7bd1798a3d20dc1492"},"schema_version":"1.0","source":{"id":"1603.05134","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05134","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05134v2","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05134","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"pith_short_12","alias_value":"GHBVKRPGSAKS","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GHBVKRPGSAKS6IHL","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GHBVKRPG","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:118781fbffe249c50853ef9e0995cf7b47277aa37ad379ed043a3ceffe57b4c9","target":"graph","created_at":"2026-05-18T00:35:44Z","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":"By a finite type-graph we mean a graph whose set of vertices is the set of all $k$-subsets of $[n]=\\{1,2,\\ldots, n\\}$ for some integers $n\\ge k\\ge 1$, and in which two such sets are adjacent if and only if they realise a certain order type specified in advance. Examples of such graphs have been investigated in a great variety of contexts in the literature with particular attention being paid to their chromatic number. In recent joint work with Tomasz {\\L}uczak, two of the authors embarked on a systematic study of the chromatic numbers of such type-graphs, formulated a general conjecture determ","authors_text":"Bill Kay, Christian Avart, Christian Reiher, Vojt\\v{e}ch R\\\"odl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-16T14:56:41Z","title":"The chromatic number of finite type-graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05134","kind":"arxiv","version":2},"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:f6d6eb9f12b1d6255ceeff7afb536b93c2d0316750167a4d088fdf174ccfe734","target":"record","created_at":"2026-05-18T00:35:44Z","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":"a4b10351837960d50e6cad987737d059d6e82452f87963753cf832f3cb9f45fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-16T14:56:41Z","title_canon_sha256":"bb960a39638f617b21b3487aa83d0d901246c542f836da7bd1798a3d20dc1492"},"schema_version":"1.0","source":{"id":"1603.05134","kind":"arxiv","version":2}},"canonical_sha256":"31c35545e690152f20eb505bef1663bb1a4e3919a821ee99c6fdad04a39d5848","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31c35545e690152f20eb505bef1663bb1a4e3919a821ee99c6fdad04a39d5848","first_computed_at":"2026-05-18T00:35:44.327795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:44.327795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"okhun9wOaj4xPYEt5Y2f86v/giToHtH3RJjtoFdo9afReOnZh4ClGOoz/bBAzUEbVvH0wS+3Q7WbXt3f/UWcBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:44.328446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05134","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6d6eb9f12b1d6255ceeff7afb536b93c2d0316750167a4d088fdf174ccfe734","sha256:118781fbffe249c50853ef9e0995cf7b47277aa37ad379ed043a3ceffe57b4c9"],"state_sha256":"8fd665466a0bb48bf5b53d24629333fff8c50ec6550a6eacffc8e16cee94adeb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w8g8PMxpBbne4Z2Bv1o9e5jW1J1ib8nTDTaZS8GlazphGM/ivYmRbxlF1OtWTFMtDzeFMA3LKQ1GyIHuRKQxBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:50:43.099917Z","bundle_sha256":"f9bb1105ac8ae00864d4a3032808d7e89faf785c1412e9a017ced844a687dc2d"}}