{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZCGBBNSWEPFADOFVY4JPGA6WB4","short_pith_number":"pith:ZCGBBNSW","canonical_record":{"source":{"id":"1902.08177","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-21T18:37:53Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ee8fa57c1d5fd109f9b4811e8a62fbb0ce826b8cc6b2322345b57d5388e0fd03","abstract_canon_sha256":"86441d7a663ae666c5f55c71d34af97573e7ab630a71964b787320992e5ce718"},"schema_version":"1.0"},"canonical_sha256":"c88c10b65623ca01b8b5c712f303d60f2e0c41ba6dae5ca3c1323094b540f078","source":{"kind":"arxiv","id":"1902.08177","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08177","created_at":"2026-05-17T23:52:50Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08177v2","created_at":"2026-05-17T23:52:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08177","created_at":"2026-05-17T23:52:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZCGBBNSWEPFA","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZCGBBNSWEPFADOFV","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZCGBBNSW","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZCGBBNSWEPFADOFVY4JPGA6WB4","target":"record","payload":{"canonical_record":{"source":{"id":"1902.08177","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-21T18:37:53Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ee8fa57c1d5fd109f9b4811e8a62fbb0ce826b8cc6b2322345b57d5388e0fd03","abstract_canon_sha256":"86441d7a663ae666c5f55c71d34af97573e7ab630a71964b787320992e5ce718"},"schema_version":"1.0"},"canonical_sha256":"c88c10b65623ca01b8b5c712f303d60f2e0c41ba6dae5ca3c1323094b540f078","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:50.710762Z","signature_b64":"s3BHAQtnD6XR9JRqZffltkksHX4uvcUv2I2EiD1GhqJ1cSyVmdELmi8wAx3G6ZNu08CIw+mWhzHNEspTDRG2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c88c10b65623ca01b8b5c712f303d60f2e0c41ba6dae5ca3c1323094b540f078","last_reissued_at":"2026-05-17T23:52:50.709996Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:50.709996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.08177","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":"2026-05-17T23:52:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Be+LsDn6y2tDIXqAPxBYYbKFkBJEhRlfYrzjsbPfLPBm6EPNJ52r7mpbrc4YTFMfBMzwBi1MSEtBr/Vdul6zBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T04:02:13.481297Z"},"content_sha256":"a5ad9d1526837fee467304705805857789b8319856892c736e110e90c2f58c8d","schema_version":"1.0","event_id":"sha256:a5ad9d1526837fee467304705805857789b8319856892c736e110e90c2f58c8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZCGBBNSWEPFADOFVY4JPGA6WB4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the growth rate of chromatic numbers of finite subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"Chris Lambie-Hanson","submitted_at":"2019-02-21T18:37:53Z","abstract_excerpt":"We prove that, for every function $f:\\mathbb{N} \\rightarrow \\mathbb{N}$, there is a graph $G$ with uncountable chromatic number such that, for every $k \\in \\mathbb{N}$ with $k \\geq 3$, every subgraph of $G$ with fewer than $f(k)$ vertices has chromatic number less than $k$. This answers a question of Erd\\H{o}s, Hajnal, and Szemeredi."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08177","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":"2026-05-17T23:52:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WBPZtNVlr3vb9IhSzba7vpJbWnCy5vsZ13a5sNBPy1C7mFlSmEs9wIkpnuf7umEACn1pGAp48nNrOoIa1Y+cAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T04:02:13.481900Z"},"content_sha256":"9cc02494538e9e1a4124bae3324d1f15e8d965571bde556b08e9fba6a7efcbb0","schema_version":"1.0","event_id":"sha256:9cc02494538e9e1a4124bae3324d1f15e8d965571bde556b08e9fba6a7efcbb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZCGBBNSWEPFADOFVY4JPGA6WB4/bundle.json","state_url":"https://pith.science/pith/ZCGBBNSWEPFADOFVY4JPGA6WB4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZCGBBNSWEPFADOFVY4JPGA6WB4/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":"2026-06-30T04:02:13Z","links":{"resolver":"https://pith.science/pith/ZCGBBNSWEPFADOFVY4JPGA6WB4","bundle":"https://pith.science/pith/ZCGBBNSWEPFADOFVY4JPGA6WB4/bundle.json","state":"https://pith.science/pith/ZCGBBNSWEPFADOFVY4JPGA6WB4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZCGBBNSWEPFADOFVY4JPGA6WB4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZCGBBNSWEPFADOFVY4JPGA6WB4","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":"86441d7a663ae666c5f55c71d34af97573e7ab630a71964b787320992e5ce718","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-21T18:37:53Z","title_canon_sha256":"ee8fa57c1d5fd109f9b4811e8a62fbb0ce826b8cc6b2322345b57d5388e0fd03"},"schema_version":"1.0","source":{"id":"1902.08177","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08177","created_at":"2026-05-17T23:52:50Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08177v2","created_at":"2026-05-17T23:52:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08177","created_at":"2026-05-17T23:52:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZCGBBNSWEPFA","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZCGBBNSWEPFADOFV","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZCGBBNSW","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:9cc02494538e9e1a4124bae3324d1f15e8d965571bde556b08e9fba6a7efcbb0","target":"graph","created_at":"2026-05-17T23:52:50Z","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 prove that, for every function $f:\\mathbb{N} \\rightarrow \\mathbb{N}$, there is a graph $G$ with uncountable chromatic number such that, for every $k \\in \\mathbb{N}$ with $k \\geq 3$, every subgraph of $G$ with fewer than $f(k)$ vertices has chromatic number less than $k$. This answers a question of Erd\\H{o}s, Hajnal, and Szemeredi.","authors_text":"Chris Lambie-Hanson","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-21T18:37:53Z","title":"On the growth rate of chromatic numbers of finite subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08177","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:a5ad9d1526837fee467304705805857789b8319856892c736e110e90c2f58c8d","target":"record","created_at":"2026-05-17T23:52:50Z","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":"86441d7a663ae666c5f55c71d34af97573e7ab630a71964b787320992e5ce718","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-21T18:37:53Z","title_canon_sha256":"ee8fa57c1d5fd109f9b4811e8a62fbb0ce826b8cc6b2322345b57d5388e0fd03"},"schema_version":"1.0","source":{"id":"1902.08177","kind":"arxiv","version":2}},"canonical_sha256":"c88c10b65623ca01b8b5c712f303d60f2e0c41ba6dae5ca3c1323094b540f078","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c88c10b65623ca01b8b5c712f303d60f2e0c41ba6dae5ca3c1323094b540f078","first_computed_at":"2026-05-17T23:52:50.709996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:50.709996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s3BHAQtnD6XR9JRqZffltkksHX4uvcUv2I2EiD1GhqJ1cSyVmdELmi8wAx3G6ZNu08CIw+mWhzHNEspTDRG2Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:50.710762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.08177","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5ad9d1526837fee467304705805857789b8319856892c736e110e90c2f58c8d","sha256:9cc02494538e9e1a4124bae3324d1f15e8d965571bde556b08e9fba6a7efcbb0"],"state_sha256":"e24f4514a9ec21ccd63b098ac9857b84284e25163ce7c8a70c3a0ed9e6c94908"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LyV8xDLrha4jhen8HSDtm6I5R9/ySSm/diK7DKlGBBL1B3K/OVoe/R9bf+ZmxPlKjcvlPcg9HT3CFXJ9MgoODQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T04:02:13.485785Z","bundle_sha256":"5ccbb6f18a21670676e88e7f0e3939c840042b03721b640645236cad9a5ce2ed"}}