{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2BKQ7H6NG363DFIYMRJWJV5VDF","short_pith_number":"pith:2BKQ7H6N","canonical_record":{"source":{"id":"2410.08644","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-11T09:11:05Z","cross_cats_sorted":[],"title_canon_sha256":"02c08c04e849d5f50ad5330f3339731a5554955c9698b582122047a116fdde23","abstract_canon_sha256":"8fe4302a9962165b024fef7f05c572ab87e520a82a87c0a813e5dfae4c3d4ed9"},"schema_version":"1.0"},"canonical_sha256":"d0550f9fcd36fdb19518645364d7b5194c5863bf84f5cace5cb93cd67ca47d37","source":{"kind":"arxiv","id":"2410.08644","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.08644","created_at":"2026-07-05T09:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"2410.08644v1","created_at":"2026-07-05T09:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.08644","created_at":"2026-07-05T09:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"2BKQ7H6NG363","created_at":"2026-07-05T09:19:15Z"},{"alias_kind":"pith_short_16","alias_value":"2BKQ7H6NG363DFIY","created_at":"2026-07-05T09:19:15Z"},{"alias_kind":"pith_short_8","alias_value":"2BKQ7H6N","created_at":"2026-07-05T09:19:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2BKQ7H6NG363DFIYMRJWJV5VDF","target":"record","payload":{"canonical_record":{"source":{"id":"2410.08644","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-11T09:11:05Z","cross_cats_sorted":[],"title_canon_sha256":"02c08c04e849d5f50ad5330f3339731a5554955c9698b582122047a116fdde23","abstract_canon_sha256":"8fe4302a9962165b024fef7f05c572ab87e520a82a87c0a813e5dfae4c3d4ed9"},"schema_version":"1.0"},"canonical_sha256":"d0550f9fcd36fdb19518645364d7b5194c5863bf84f5cace5cb93cd67ca47d37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:19:15.580772Z","signature_b64":"IMSr5E6NhtdxgUeH/q/3ymzeYL3oN9KRW231XqVml+mYR6wcG0qTDLhcXRdIZaZOphB75XJW/cw95Lb9GPzwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0550f9fcd36fdb19518645364d7b5194c5863bf84f5cace5cb93cd67ca47d37","last_reissued_at":"2026-07-05T09:19:15.580402Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:19:15.580402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.08644","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":"2026-07-05T09:19:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wErJXUXfPV23+m8lJUSyDU0wOSXAy8wT0RWtZauM3IirES5SLDSqW6lJOIOOoEtT5VggIrOOqvjgHxbQJoT8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:45:07.277666Z"},"content_sha256":"8da397b584005295fbe7a510852a7382f285bdd0803de1bbed8c150f8fc1d894","schema_version":"1.0","event_id":"sha256:8da397b584005295fbe7a510852a7382f285bdd0803de1bbed8c150f8fc1d894"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2BKQ7H6NG363DFIYMRJWJV5VDF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Canonical Ramsey numbers of sparse graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aleksa Milojevi\\'c, Benny Sudakov, Lior Gishboliner, Yuval Wigderson","submitted_at":"2024-10-11T09:11:05Z","abstract_excerpt":"The canonical Ramsey theorem of Erd\\H{o}s and Rado implies that for any graph $H$, any edge-coloring (with an arbitrary number of colors) of a sufficiently large complete graph $K_N$ contains a monochromatic, lexicographic, or rainbow copy of $H$. The least such $N$ is called the Erd\\H{o}s-Rado number of $H$, denoted by $ER(H)$. Erd\\H{o}s-Rado numbers of cliques have received considerable attention, and in this paper we extend this line of research by studying Erd\\H{o}s-Rado numbers of sparse graphs. For example, we prove that if $H$ has bounded degree, then $ER(H)$ is polynomial in $|V(H)|$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.08644","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/2410.08644/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":"2026-07-05T09:19:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oYoEomi+fO+S+HCcun8rP/vy8M6G3izrxDr8jXuvHDfcIETjV1oE906eQChRrmuuk8KI7olEdTDLcGZhNN1QAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:45:07.278221Z"},"content_sha256":"29aad9bffc056a7c2f2e700e92155e1ff30c9cac04cdb6cce403a59ce915baa8","schema_version":"1.0","event_id":"sha256:29aad9bffc056a7c2f2e700e92155e1ff30c9cac04cdb6cce403a59ce915baa8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2BKQ7H6NG363DFIYMRJWJV5VDF/bundle.json","state_url":"https://pith.science/pith/2BKQ7H6NG363DFIYMRJWJV5VDF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2BKQ7H6NG363DFIYMRJWJV5VDF/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":"2026-08-12T23:45:07Z","links":{"resolver":"https://pith.science/pith/2BKQ7H6NG363DFIYMRJWJV5VDF","bundle":"https://pith.science/pith/2BKQ7H6NG363DFIYMRJWJV5VDF/bundle.json","state":"https://pith.science/pith/2BKQ7H6NG363DFIYMRJWJV5VDF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2BKQ7H6NG363DFIYMRJWJV5VDF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2BKQ7H6NG363DFIYMRJWJV5VDF","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":"8fe4302a9962165b024fef7f05c572ab87e520a82a87c0a813e5dfae4c3d4ed9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-11T09:11:05Z","title_canon_sha256":"02c08c04e849d5f50ad5330f3339731a5554955c9698b582122047a116fdde23"},"schema_version":"1.0","source":{"id":"2410.08644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.08644","created_at":"2026-07-05T09:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"2410.08644v1","created_at":"2026-07-05T09:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.08644","created_at":"2026-07-05T09:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"2BKQ7H6NG363","created_at":"2026-07-05T09:19:15Z"},{"alias_kind":"pith_short_16","alias_value":"2BKQ7H6NG363DFIY","created_at":"2026-07-05T09:19:15Z"},{"alias_kind":"pith_short_8","alias_value":"2BKQ7H6N","created_at":"2026-07-05T09:19:15Z"}],"graph_snapshots":[{"event_id":"sha256:29aad9bffc056a7c2f2e700e92155e1ff30c9cac04cdb6cce403a59ce915baa8","target":"graph","created_at":"2026-07-05T09:19:15Z","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/2410.08644/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The canonical Ramsey theorem of Erd\\H{o}s and Rado implies that for any graph $H$, any edge-coloring (with an arbitrary number of colors) of a sufficiently large complete graph $K_N$ contains a monochromatic, lexicographic, or rainbow copy of $H$. The least such $N$ is called the Erd\\H{o}s-Rado number of $H$, denoted by $ER(H)$. Erd\\H{o}s-Rado numbers of cliques have received considerable attention, and in this paper we extend this line of research by studying Erd\\H{o}s-Rado numbers of sparse graphs. For example, we prove that if $H$ has bounded degree, then $ER(H)$ is polynomial in $|V(H)|$ i","authors_text":"Aleksa Milojevi\\'c, Benny Sudakov, Lior Gishboliner, Yuval Wigderson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-11T09:11:05Z","title":"Canonical Ramsey numbers of sparse graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.08644","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":"sha256:8da397b584005295fbe7a510852a7382f285bdd0803de1bbed8c150f8fc1d894","target":"record","created_at":"2026-07-05T09:19:15Z","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":"8fe4302a9962165b024fef7f05c572ab87e520a82a87c0a813e5dfae4c3d4ed9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-10-11T09:11:05Z","title_canon_sha256":"02c08c04e849d5f50ad5330f3339731a5554955c9698b582122047a116fdde23"},"schema_version":"1.0","source":{"id":"2410.08644","kind":"arxiv","version":1}},"canonical_sha256":"d0550f9fcd36fdb19518645364d7b5194c5863bf84f5cace5cb93cd67ca47d37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0550f9fcd36fdb19518645364d7b5194c5863bf84f5cace5cb93cd67ca47d37","first_computed_at":"2026-07-05T09:19:15.580402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:19:15.580402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IMSr5E6NhtdxgUeH/q/3ymzeYL3oN9KRW231XqVml+mYR6wcG0qTDLhcXRdIZaZOphB75XJW/cw95Lb9GPzwDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:19:15.580772Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.08644","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8da397b584005295fbe7a510852a7382f285bdd0803de1bbed8c150f8fc1d894","sha256:29aad9bffc056a7c2f2e700e92155e1ff30c9cac04cdb6cce403a59ce915baa8"],"state_sha256":"5e4f837d764aa102906f9036669aa8b1429a5b90be55bd485c71e1b5603ffbfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E+S7TqcfSVIu5Sa4UjdGMtt70NOYAxPUKphWs8P1NqbNQ9XFB8s7FdXkkRl4g7pZVEAwVFmAUYvYYF46cNX+Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T23:45:07.283604Z","bundle_sha256":"54c829a227aeba399d96d208dc564a64f9cf6ca248d0bf4b19afd04f8bf68264"}}