{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:CF7VZNVJNXYOB3CBHPWHEOTUY3","short_pith_number":"pith:CF7VZNVJ","canonical_record":{"source":{"id":"2212.02455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-12-05T17:55:38Z","cross_cats_sorted":[],"title_canon_sha256":"bee6561dc8e41636ca8758bca14ccd1b830bbc3650da1777c82dbd0d014a6033","abstract_canon_sha256":"1edf262776f894c150b72b82cb525de3daa241e5f623eea9c346dda55e42c046"},"schema_version":"1.0"},"canonical_sha256":"117f5cb6a96df0e0ec413bec723a74c6c6e01c3a9735b7bbf9490c00c0b6ef0d","source":{"kind":"arxiv","id":"2212.02455","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.02455","created_at":"2026-07-05T05:22:24Z"},{"alias_kind":"arxiv_version","alias_value":"2212.02455v1","created_at":"2026-07-05T05:22:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.02455","created_at":"2026-07-05T05:22:24Z"},{"alias_kind":"pith_short_12","alias_value":"CF7VZNVJNXYO","created_at":"2026-07-05T05:22:24Z"},{"alias_kind":"pith_short_16","alias_value":"CF7VZNVJNXYOB3CB","created_at":"2026-07-05T05:22:24Z"},{"alias_kind":"pith_short_8","alias_value":"CF7VZNVJ","created_at":"2026-07-05T05:22:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:CF7VZNVJNXYOB3CBHPWHEOTUY3","target":"record","payload":{"canonical_record":{"source":{"id":"2212.02455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-12-05T17:55:38Z","cross_cats_sorted":[],"title_canon_sha256":"bee6561dc8e41636ca8758bca14ccd1b830bbc3650da1777c82dbd0d014a6033","abstract_canon_sha256":"1edf262776f894c150b72b82cb525de3daa241e5f623eea9c346dda55e42c046"},"schema_version":"1.0"},"canonical_sha256":"117f5cb6a96df0e0ec413bec723a74c6c6e01c3a9735b7bbf9490c00c0b6ef0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:22:24.608516Z","signature_b64":"NgfQHWIAsT+IdCTS89U/cJnbqYOIWMb2kiGDMnXnn5FQCTuRxPPXugquB8jINS54vz+xaSmoeecEp1xTkrT0Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"117f5cb6a96df0e0ec413bec723a74c6c6e01c3a9735b7bbf9490c00c0b6ef0d","last_reissued_at":"2026-07-05T05:22:24.608058Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:22:24.608058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.02455","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":"2026-07-05T05:22:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BILGrlZ13R1/zU5pKIff6SQFuiPoyybC+1KKDuizMdd6v4uaCmtYLuitEbknfny8H4Ndqp3jq10iAtBcIpYMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T22:12:52.286336Z"},"content_sha256":"4c9bdc4c18fdee27de8c81fa5164e8ab0bf4b3e18dab08c9f5274a856e6c6b28","schema_version":"1.0","event_id":"sha256:4c9bdc4c18fdee27de8c81fa5164e8ab0bf4b3e18dab08c9f5274a856e6c6b28"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:CF7VZNVJNXYOB3CBHPWHEOTUY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ramsey numbers for multiple copies of sparse graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aurelio Sulser, Milo\\v{s} Truji\\'c","submitted_at":"2022-12-05T17:55:38Z","abstract_excerpt":"For a graph $H$ and an integer $n$, we let $nH$ denote the disjoint union of\n  $n$ copies of $H$. In 1975, Burr, Erd\\H{o}s, and Spencer initiated the study\n  of Ramsey numbers for $nH$, one of few instances for which Ramsey numbers are\n  now known precisely. They showed that there is a constant $c = c(H)$ such that\n  $r(nH) = (2|H| - \\alpha(H))n + c$, provided $n$ is sufficiently large.\n  Subsequently, Burr gave an implicit way of computing $c$ and noted that this\n  long term behaviour occurs when $n$ is triply exponential in $|H|$. Very\n  recently, Buci\\'{c} and Sudakov revived the problem an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.02455","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/2212.02455/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":"2026-07-05T05:22:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B3xlPrhIK8jnst0GYvcPEQEL904SvFAOqTU7P2kcPPkPQn7/Tcz4+jGh5C92e6pa8zKzX+MO8oMMR7wj0LxtAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T22:12:52.286872Z"},"content_sha256":"b7b27d33506ec8c6dff183658cb218002ba982dbe8b3ecd7d534933df8a08155","schema_version":"1.0","event_id":"sha256:b7b27d33506ec8c6dff183658cb218002ba982dbe8b3ecd7d534933df8a08155"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CF7VZNVJNXYOB3CBHPWHEOTUY3/bundle.json","state_url":"https://pith.science/pith/CF7VZNVJNXYOB3CBHPWHEOTUY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CF7VZNVJNXYOB3CBHPWHEOTUY3/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":"2026-08-15T22:12:52Z","links":{"resolver":"https://pith.science/pith/CF7VZNVJNXYOB3CBHPWHEOTUY3","bundle":"https://pith.science/pith/CF7VZNVJNXYOB3CBHPWHEOTUY3/bundle.json","state":"https://pith.science/pith/CF7VZNVJNXYOB3CBHPWHEOTUY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CF7VZNVJNXYOB3CBHPWHEOTUY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:CF7VZNVJNXYOB3CBHPWHEOTUY3","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":"1edf262776f894c150b72b82cb525de3daa241e5f623eea9c346dda55e42c046","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-12-05T17:55:38Z","title_canon_sha256":"bee6561dc8e41636ca8758bca14ccd1b830bbc3650da1777c82dbd0d014a6033"},"schema_version":"1.0","source":{"id":"2212.02455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.02455","created_at":"2026-07-05T05:22:24Z"},{"alias_kind":"arxiv_version","alias_value":"2212.02455v1","created_at":"2026-07-05T05:22:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.02455","created_at":"2026-07-05T05:22:24Z"},{"alias_kind":"pith_short_12","alias_value":"CF7VZNVJNXYO","created_at":"2026-07-05T05:22:24Z"},{"alias_kind":"pith_short_16","alias_value":"CF7VZNVJNXYOB3CB","created_at":"2026-07-05T05:22:24Z"},{"alias_kind":"pith_short_8","alias_value":"CF7VZNVJ","created_at":"2026-07-05T05:22:24Z"}],"graph_snapshots":[{"event_id":"sha256:b7b27d33506ec8c6dff183658cb218002ba982dbe8b3ecd7d534933df8a08155","target":"graph","created_at":"2026-07-05T05:22:24Z","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/2212.02455/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a graph $H$ and an integer $n$, we let $nH$ denote the disjoint union of\n  $n$ copies of $H$. In 1975, Burr, Erd\\H{o}s, and Spencer initiated the study\n  of Ramsey numbers for $nH$, one of few instances for which Ramsey numbers are\n  now known precisely. They showed that there is a constant $c = c(H)$ such that\n  $r(nH) = (2|H| - \\alpha(H))n + c$, provided $n$ is sufficiently large.\n  Subsequently, Burr gave an implicit way of computing $c$ and noted that this\n  long term behaviour occurs when $n$ is triply exponential in $|H|$. Very\n  recently, Buci\\'{c} and Sudakov revived the problem an","authors_text":"Aurelio Sulser, Milo\\v{s} Truji\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-12-05T17:55:38Z","title":"Ramsey numbers for multiple copies of sparse graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.02455","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":"sha256:4c9bdc4c18fdee27de8c81fa5164e8ab0bf4b3e18dab08c9f5274a856e6c6b28","target":"record","created_at":"2026-07-05T05:22:24Z","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":"1edf262776f894c150b72b82cb525de3daa241e5f623eea9c346dda55e42c046","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-12-05T17:55:38Z","title_canon_sha256":"bee6561dc8e41636ca8758bca14ccd1b830bbc3650da1777c82dbd0d014a6033"},"schema_version":"1.0","source":{"id":"2212.02455","kind":"arxiv","version":1}},"canonical_sha256":"117f5cb6a96df0e0ec413bec723a74c6c6e01c3a9735b7bbf9490c00c0b6ef0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"117f5cb6a96df0e0ec413bec723a74c6c6e01c3a9735b7bbf9490c00c0b6ef0d","first_computed_at":"2026-07-05T05:22:24.608058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:22:24.608058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NgfQHWIAsT+IdCTS89U/cJnbqYOIWMb2kiGDMnXnn5FQCTuRxPPXugquB8jINS54vz+xaSmoeecEp1xTkrT0Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:22:24.608516Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.02455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c9bdc4c18fdee27de8c81fa5164e8ab0bf4b3e18dab08c9f5274a856e6c6b28","sha256:b7b27d33506ec8c6dff183658cb218002ba982dbe8b3ecd7d534933df8a08155"],"state_sha256":"4ef0f92ba4dfcec1c0f4d7c7805ad562f8cc08ae80e0ce309a9d1f2cdb70fa8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wm8C724YMJSrbJ7YajA4Uuobxdxkw9p6u3AW3gtZb+/k8cEcSVlBrUWTt4b91EAqDg0q264QxA0g2VB6wGlaCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T22:12:52.291952Z","bundle_sha256":"a3e6523173600a44c2f13747e248816fee40bfab47b07173ec39fd13490be93a"}}