{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:N3I5OFIKQVGQNBHWXT6HMVGGRB","short_pith_number":"pith:N3I5OFIK","canonical_record":{"source":{"id":"1512.07874","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-24T18:05:12Z","cross_cats_sorted":[],"title_canon_sha256":"0971cbef665a2193401de69d35eb14aff0c992eef0a7691a07bfe7da2df7dfa8","abstract_canon_sha256":"4916f2a62f902563b81732073febc22d8eb4195ab15515e6499d985006b55393"},"schema_version":"1.0"},"canonical_sha256":"6ed1d7150a854d0684f6bcfc7654c68860ace8a8c98ebf7a03a7b7a90c9dfc31","source":{"kind":"arxiv","id":"1512.07874","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07874","created_at":"2026-05-18T01:11:54Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07874v3","created_at":"2026-05-18T01:11:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07874","created_at":"2026-05-18T01:11:54Z"},{"alias_kind":"pith_short_12","alias_value":"N3I5OFIKQVGQ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N3I5OFIKQVGQNBHW","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N3I5OFIK","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:N3I5OFIKQVGQNBHWXT6HMVGGRB","target":"record","payload":{"canonical_record":{"source":{"id":"1512.07874","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-24T18:05:12Z","cross_cats_sorted":[],"title_canon_sha256":"0971cbef665a2193401de69d35eb14aff0c992eef0a7691a07bfe7da2df7dfa8","abstract_canon_sha256":"4916f2a62f902563b81732073febc22d8eb4195ab15515e6499d985006b55393"},"schema_version":"1.0"},"canonical_sha256":"6ed1d7150a854d0684f6bcfc7654c68860ace8a8c98ebf7a03a7b7a90c9dfc31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:54.830200Z","signature_b64":"keLOhSw+/d4tBakkbBsbO9HbTbygoWJChMX7iuFniv5HB78oishr+a62j1hotmOhVyKQutvUYrRb7S/JGIJ4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ed1d7150a854d0684f6bcfc7654c68860ace8a8c98ebf7a03a7b7a90c9dfc31","last_reissued_at":"2026-05-18T01:11:54.829845Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:54.829845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.07874","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aQ4bJXTZERFB6toJH9RrHVe0Z1fSLa520qt3wIT0D1LQ08fmkMLvdVo4fc0ZeRrTF4gT3cM52uavmRIslVafBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:35:28.120009Z"},"content_sha256":"336480a11fb72cda9ba68d9cb1023131c5f5d2934b1ee0538a6f7a3edbc6dfbd","schema_version":"1.0","event_id":"sha256:336480a11fb72cda9ba68d9cb1023131c5f5d2934b1ee0538a6f7a3edbc6dfbd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:N3I5OFIKQVGQNBHWXT6HMVGGRB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ramsey goodness of paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexey Pokrovskiy, Benny Sudakov","submitted_at":"2015-12-24T18:05:12Z","abstract_excerpt":"Given a pair of graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the smallest $N$ such that every red-blue coloring of the edges of the complete graph $K_N$ contains a red copy of $G$ or a blue copy of $H$. If graph $G$ is connected, it is well known and easy to show that $R(G,H) \\geq (|G|-1)(\\chi(H)-1)+\\sigma(H)$, where $\\chi(H)$ is the chromatic number of $H$ and $\\sigma$ the size of the smallest color class in a $\\chi(H)$-coloring of $H$. A graph $G$ is called $H$-good if $R(G,H)= (|G|-1)(\\chi(H)-1)+\\sigma(H)$. The notion of Ramsey goodness was introduced by Burr and Erd\\H{o}s in 1983 and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07874","kind":"arxiv","version":3},"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":"2026-05-18T01:11:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uZGnaPCCwNE+Sz6mx0S0anrDDp7InvGsKgsDQpsfK04gDJTWJCyhwPxjvd5YbkrHzxNFdT9aYE17cO5tLm7yCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:35:28.120457Z"},"content_sha256":"67102feb3af86a6d6881c2d433a1fd25fdd547e56c3faf2d141517c506c7e032","schema_version":"1.0","event_id":"sha256:67102feb3af86a6d6881c2d433a1fd25fdd547e56c3faf2d141517c506c7e032"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N3I5OFIKQVGQNBHWXT6HMVGGRB/bundle.json","state_url":"https://pith.science/pith/N3I5OFIKQVGQNBHWXT6HMVGGRB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N3I5OFIKQVGQNBHWXT6HMVGGRB/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":"2026-05-31T07:35:28Z","links":{"resolver":"https://pith.science/pith/N3I5OFIKQVGQNBHWXT6HMVGGRB","bundle":"https://pith.science/pith/N3I5OFIKQVGQNBHWXT6HMVGGRB/bundle.json","state":"https://pith.science/pith/N3I5OFIKQVGQNBHWXT6HMVGGRB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N3I5OFIKQVGQNBHWXT6HMVGGRB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N3I5OFIKQVGQNBHWXT6HMVGGRB","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":"4916f2a62f902563b81732073febc22d8eb4195ab15515e6499d985006b55393","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-24T18:05:12Z","title_canon_sha256":"0971cbef665a2193401de69d35eb14aff0c992eef0a7691a07bfe7da2df7dfa8"},"schema_version":"1.0","source":{"id":"1512.07874","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07874","created_at":"2026-05-18T01:11:54Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07874v3","created_at":"2026-05-18T01:11:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07874","created_at":"2026-05-18T01:11:54Z"},{"alias_kind":"pith_short_12","alias_value":"N3I5OFIKQVGQ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N3I5OFIKQVGQNBHW","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N3I5OFIK","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:67102feb3af86a6d6881c2d433a1fd25fdd547e56c3faf2d141517c506c7e032","target":"graph","created_at":"2026-05-18T01:11:54Z","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":"Given a pair of graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the smallest $N$ such that every red-blue coloring of the edges of the complete graph $K_N$ contains a red copy of $G$ or a blue copy of $H$. If graph $G$ is connected, it is well known and easy to show that $R(G,H) \\geq (|G|-1)(\\chi(H)-1)+\\sigma(H)$, where $\\chi(H)$ is the chromatic number of $H$ and $\\sigma$ the size of the smallest color class in a $\\chi(H)$-coloring of $H$. A graph $G$ is called $H$-good if $R(G,H)= (|G|-1)(\\chi(H)-1)+\\sigma(H)$. The notion of Ramsey goodness was introduced by Burr and Erd\\H{o}s in 1983 and ","authors_text":"Alexey Pokrovskiy, Benny Sudakov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-24T18:05:12Z","title":"Ramsey goodness of paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07874","kind":"arxiv","version":3},"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":"sha256:336480a11fb72cda9ba68d9cb1023131c5f5d2934b1ee0538a6f7a3edbc6dfbd","target":"record","created_at":"2026-05-18T01:11:54Z","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":"4916f2a62f902563b81732073febc22d8eb4195ab15515e6499d985006b55393","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-24T18:05:12Z","title_canon_sha256":"0971cbef665a2193401de69d35eb14aff0c992eef0a7691a07bfe7da2df7dfa8"},"schema_version":"1.0","source":{"id":"1512.07874","kind":"arxiv","version":3}},"canonical_sha256":"6ed1d7150a854d0684f6bcfc7654c68860ace8a8c98ebf7a03a7b7a90c9dfc31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ed1d7150a854d0684f6bcfc7654c68860ace8a8c98ebf7a03a7b7a90c9dfc31","first_computed_at":"2026-05-18T01:11:54.829845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:54.829845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"keLOhSw+/d4tBakkbBsbO9HbTbygoWJChMX7iuFniv5HB78oishr+a62j1hotmOhVyKQutvUYrRb7S/JGIJ4DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:54.830200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07874","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:336480a11fb72cda9ba68d9cb1023131c5f5d2934b1ee0538a6f7a3edbc6dfbd","sha256:67102feb3af86a6d6881c2d433a1fd25fdd547e56c3faf2d141517c506c7e032"],"state_sha256":"b72a3552338aa6cecb218bf663c5d14abec8776f5b727e27c534a45ccc9d3631"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EDTIANwtjNRAj6gRCBua0XpZK9L7sKm1KpMAbCa98AQ0xan1lUb1nK28/ccmzYK6rRD2elupQ9oaKv607LLaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:35:28.123679Z","bundle_sha256":"ba042e6aae2383c75791e858056a7ee06801c486a02e357cb37b210581c3cb8c"}}