{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NMH2KNI5HZN4HV6HZCJTDI4J2R","short_pith_number":"pith:NMH2KNI5","canonical_record":{"source":{"id":"1806.00541","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-06-01T20:59:09Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"aa00ceba7b66f94d8915cf57b58eee5fa10f973ae73a0b3bb73bacd24ec5885b","abstract_canon_sha256":"ed3892595ffab82b28d78fd25e292e291b8da28661677d2fd622030ad2ccabcc"},"schema_version":"1.0"},"canonical_sha256":"6b0fa5351d3e5bc3d7c7c89331a389d468d9d20dd4411d1d73aed3cfc2ecd9bd","source":{"kind":"arxiv","id":"1806.00541","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00541","created_at":"2026-05-18T00:02:53Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00541v2","created_at":"2026-05-18T00:02:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00541","created_at":"2026-05-18T00:02:53Z"},{"alias_kind":"pith_short_12","alias_value":"NMH2KNI5HZN4","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NMH2KNI5HZN4HV6H","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NMH2KNI5","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NMH2KNI5HZN4HV6HZCJTDI4J2R","target":"record","payload":{"canonical_record":{"source":{"id":"1806.00541","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-06-01T20:59:09Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"aa00ceba7b66f94d8915cf57b58eee5fa10f973ae73a0b3bb73bacd24ec5885b","abstract_canon_sha256":"ed3892595ffab82b28d78fd25e292e291b8da28661677d2fd622030ad2ccabcc"},"schema_version":"1.0"},"canonical_sha256":"6b0fa5351d3e5bc3d7c7c89331a389d468d9d20dd4411d1d73aed3cfc2ecd9bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:53.203661Z","signature_b64":"RSoC4ggGZQQLg7O+JQLjTE+0v1GIu7ZPTImNONoymxRbFLdBNdl8/vKn4P03h75GuoSk7opYJq4MlmneHxx7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b0fa5351d3e5bc3d7c7c89331a389d468d9d20dd4411d1d73aed3cfc2ecd9bd","last_reissued_at":"2026-05-18T00:02:53.203096Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:53.203096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.00541","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":"2026-05-18T00:02:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BynD/I3Hfjh1IDLRatNAUmsg94KRBZa9Ekgh4HqPmFApZytv93Y8qSY5/PuitLhWxnYxRoOWdS8hMdVjA2iQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:24:36.656683Z"},"content_sha256":"be72a1eb3947f7201bf2bd727112bb3f5115c93e1a75275ec7d876a0fa6bb164","schema_version":"1.0","event_id":"sha256:be72a1eb3947f7201bf2bd727112bb3f5115c93e1a75275ec7d876a0fa6bb164"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NMH2KNI5HZN4HV6HZCJTDI4J2R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extension Complexity of the Correlation Polytope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DM","authors_text":"Johanna Seif, Marco Macchia, Pierre Aboulker, Samuel Fiorini, Tony Huynh","submitted_at":"2018-06-01T20:59:09Z","abstract_excerpt":"We prove that for every $n$-vertex graph $G$, the extension complexity of the correlation polytope of $G$ is $2^{O(\\mathrm{tw}(G) + \\log n)}$, where $\\mathrm{tw}(G)$ is the treewidth of $G$. Our main result is that this bound is tight for graphs contained in minor-closed classes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00541","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":"2026-05-18T00:02:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+0Q7EUabeAMT0O8tw5XIEguduLISSFd6TnqQ46ZZEtZ2zQF8sOY0SbaGj3xrYKbcU4buemi40tT+G3lDkaSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:24:36.657030Z"},"content_sha256":"dd3cc69d554e65736efba397373805077e0230c11fc6618172b609d9fa5506ab","schema_version":"1.0","event_id":"sha256:dd3cc69d554e65736efba397373805077e0230c11fc6618172b609d9fa5506ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NMH2KNI5HZN4HV6HZCJTDI4J2R/bundle.json","state_url":"https://pith.science/pith/NMH2KNI5HZN4HV6HZCJTDI4J2R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NMH2KNI5HZN4HV6HZCJTDI4J2R/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":"2026-05-28T16:24:36Z","links":{"resolver":"https://pith.science/pith/NMH2KNI5HZN4HV6HZCJTDI4J2R","bundle":"https://pith.science/pith/NMH2KNI5HZN4HV6HZCJTDI4J2R/bundle.json","state":"https://pith.science/pith/NMH2KNI5HZN4HV6HZCJTDI4J2R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NMH2KNI5HZN4HV6HZCJTDI4J2R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NMH2KNI5HZN4HV6HZCJTDI4J2R","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":"ed3892595ffab82b28d78fd25e292e291b8da28661677d2fd622030ad2ccabcc","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-06-01T20:59:09Z","title_canon_sha256":"aa00ceba7b66f94d8915cf57b58eee5fa10f973ae73a0b3bb73bacd24ec5885b"},"schema_version":"1.0","source":{"id":"1806.00541","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00541","created_at":"2026-05-18T00:02:53Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00541v2","created_at":"2026-05-18T00:02:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00541","created_at":"2026-05-18T00:02:53Z"},{"alias_kind":"pith_short_12","alias_value":"NMH2KNI5HZN4","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NMH2KNI5HZN4HV6H","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NMH2KNI5","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:dd3cc69d554e65736efba397373805077e0230c11fc6618172b609d9fa5506ab","target":"graph","created_at":"2026-05-18T00:02:53Z","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 $n$-vertex graph $G$, the extension complexity of the correlation polytope of $G$ is $2^{O(\\mathrm{tw}(G) + \\log n)}$, where $\\mathrm{tw}(G)$ is the treewidth of $G$. Our main result is that this bound is tight for graphs contained in minor-closed classes.","authors_text":"Johanna Seif, Marco Macchia, Pierre Aboulker, Samuel Fiorini, Tony Huynh","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-06-01T20:59:09Z","title":"Extension Complexity of the Correlation Polytope"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00541","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:be72a1eb3947f7201bf2bd727112bb3f5115c93e1a75275ec7d876a0fa6bb164","target":"record","created_at":"2026-05-18T00:02:53Z","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":"ed3892595ffab82b28d78fd25e292e291b8da28661677d2fd622030ad2ccabcc","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-06-01T20:59:09Z","title_canon_sha256":"aa00ceba7b66f94d8915cf57b58eee5fa10f973ae73a0b3bb73bacd24ec5885b"},"schema_version":"1.0","source":{"id":"1806.00541","kind":"arxiv","version":2}},"canonical_sha256":"6b0fa5351d3e5bc3d7c7c89331a389d468d9d20dd4411d1d73aed3cfc2ecd9bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b0fa5351d3e5bc3d7c7c89331a389d468d9d20dd4411d1d73aed3cfc2ecd9bd","first_computed_at":"2026-05-18T00:02:53.203096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:53.203096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RSoC4ggGZQQLg7O+JQLjTE+0v1GIu7ZPTImNONoymxRbFLdBNdl8/vKn4P03h75GuoSk7opYJq4MlmneHxx7Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:53.203661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.00541","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be72a1eb3947f7201bf2bd727112bb3f5115c93e1a75275ec7d876a0fa6bb164","sha256:dd3cc69d554e65736efba397373805077e0230c11fc6618172b609d9fa5506ab"],"state_sha256":"bf874916d081aca27f687b5fc88f2acf273355a2614e4ae9072f2b1071be289f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pGEY1QA8tIFaKMMhSGv1J+n4shvmjyR9M19mSccZUflfV9rrrtLTGMuNdBs9/Zlx6n82HxNQ+azttKcvjrnuAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:24:36.658975Z","bundle_sha256":"58295ff6f7e5eef702721bfcdee9ce033251e7260a4a71f211e91e07d0bb4b9b"}}