{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2EKRYVVHLMZ5SNI2MJKGR33SLM","short_pith_number":"pith:2EKRYVVH","canonical_record":{"source":{"id":"1403.6710","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-03-26T15:25:32Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8a63a585484a5608ba717cfcfb56efa2da6e74955a50835ef91d5a77c43aa189","abstract_canon_sha256":"8a1c1c21e0ed4fad6422fc7213c07ec4db6ec742c8834c4f8bfd96cf668291b9"},"schema_version":"1.0"},"canonical_sha256":"d1151c56a75b33d9351a625468ef725b2896dcb1be79faae88e2632da60091e9","source":{"kind":"arxiv","id":"1403.6710","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6710","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6710v6","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6710","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"pith_short_12","alias_value":"2EKRYVVHLMZ5","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2EKRYVVHLMZ5SNI2","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2EKRYVVH","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2EKRYVVHLMZ5SNI2MJKGR33SLM","target":"record","payload":{"canonical_record":{"source":{"id":"1403.6710","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-03-26T15:25:32Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8a63a585484a5608ba717cfcfb56efa2da6e74955a50835ef91d5a77c43aa189","abstract_canon_sha256":"8a1c1c21e0ed4fad6422fc7213c07ec4db6ec742c8834c4f8bfd96cf668291b9"},"schema_version":"1.0"},"canonical_sha256":"d1151c56a75b33d9351a625468ef725b2896dcb1be79faae88e2632da60091e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:29.529541Z","signature_b64":"R7A8czrFEcPtDa4gXTRpewW1/tsyPUYKN7i0G52Aw28mSLzKBHrBF2cQNWEkaQ5JdKEcoL+aXMo7A815ZO4DDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1151c56a75b33d9351a625468ef725b2896dcb1be79faae88e2632da60091e9","last_reissued_at":"2026-05-18T01:01:29.529078Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:29.529078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.6710","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:01:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/zU4cMNk8rJJH1ipouIeBJmMo8i8FAfl6750t3eF3nAiLGx4XiQikhBNmmyKswYWLqe6hwANr80N3C0qIKGXDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T04:24:57.279959Z"},"content_sha256":"f8528ca2f867546c4a71faadfabcba70dfaa62aa313fa85691e05437d56756b0","schema_version":"1.0","event_id":"sha256:f8528ca2f867546c4a71faadfabcba70dfaa62aa313fa85691e05437d56756b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2EKRYVVHLMZ5SNI2MJKGR33SLM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The matching polytope does not admit fully-polynomial size relaxation schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"G\\'abor Braun, Sebastian Pokutta","submitted_at":"2014-03-26T15:25:32Z","abstract_excerpt":"The groundbreaking work of Rothvo{\\ss} [arxiv:1311.2369] established that every linear program expressing the matching polytope has an exponential number of inequalities (formally, the matching polytope has exponential extension complexity). We generalize this result by deriving strong bounds on the polyhedral inapproximability of the matching polytope: for fixed $0 < \\varepsilon < 1$, every polyhedral $(1 + \\varepsilon / n)$-approximation requires an exponential number of inequalities, where $n$ is the number of vertices. This is sharp given the well-known $\\rho$-approximation of size $O(\\bin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6710","kind":"arxiv","version":6},"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":"2026-05-18T01:01:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tN/FB+7RhW9b4pUIR/OdQDD+Vv0zM0KhXI9smffJhdPCurH3QehAaL7agtOj99zgLdM3XNv17lqLQDxMZiteDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T04:24:57.280671Z"},"content_sha256":"84c068729f5ccc2a750dbbe9ad23e9bdac08b16fe304fa18e6f3e5cbff7c3a5c","schema_version":"1.0","event_id":"sha256:84c068729f5ccc2a750dbbe9ad23e9bdac08b16fe304fa18e6f3e5cbff7c3a5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2EKRYVVHLMZ5SNI2MJKGR33SLM/bundle.json","state_url":"https://pith.science/pith/2EKRYVVHLMZ5SNI2MJKGR33SLM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2EKRYVVHLMZ5SNI2MJKGR33SLM/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":"2026-05-24T04:24:57Z","links":{"resolver":"https://pith.science/pith/2EKRYVVHLMZ5SNI2MJKGR33SLM","bundle":"https://pith.science/pith/2EKRYVVHLMZ5SNI2MJKGR33SLM/bundle.json","state":"https://pith.science/pith/2EKRYVVHLMZ5SNI2MJKGR33SLM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2EKRYVVHLMZ5SNI2MJKGR33SLM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2EKRYVVHLMZ5SNI2MJKGR33SLM","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":"8a1c1c21e0ed4fad6422fc7213c07ec4db6ec742c8834c4f8bfd96cf668291b9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-03-26T15:25:32Z","title_canon_sha256":"8a63a585484a5608ba717cfcfb56efa2da6e74955a50835ef91d5a77c43aa189"},"schema_version":"1.0","source":{"id":"1403.6710","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6710","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6710v6","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6710","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"pith_short_12","alias_value":"2EKRYVVHLMZ5","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2EKRYVVHLMZ5SNI2","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2EKRYVVH","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:84c068729f5ccc2a750dbbe9ad23e9bdac08b16fe304fa18e6f3e5cbff7c3a5c","target":"graph","created_at":"2026-05-18T01:01:29Z","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":"The groundbreaking work of Rothvo{\\ss} [arxiv:1311.2369] established that every linear program expressing the matching polytope has an exponential number of inequalities (formally, the matching polytope has exponential extension complexity). We generalize this result by deriving strong bounds on the polyhedral inapproximability of the matching polytope: for fixed $0 < \\varepsilon < 1$, every polyhedral $(1 + \\varepsilon / n)$-approximation requires an exponential number of inequalities, where $n$ is the number of vertices. This is sharp given the well-known $\\rho$-approximation of size $O(\\bin","authors_text":"G\\'abor Braun, Sebastian Pokutta","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-03-26T15:25:32Z","title":"The matching polytope does not admit fully-polynomial size relaxation schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6710","kind":"arxiv","version":6},"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:f8528ca2f867546c4a71faadfabcba70dfaa62aa313fa85691e05437d56756b0","target":"record","created_at":"2026-05-18T01:01:29Z","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":"8a1c1c21e0ed4fad6422fc7213c07ec4db6ec742c8834c4f8bfd96cf668291b9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-03-26T15:25:32Z","title_canon_sha256":"8a63a585484a5608ba717cfcfb56efa2da6e74955a50835ef91d5a77c43aa189"},"schema_version":"1.0","source":{"id":"1403.6710","kind":"arxiv","version":6}},"canonical_sha256":"d1151c56a75b33d9351a625468ef725b2896dcb1be79faae88e2632da60091e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1151c56a75b33d9351a625468ef725b2896dcb1be79faae88e2632da60091e9","first_computed_at":"2026-05-18T01:01:29.529078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:29.529078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R7A8czrFEcPtDa4gXTRpewW1/tsyPUYKN7i0G52Aw28mSLzKBHrBF2cQNWEkaQ5JdKEcoL+aXMo7A815ZO4DDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:29.529541Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6710","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8528ca2f867546c4a71faadfabcba70dfaa62aa313fa85691e05437d56756b0","sha256:84c068729f5ccc2a750dbbe9ad23e9bdac08b16fe304fa18e6f3e5cbff7c3a5c"],"state_sha256":"df4f2ba1b920909af57340a2e71c6c4350ad90f291a79bc9dd1d2c830821283a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JwNAOirVoWE4AhrF0Sydz8ZgPgCmxLYIJ5TqLZfmxKq+sDKJmK0+vnA4TZu3HZgoPuaAc/pgTVrVOK/czHAxBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T04:24:57.286282Z","bundle_sha256":"f23120fb632bd66bd28e7ae5b520aafb175fa2b1f025e7567ac198d0a54a5843"}}