{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:UZCA753UPXOR5HEKJE4SHAJABE","short_pith_number":"pith:UZCA753U","canonical_record":{"source":{"id":"2203.13899","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-25T20:34:08Z","cross_cats_sorted":[],"title_canon_sha256":"eb9538547745ff1137e3eadef716b8de075cb2f4a6992aa9e458b4cbac14776b","abstract_canon_sha256":"c6451d6cdc6e4374e5566bdf8c6bb3c7fdeb558ce13908660ce3a741fa425bea"},"schema_version":"1.0"},"canonical_sha256":"a6440ff7747ddd1e9c8a49392381200938512046f6bc22ea4a56544df9056d32","source":{"kind":"arxiv","id":"2203.13899","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.13899","created_at":"2026-07-05T05:28:44Z"},{"alias_kind":"arxiv_version","alias_value":"2203.13899v4","created_at":"2026-07-05T05:28:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.13899","created_at":"2026-07-05T05:28:44Z"},{"alias_kind":"pith_short_12","alias_value":"UZCA753UPXOR","created_at":"2026-07-05T05:28:44Z"},{"alias_kind":"pith_short_16","alias_value":"UZCA753UPXOR5HEK","created_at":"2026-07-05T05:28:44Z"},{"alias_kind":"pith_short_8","alias_value":"UZCA753U","created_at":"2026-07-05T05:28:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:UZCA753UPXOR5HEKJE4SHAJABE","target":"record","payload":{"canonical_record":{"source":{"id":"2203.13899","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-25T20:34:08Z","cross_cats_sorted":[],"title_canon_sha256":"eb9538547745ff1137e3eadef716b8de075cb2f4a6992aa9e458b4cbac14776b","abstract_canon_sha256":"c6451d6cdc6e4374e5566bdf8c6bb3c7fdeb558ce13908660ce3a741fa425bea"},"schema_version":"1.0"},"canonical_sha256":"a6440ff7747ddd1e9c8a49392381200938512046f6bc22ea4a56544df9056d32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:28:44.238769Z","signature_b64":"uHZ5p4l46A7jVfSy/4bdLQW9nNFDmf3h2ULPsuxWraIT+TSrceEXUrKpmHWqECWcu6uIxJhIuc3St+CmTVYjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6440ff7747ddd1e9c8a49392381200938512046f6bc22ea4a56544df9056d32","last_reissued_at":"2026-07-05T05:28:44.238335Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:28:44.238335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.13899","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:28:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXZeVUDCtYZ7DCvrzzDCL5VnI+KJY3C+eLJjEHQBglIDU5TU+0u37y5b1X3+mCCcmkqhfNF3QU+B+bUO+vCiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:26:05.421054Z"},"content_sha256":"1981d0ef7a06c919317140f37d4333078a998dfc036677b3dd8f82002fc21edf","schema_version":"1.0","event_id":"sha256:1981d0ef7a06c919317140f37d4333078a998dfc036677b3dd8f82002fc21edf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:UZCA753UPXOR5HEKJE4SHAJABE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact Matching: Algorithms and Related Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Nicolas El Maalouly","submitted_at":"2022-03-25T20:34:08Z","abstract_excerpt":"In 1982, Papadimitriou and Yannakakis introduced the Exact Matching (EM) problem where given an edge colored graph, with colors red and blue, and an integer $k$, the goal is to decide whether or not the graph contains a perfect matching with exactly $k$ red edges. Although they conjectured it to be $\\textbf{NP}$-complete, soon after it was shown to be solvable in randomized polynomial time in the seminal work of Mulmuley et al., placing it in the complexity class $\\textbf{RP}$. Since then, all attempts at finding a deterministic algorithm for EM have failed, thus leaving it as one of the few n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.13899","kind":"arxiv","version":4},"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/2203.13899/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":"2026-07-05T05:28:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5bvsbFUBN92EEf6n8KNc1m6OLeWC35M6Rpo/5HMMoz5WYOQZSNrhZdLjkttQ8ASL57LPnKRkLJ3y+JbuCSMHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:26:05.421647Z"},"content_sha256":"f10c6ce48e9b628043d65d9dda24e1adee0272832a8b5615e64f3afa79616ff1","schema_version":"1.0","event_id":"sha256:f10c6ce48e9b628043d65d9dda24e1adee0272832a8b5615e64f3afa79616ff1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UZCA753UPXOR5HEKJE4SHAJABE/bundle.json","state_url":"https://pith.science/pith/UZCA753UPXOR5HEKJE4SHAJABE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UZCA753UPXOR5HEKJE4SHAJABE/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":"2026-08-04T17:26:05Z","links":{"resolver":"https://pith.science/pith/UZCA753UPXOR5HEKJE4SHAJABE","bundle":"https://pith.science/pith/UZCA753UPXOR5HEKJE4SHAJABE/bundle.json","state":"https://pith.science/pith/UZCA753UPXOR5HEKJE4SHAJABE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UZCA753UPXOR5HEKJE4SHAJABE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:UZCA753UPXOR5HEKJE4SHAJABE","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":"c6451d6cdc6e4374e5566bdf8c6bb3c7fdeb558ce13908660ce3a741fa425bea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-25T20:34:08Z","title_canon_sha256":"eb9538547745ff1137e3eadef716b8de075cb2f4a6992aa9e458b4cbac14776b"},"schema_version":"1.0","source":{"id":"2203.13899","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.13899","created_at":"2026-07-05T05:28:44Z"},{"alias_kind":"arxiv_version","alias_value":"2203.13899v4","created_at":"2026-07-05T05:28:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.13899","created_at":"2026-07-05T05:28:44Z"},{"alias_kind":"pith_short_12","alias_value":"UZCA753UPXOR","created_at":"2026-07-05T05:28:44Z"},{"alias_kind":"pith_short_16","alias_value":"UZCA753UPXOR5HEK","created_at":"2026-07-05T05:28:44Z"},{"alias_kind":"pith_short_8","alias_value":"UZCA753U","created_at":"2026-07-05T05:28:44Z"}],"graph_snapshots":[{"event_id":"sha256:f10c6ce48e9b628043d65d9dda24e1adee0272832a8b5615e64f3afa79616ff1","target":"graph","created_at":"2026-07-05T05:28:44Z","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/2203.13899/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 1982, Papadimitriou and Yannakakis introduced the Exact Matching (EM) problem where given an edge colored graph, with colors red and blue, and an integer $k$, the goal is to decide whether or not the graph contains a perfect matching with exactly $k$ red edges. Although they conjectured it to be $\\textbf{NP}$-complete, soon after it was shown to be solvable in randomized polynomial time in the seminal work of Mulmuley et al., placing it in the complexity class $\\textbf{RP}$. Since then, all attempts at finding a deterministic algorithm for EM have failed, thus leaving it as one of the few n","authors_text":"Nicolas El Maalouly","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-25T20:34:08Z","title":"Exact Matching: Algorithms and Related Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.13899","kind":"arxiv","version":4},"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":"sha256:1981d0ef7a06c919317140f37d4333078a998dfc036677b3dd8f82002fc21edf","target":"record","created_at":"2026-07-05T05:28:44Z","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":"c6451d6cdc6e4374e5566bdf8c6bb3c7fdeb558ce13908660ce3a741fa425bea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-25T20:34:08Z","title_canon_sha256":"eb9538547745ff1137e3eadef716b8de075cb2f4a6992aa9e458b4cbac14776b"},"schema_version":"1.0","source":{"id":"2203.13899","kind":"arxiv","version":4}},"canonical_sha256":"a6440ff7747ddd1e9c8a49392381200938512046f6bc22ea4a56544df9056d32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6440ff7747ddd1e9c8a49392381200938512046f6bc22ea4a56544df9056d32","first_computed_at":"2026-07-05T05:28:44.238335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:28:44.238335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uHZ5p4l46A7jVfSy/4bdLQW9nNFDmf3h2ULPsuxWraIT+TSrceEXUrKpmHWqECWcu6uIxJhIuc3St+CmTVYjBg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:28:44.238769Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.13899","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1981d0ef7a06c919317140f37d4333078a998dfc036677b3dd8f82002fc21edf","sha256:f10c6ce48e9b628043d65d9dda24e1adee0272832a8b5615e64f3afa79616ff1"],"state_sha256":"61af1f869d0bac086b52f980f773fe96193ed8fe78107a34851acf074c92bf1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XvO1dNwXNaCwCx2hSFCaLhTbdvPpsfsoi5VdkTrEnsYAgPy7u7tbU+KFXo2wV6luqxZ5PVdOjoQtdvhspPvtCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T17:26:05.426504Z","bundle_sha256":"d569488a96062e613ab91c502e1f14a8fc8754d8d6473b4895ac5e98062adf7b"}}