{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:W7NO4E4L3VRVT5DC7XQ27TUTFD","short_pith_number":"pith:W7NO4E4L","canonical_record":{"source":{"id":"1208.2721","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-08-13T22:24:45Z","cross_cats_sorted":[],"title_canon_sha256":"27e66f89d6d89570d575e0c62fae7cc1a9ba91ccab63a6367af079e3df638dc8","abstract_canon_sha256":"538c4b73c0ffe4e27bf2cbc2c2a7aee71ac4e685d94934eb24040afa79ffbfee"},"schema_version":"1.0"},"canonical_sha256":"b7daee138bdd6359f462fde1afce9328d481157d1c5c70e50dcbf66b20dba835","source":{"kind":"arxiv","id":"1208.2721","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2721","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2721v3","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2721","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"W7NO4E4L3VRV","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W7NO4E4L3VRVT5DC","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W7NO4E4L","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:W7NO4E4L3VRVT5DC7XQ27TUTFD","target":"record","payload":{"canonical_record":{"source":{"id":"1208.2721","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-08-13T22:24:45Z","cross_cats_sorted":[],"title_canon_sha256":"27e66f89d6d89570d575e0c62fae7cc1a9ba91ccab63a6367af079e3df638dc8","abstract_canon_sha256":"538c4b73c0ffe4e27bf2cbc2c2a7aee71ac4e685d94934eb24040afa79ffbfee"},"schema_version":"1.0"},"canonical_sha256":"b7daee138bdd6359f462fde1afce9328d481157d1c5c70e50dcbf66b20dba835","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:34.219080Z","signature_b64":"tA33b9SJK231YYNX8PJ9RHnMpv0/h+v4OVmHLbFekdo6RJtSeogt4cAY9Dy7ooQo2nD9zcVHN79tbMUjUReBBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7daee138bdd6359f462fde1afce9328d481157d1c5c70e50dcbf66b20dba835","last_reissued_at":"2026-05-18T03:17:34.218503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:34.218503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.2721","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":"2026-05-18T03:17:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LXrruQLCvH15bfCXVlMwCB/I5g5fwd3ibV9dVQNUr53tXlyoBAe3sTL5tsmywPSkeULhiiX2TuOeVQ5hGhk5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:09:24.128964Z"},"content_sha256":"2cc2248d4f0762cad8dfb8642ac5a82c51aab48c8946611e6effe8f4b85f6fec","schema_version":"1.0","event_id":"sha256:2cc2248d4f0762cad8dfb8642ac5a82c51aab48c8946611e6effe8f4b85f6fec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:W7NO4E4L3VRVT5DC7XQ27TUTFD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Complexity of the Comparator Circuit Value Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Dai Tri Man Le, Stephen A. Cook, Yuval Filmus","submitted_at":"2012-08-13T22:24:45Z","abstract_excerpt":"In 1990 Subramanian defined the complexity class CC as the set of problems log-space reducible to the comparator circuit value problem (CCV). He and Mayr showed that NL \\subseteq CC \\subseteq P, and proved that in addition to CCV several other problems are complete for CC, including the stable marriage problem, and finding the lexicographically first maximal matching in a bipartite graph. We are interested in CC because we conjecture that it is incomparable with the parallel class NC which also satisfies NL \\subseteq NC \\subseteq P, and note that this conjecture implies that none of the CC-com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2721","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":"2026-05-18T03:17:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bdM9Ssx++M8khZ/uuLuI9Q1m+Q6nFbKxd/dLujFn8A+enqR6t73PpjmZ7My+KG10thibd9p1XKnKJy9WIwQfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:09:24.129302Z"},"content_sha256":"7dc0ab61295055f33ff0e12b289293087f1d6b39e1ae22d57dc97dba6bd6e7b5","schema_version":"1.0","event_id":"sha256:7dc0ab61295055f33ff0e12b289293087f1d6b39e1ae22d57dc97dba6bd6e7b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W7NO4E4L3VRVT5DC7XQ27TUTFD/bundle.json","state_url":"https://pith.science/pith/W7NO4E4L3VRVT5DC7XQ27TUTFD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W7NO4E4L3VRVT5DC7XQ27TUTFD/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":"2026-06-09T13:09:24Z","links":{"resolver":"https://pith.science/pith/W7NO4E4L3VRVT5DC7XQ27TUTFD","bundle":"https://pith.science/pith/W7NO4E4L3VRVT5DC7XQ27TUTFD/bundle.json","state":"https://pith.science/pith/W7NO4E4L3VRVT5DC7XQ27TUTFD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W7NO4E4L3VRVT5DC7XQ27TUTFD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:W7NO4E4L3VRVT5DC7XQ27TUTFD","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":"538c4b73c0ffe4e27bf2cbc2c2a7aee71ac4e685d94934eb24040afa79ffbfee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-08-13T22:24:45Z","title_canon_sha256":"27e66f89d6d89570d575e0c62fae7cc1a9ba91ccab63a6367af079e3df638dc8"},"schema_version":"1.0","source":{"id":"1208.2721","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2721","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2721v3","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2721","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"W7NO4E4L3VRV","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W7NO4E4L3VRVT5DC","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W7NO4E4L","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:7dc0ab61295055f33ff0e12b289293087f1d6b39e1ae22d57dc97dba6bd6e7b5","target":"graph","created_at":"2026-05-18T03:17:34Z","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":"In 1990 Subramanian defined the complexity class CC as the set of problems log-space reducible to the comparator circuit value problem (CCV). He and Mayr showed that NL \\subseteq CC \\subseteq P, and proved that in addition to CCV several other problems are complete for CC, including the stable marriage problem, and finding the lexicographically first maximal matching in a bipartite graph. We are interested in CC because we conjecture that it is incomparable with the parallel class NC which also satisfies NL \\subseteq NC \\subseteq P, and note that this conjecture implies that none of the CC-com","authors_text":"Dai Tri Man Le, Stephen A. Cook, Yuval Filmus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-08-13T22:24:45Z","title":"The Complexity of the Comparator Circuit Value Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2721","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":"sha256:2cc2248d4f0762cad8dfb8642ac5a82c51aab48c8946611e6effe8f4b85f6fec","target":"record","created_at":"2026-05-18T03:17:34Z","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":"538c4b73c0ffe4e27bf2cbc2c2a7aee71ac4e685d94934eb24040afa79ffbfee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-08-13T22:24:45Z","title_canon_sha256":"27e66f89d6d89570d575e0c62fae7cc1a9ba91ccab63a6367af079e3df638dc8"},"schema_version":"1.0","source":{"id":"1208.2721","kind":"arxiv","version":3}},"canonical_sha256":"b7daee138bdd6359f462fde1afce9328d481157d1c5c70e50dcbf66b20dba835","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7daee138bdd6359f462fde1afce9328d481157d1c5c70e50dcbf66b20dba835","first_computed_at":"2026-05-18T03:17:34.218503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:34.218503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tA33b9SJK231YYNX8PJ9RHnMpv0/h+v4OVmHLbFekdo6RJtSeogt4cAY9Dy7ooQo2nD9zcVHN79tbMUjUReBBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:34.219080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2721","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cc2248d4f0762cad8dfb8642ac5a82c51aab48c8946611e6effe8f4b85f6fec","sha256:7dc0ab61295055f33ff0e12b289293087f1d6b39e1ae22d57dc97dba6bd6e7b5"],"state_sha256":"f3e48ce73a97746699400964286df8a17d6fff028829662b856588510fb1a74c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lYqoIyvJIX3oYTocg5Mhb4EyG7cTp+NBge1HrqJWChZ0XjBtJceTevQpJDnIEw+gumvFUTJXSePeVJnWTz7CCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:09:24.131247Z","bundle_sha256":"aad2d27ac308abe241286424ef03b9b956a2b7568d5bb707777baf12cf91d2b2"}}