{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:OBVIAIIIGWTQFD23P6IYSSMZ4Q","short_pith_number":"pith:OBVIAIII","canonical_record":{"source":{"id":"cs/0008001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.LO","submitted_at":"2000-08-01T13:51:56Z","cross_cats_sorted":[],"title_canon_sha256":"58e17833aeba795478bbc6b7ccd746806852daa7d14d34706ad9f189a3bd358e","abstract_canon_sha256":"7cdf7a582c42a17b127ac6743018d1589504369b0e86414a763778dff57a39f8"},"schema_version":"1.0"},"canonical_sha256":"706a80210835a7028f5b7f91894999e4089f9542125b45501c887c6653fc46f7","source":{"kind":"arxiv","id":"cs/0008001","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0008001","created_at":"2026-07-04T14:24:03Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0008001v1","created_at":"2026-07-04T14:24:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0008001","created_at":"2026-07-04T14:24:03Z"},{"alias_kind":"pith_short_12","alias_value":"OBVIAIIIGWTQ","created_at":"2026-07-04T14:24:03Z"},{"alias_kind":"pith_short_16","alias_value":"OBVIAIIIGWTQFD23","created_at":"2026-07-04T14:24:03Z"},{"alias_kind":"pith_short_8","alias_value":"OBVIAIII","created_at":"2026-07-04T14:24:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:OBVIAIIIGWTQFD23P6IYSSMZ4Q","target":"record","payload":{"canonical_record":{"source":{"id":"cs/0008001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.LO","submitted_at":"2000-08-01T13:51:56Z","cross_cats_sorted":[],"title_canon_sha256":"58e17833aeba795478bbc6b7ccd746806852daa7d14d34706ad9f189a3bd358e","abstract_canon_sha256":"7cdf7a582c42a17b127ac6743018d1589504369b0e86414a763778dff57a39f8"},"schema_version":"1.0"},"canonical_sha256":"706a80210835a7028f5b7f91894999e4089f9542125b45501c887c6653fc46f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:24:03.875749Z","signature_b64":"dm8DZRYUAxzh4ttAl9dz4SB1TgiKmbewyJ24zP01HOVjfKd+yaGFzviNglLRzy6qmWR9KAMLdNll3XvA9YleAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"706a80210835a7028f5b7f91894999e4089f9542125b45501c887c6653fc46f7","last_reissued_at":"2026-07-04T14:24:03.875241Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:24:03.875241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cs/0008001","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:24:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lDWZlooOWrBuYTPO/HH8UwrozyBVA9niWjblwlB1kf7MYLMXmRhUSHixLdqj3lybPZvANnn72I9spNryAjQBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T21:28:58.805004Z"},"content_sha256":"6e90a16f843baa9d0c5d77c7adcf155df304b302ce48697ff580871df6424e55","schema_version":"1.0","event_id":"sha256:6e90a16f843baa9d0c5d77c7adcf155df304b302ce48697ff580871df6424e55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:OBVIAIIIGWTQFD23P6IYSSMZ4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boolean Satisfiability with Transitivity Constraints","license":"","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Miroslav N. Velev, Randal E. Bryant","submitted_at":"2000-08-01T13:51:56Z","abstract_excerpt":"We consider a variant of the Boolean satisfiability problem where a subset E of the propositional variables appearing in formula Fsat encode a symmetric, transitive, binary relation over N elements. Each of these relational variables, e[i,j], for 1 <= i < j <= N, expresses whether or not the relation holds between elements i and j. The task is to either find a satisfying assignment to Fsat that also satisfies all transitivity constraints over the relational variables (e.g., e[1,2] & e[2,3] ==> e[1,3]), or to prove that no such assignment exists. Solving this satisfiability problem is the final"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0008001","kind":"arxiv","version":1},"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/cs/0008001/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":"2026-07-04T14:24:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W9qLZ5eYWEiuiax2s1CWBofrNMr1s5HweaWyHXI4iEGiDplHmXaSDIPITuBB37/Gbehr8gOphwfk636eM0exCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T21:28:58.805405Z"},"content_sha256":"edeca54b371f5646d779eccf182905d217cb5d15112d4fd11719e74f50fb8311","schema_version":"1.0","event_id":"sha256:edeca54b371f5646d779eccf182905d217cb5d15112d4fd11719e74f50fb8311"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OBVIAIIIGWTQFD23P6IYSSMZ4Q/bundle.json","state_url":"https://pith.science/pith/OBVIAIIIGWTQFD23P6IYSSMZ4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OBVIAIIIGWTQFD23P6IYSSMZ4Q/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":"2026-07-08T21:28:58Z","links":{"resolver":"https://pith.science/pith/OBVIAIIIGWTQFD23P6IYSSMZ4Q","bundle":"https://pith.science/pith/OBVIAIIIGWTQFD23P6IYSSMZ4Q/bundle.json","state":"https://pith.science/pith/OBVIAIIIGWTQFD23P6IYSSMZ4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OBVIAIIIGWTQFD23P6IYSSMZ4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:OBVIAIIIGWTQFD23P6IYSSMZ4Q","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":"7cdf7a582c42a17b127ac6743018d1589504369b0e86414a763778dff57a39f8","cross_cats_sorted":[],"license":"","primary_cat":"cs.LO","submitted_at":"2000-08-01T13:51:56Z","title_canon_sha256":"58e17833aeba795478bbc6b7ccd746806852daa7d14d34706ad9f189a3bd358e"},"schema_version":"1.0","source":{"id":"cs/0008001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0008001","created_at":"2026-07-04T14:24:03Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0008001v1","created_at":"2026-07-04T14:24:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0008001","created_at":"2026-07-04T14:24:03Z"},{"alias_kind":"pith_short_12","alias_value":"OBVIAIIIGWTQ","created_at":"2026-07-04T14:24:03Z"},{"alias_kind":"pith_short_16","alias_value":"OBVIAIIIGWTQFD23","created_at":"2026-07-04T14:24:03Z"},{"alias_kind":"pith_short_8","alias_value":"OBVIAIII","created_at":"2026-07-04T14:24:03Z"}],"graph_snapshots":[{"event_id":"sha256:edeca54b371f5646d779eccf182905d217cb5d15112d4fd11719e74f50fb8311","target":"graph","created_at":"2026-07-04T14:24:03Z","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/cs/0008001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a variant of the Boolean satisfiability problem where a subset E of the propositional variables appearing in formula Fsat encode a symmetric, transitive, binary relation over N elements. Each of these relational variables, e[i,j], for 1 <= i < j <= N, expresses whether or not the relation holds between elements i and j. The task is to either find a satisfying assignment to Fsat that also satisfies all transitivity constraints over the relational variables (e.g., e[1,2] & e[2,3] ==> e[1,3]), or to prove that no such assignment exists. Solving this satisfiability problem is the final","authors_text":"Miroslav N. Velev, Randal E. Bryant","cross_cats":[],"headline":"","license":"","primary_cat":"cs.LO","submitted_at":"2000-08-01T13:51:56Z","title":"Boolean Satisfiability with Transitivity Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0008001","kind":"arxiv","version":1},"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":"sha256:6e90a16f843baa9d0c5d77c7adcf155df304b302ce48697ff580871df6424e55","target":"record","created_at":"2026-07-04T14:24:03Z","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":"7cdf7a582c42a17b127ac6743018d1589504369b0e86414a763778dff57a39f8","cross_cats_sorted":[],"license":"","primary_cat":"cs.LO","submitted_at":"2000-08-01T13:51:56Z","title_canon_sha256":"58e17833aeba795478bbc6b7ccd746806852daa7d14d34706ad9f189a3bd358e"},"schema_version":"1.0","source":{"id":"cs/0008001","kind":"arxiv","version":1}},"canonical_sha256":"706a80210835a7028f5b7f91894999e4089f9542125b45501c887c6653fc46f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"706a80210835a7028f5b7f91894999e4089f9542125b45501c887c6653fc46f7","first_computed_at":"2026-07-04T14:24:03.875241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:24:03.875241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dm8DZRYUAxzh4ttAl9dz4SB1TgiKmbewyJ24zP01HOVjfKd+yaGFzviNglLRzy6qmWR9KAMLdNll3XvA9YleAg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:24:03.875749Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0008001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e90a16f843baa9d0c5d77c7adcf155df304b302ce48697ff580871df6424e55","sha256:edeca54b371f5646d779eccf182905d217cb5d15112d4fd11719e74f50fb8311"],"state_sha256":"ba6d4e249e28ca0c487ae7da38ac8412f498a02958e4a95570685ce5231b2dc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D68GYMrBcevwmR95Ds7ivrdphgMpvm8PckukOuo8rnTWerJplzVxtk1+HOB2tOeeaeE0ub8tAwru4Mf82jg0DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T21:28:58.807590Z","bundle_sha256":"cab186eb8d82809d74523f15b9914e0f2dffaa7ae34f4e64cd07d2c2d80ded4f"}}