{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PQIUWE5OP4CBVKZPKGKWPDRPR6","short_pith_number":"pith:PQIUWE5O","canonical_record":{"source":{"id":"1203.3706","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-03-16T13:53:33Z","cross_cats_sorted":[],"title_canon_sha256":"2d6639a92f84cc1328c7392533d2f7bb7f10722c44598657e17f8bfc3af22103","abstract_canon_sha256":"a356f7bd1f65e0e58b0e6ac37ca250ca128de5d6e78c044c0fc896e422ef6693"},"schema_version":"1.0"},"canonical_sha256":"7c114b13ae7f041aab2f5195678e2f8fa47e89a9cc2e2ad7a6c632709763653e","source":{"kind":"arxiv","id":"1203.3706","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3706","created_at":"2026-05-18T03:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3706v2","created_at":"2026-05-18T03:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3706","created_at":"2026-05-18T03:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"PQIUWE5OP4CB","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PQIUWE5OP4CBVKZP","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PQIUWE5O","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PQIUWE5OP4CBVKZPKGKWPDRPR6","target":"record","payload":{"canonical_record":{"source":{"id":"1203.3706","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-03-16T13:53:33Z","cross_cats_sorted":[],"title_canon_sha256":"2d6639a92f84cc1328c7392533d2f7bb7f10722c44598657e17f8bfc3af22103","abstract_canon_sha256":"a356f7bd1f65e0e58b0e6ac37ca250ca128de5d6e78c044c0fc896e422ef6693"},"schema_version":"1.0"},"canonical_sha256":"7c114b13ae7f041aab2f5195678e2f8fa47e89a9cc2e2ad7a6c632709763653e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:26.937766Z","signature_b64":"QppO0OShhRaz3YNnURi2jkzF7vCxkhO99xboiuY1BSExp+NVV6bEz+CXq17etfIhaEUhaIn/SZBjQkUOP07YBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c114b13ae7f041aab2f5195678e2f8fa47e89a9cc2e2ad7a6c632709763653e","last_reissued_at":"2026-05-18T03:59:26.936995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:26.936995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.3706","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":"2026-05-18T03:59:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a8MKQHkO3T90Ny4kZlPBZgwapLwm+RGqJSnoaVLn3+SZt0zvZoFIr8svTX6EhFa0YLIOOkbekCV1Ckzu9yYMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:37:31.298269Z"},"content_sha256":"064a8e5df9b4300ebd570688e8fa2e8d6d140550648e382cc9fdd04b326c8768","schema_version":"1.0","event_id":"sha256:064a8e5df9b4300ebd570688e8fa2e8d6d140550648e382cc9fdd04b326c8768"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PQIUWE5OP4CBVKZPKGKWPDRPR6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Complexity of Computing Minimal Unsatisfiable LTL formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Francois Hantry, Lakhdar Sa\\\"is, Mohand-Sa\\\"id Hacid","submitted_at":"2012-03-16T13:53:33Z","abstract_excerpt":"We show that (1) the Minimal False QCNF search-problem (MF-search) and the Minimal Unsatisfiable LTL formula search problem (MU-search) are FPSPACE complete because of the very expressive power of QBF/LTL, (2) we extend the PSPACE-hardness of the MF decision problem to the MU decision problem. As a consequence, we deduce a positive answer to the open question of PSPACE hardness of the inherent Vacuity Checking problem. We even show that the Inherent Non Vacuous formula search problem is also FPSPACE-complete."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3706","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":"2026-05-18T03:59:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sGQa9reV1SfyEf7JNrMdZdJdCGu3RKroBXDsZXCWIyv+22DbspvXExfK2q/tZOzZLWVtnNKwTLrP2/PodACGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:37:31.298625Z"},"content_sha256":"1236b6dbb7b43248ea5676610f24213120d709c470755fcf9450587f938d9023","schema_version":"1.0","event_id":"sha256:1236b6dbb7b43248ea5676610f24213120d709c470755fcf9450587f938d9023"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQIUWE5OP4CBVKZPKGKWPDRPR6/bundle.json","state_url":"https://pith.science/pith/PQIUWE5OP4CBVKZPKGKWPDRPR6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQIUWE5OP4CBVKZPKGKWPDRPR6/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":"2026-06-27T12:37:31Z","links":{"resolver":"https://pith.science/pith/PQIUWE5OP4CBVKZPKGKWPDRPR6","bundle":"https://pith.science/pith/PQIUWE5OP4CBVKZPKGKWPDRPR6/bundle.json","state":"https://pith.science/pith/PQIUWE5OP4CBVKZPKGKWPDRPR6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQIUWE5OP4CBVKZPKGKWPDRPR6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PQIUWE5OP4CBVKZPKGKWPDRPR6","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":"a356f7bd1f65e0e58b0e6ac37ca250ca128de5d6e78c044c0fc896e422ef6693","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-03-16T13:53:33Z","title_canon_sha256":"2d6639a92f84cc1328c7392533d2f7bb7f10722c44598657e17f8bfc3af22103"},"schema_version":"1.0","source":{"id":"1203.3706","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3706","created_at":"2026-05-18T03:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3706v2","created_at":"2026-05-18T03:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3706","created_at":"2026-05-18T03:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"PQIUWE5OP4CB","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PQIUWE5OP4CBVKZP","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PQIUWE5O","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:1236b6dbb7b43248ea5676610f24213120d709c470755fcf9450587f938d9023","target":"graph","created_at":"2026-05-18T03:59:26Z","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 show that (1) the Minimal False QCNF search-problem (MF-search) and the Minimal Unsatisfiable LTL formula search problem (MU-search) are FPSPACE complete because of the very expressive power of QBF/LTL, (2) we extend the PSPACE-hardness of the MF decision problem to the MU decision problem. As a consequence, we deduce a positive answer to the open question of PSPACE hardness of the inherent Vacuity Checking problem. We even show that the Inherent Non Vacuous formula search problem is also FPSPACE-complete.","authors_text":"Francois Hantry, Lakhdar Sa\\\"is, Mohand-Sa\\\"id Hacid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-03-16T13:53:33Z","title":"On the Complexity of Computing Minimal Unsatisfiable LTL formulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3706","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":"sha256:064a8e5df9b4300ebd570688e8fa2e8d6d140550648e382cc9fdd04b326c8768","target":"record","created_at":"2026-05-18T03:59:26Z","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":"a356f7bd1f65e0e58b0e6ac37ca250ca128de5d6e78c044c0fc896e422ef6693","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-03-16T13:53:33Z","title_canon_sha256":"2d6639a92f84cc1328c7392533d2f7bb7f10722c44598657e17f8bfc3af22103"},"schema_version":"1.0","source":{"id":"1203.3706","kind":"arxiv","version":2}},"canonical_sha256":"7c114b13ae7f041aab2f5195678e2f8fa47e89a9cc2e2ad7a6c632709763653e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c114b13ae7f041aab2f5195678e2f8fa47e89a9cc2e2ad7a6c632709763653e","first_computed_at":"2026-05-18T03:59:26.936995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:26.936995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QppO0OShhRaz3YNnURi2jkzF7vCxkhO99xboiuY1BSExp+NVV6bEz+CXq17etfIhaEUhaIn/SZBjQkUOP07YBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:26.937766Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3706","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:064a8e5df9b4300ebd570688e8fa2e8d6d140550648e382cc9fdd04b326c8768","sha256:1236b6dbb7b43248ea5676610f24213120d709c470755fcf9450587f938d9023"],"state_sha256":"92eba5a71806f51e860faa99fb2a998f0c5da25fae536301e63cae6f8ac7c527"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lSh8D5nWzsdp8ty6cHUoHyMgM/Y5FY8Ytsqhg1QCL007UqUqcv1bRYFh0SOAsOEt54KeGHbLvam1qHdXNKafCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:37:31.300435Z","bundle_sha256":"945b7d8eda609fd859cfb322ee3683915f61030d569d9279f8dca67f2f3fe147"}}