{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZOM422DEY3MTVSVNJDIBHNUFHZ","short_pith_number":"pith:ZOM422DE","canonical_record":{"source":{"id":"1204.1746","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-04-08T17:00:25Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"8ec806ae1c7047f32d07766d24336996c409c814a3ef20f544ed10592b1872ea","abstract_canon_sha256":"5b1ecad06dde47c3ce5b74b26ef1c0b09575465e726acd055019144e2b5001e2"},"schema_version":"1.0"},"canonical_sha256":"cb99cd6864c6d93acaad48d013b6853e56f4e8cc60f03100c552c18c423b4ebe","source":{"kind":"arxiv","id":"1204.1746","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1746","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1746v2","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1746","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZOM422DEY3MT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZOM422DEY3MTVSVN","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZOM422DE","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZOM422DEY3MTVSVNJDIBHNUFHZ","target":"record","payload":{"canonical_record":{"source":{"id":"1204.1746","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-04-08T17:00:25Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"8ec806ae1c7047f32d07766d24336996c409c814a3ef20f544ed10592b1872ea","abstract_canon_sha256":"5b1ecad06dde47c3ce5b74b26ef1c0b09575465e726acd055019144e2b5001e2"},"schema_version":"1.0"},"canonical_sha256":"cb99cd6864c6d93acaad48d013b6853e56f4e8cc60f03100c552c18c423b4ebe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:15.814600Z","signature_b64":"U/KLyElAVqKaWLQGWvUvV9mPfmq+DjHhrx7S1mnGGYsXGcSfh7z1L6FtwAHglhfcSG1Pi807KDdw3XnY229VDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb99cd6864c6d93acaad48d013b6853e56f4e8cc60f03100c552c18c423b4ebe","last_reissued_at":"2026-05-18T03:54:15.814129Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:15.814129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.1746","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":"2026-05-18T03:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pa2VEr2xnh7P+52UHRUlbpl/kvVvRcGk70M39JpYy2irDGDSeQBErj8JWWsxy+MTUctcXvgaBfOEZSDrUGHNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T14:38:49.761797Z"},"content_sha256":"b3c7cd8a98ef65be3637a8df6e86cf503672816417ca722ab9ec68d5daa6b3ef","schema_version":"1.0","event_id":"sha256:b3c7cd8a98ef65be3637a8df6e86cf503672816417ca722ab9ec68d5daa6b3ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZOM422DEY3MTVSVNJDIBHNUFHZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Removal of Quantifiers by Elimination of Boundary Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.LO","authors_text":"Eugene Goldberg, Panagiotis Manolios","submitted_at":"2012-04-08T17:00:25Z","abstract_excerpt":"We consider the problem of elimination of existential quantifiers from a Boolean CNF formula. Our approach is based on the following observation. One can get rid of dependency on a set of variables of a quantified CNF formula F by adding resolvent clauses of F eliminating boundary points. This approach is similar to the method of quantifier elimination described in [9]. The difference of the method described in the present paper is twofold: {\\bullet} branching is performed only on quantified variables, {\\bullet} an explicit search for boundary points is performed by calls to a SAT-solver Altho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1746","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":"2026-05-18T03:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/EtWCqdPez2SaW7/+7NV6kRhAepKZrWKWtTX2AhGgk+nAKSJqZA4nDqdApjQGg9Tu4m+QJaSwvaVPiHC4q2uDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T14:38:49.762140Z"},"content_sha256":"4c5a37c01d7012c2963da99d3e5f0507eb18a6d808c85c2fe592796207e656d7","schema_version":"1.0","event_id":"sha256:4c5a37c01d7012c2963da99d3e5f0507eb18a6d808c85c2fe592796207e656d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZOM422DEY3MTVSVNJDIBHNUFHZ/bundle.json","state_url":"https://pith.science/pith/ZOM422DEY3MTVSVNJDIBHNUFHZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZOM422DEY3MTVSVNJDIBHNUFHZ/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":"2026-06-28T14:38:49Z","links":{"resolver":"https://pith.science/pith/ZOM422DEY3MTVSVNJDIBHNUFHZ","bundle":"https://pith.science/pith/ZOM422DEY3MTVSVNJDIBHNUFHZ/bundle.json","state":"https://pith.science/pith/ZOM422DEY3MTVSVNJDIBHNUFHZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZOM422DEY3MTVSVNJDIBHNUFHZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZOM422DEY3MTVSVNJDIBHNUFHZ","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":"5b1ecad06dde47c3ce5b74b26ef1c0b09575465e726acd055019144e2b5001e2","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-04-08T17:00:25Z","title_canon_sha256":"8ec806ae1c7047f32d07766d24336996c409c814a3ef20f544ed10592b1872ea"},"schema_version":"1.0","source":{"id":"1204.1746","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1746","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1746v2","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1746","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZOM422DEY3MT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZOM422DEY3MTVSVN","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZOM422DE","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:4c5a37c01d7012c2963da99d3e5f0507eb18a6d808c85c2fe592796207e656d7","target":"graph","created_at":"2026-05-18T03:54:15Z","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 consider the problem of elimination of existential quantifiers from a Boolean CNF formula. Our approach is based on the following observation. One can get rid of dependency on a set of variables of a quantified CNF formula F by adding resolvent clauses of F eliminating boundary points. This approach is similar to the method of quantifier elimination described in [9]. The difference of the method described in the present paper is twofold: {\\bullet} branching is performed only on quantified variables, {\\bullet} an explicit search for boundary points is performed by calls to a SAT-solver Altho","authors_text":"Eugene Goldberg, Panagiotis Manolios","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-04-08T17:00:25Z","title":"Removal of Quantifiers by Elimination of Boundary Points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1746","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:b3c7cd8a98ef65be3637a8df6e86cf503672816417ca722ab9ec68d5daa6b3ef","target":"record","created_at":"2026-05-18T03:54:15Z","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":"5b1ecad06dde47c3ce5b74b26ef1c0b09575465e726acd055019144e2b5001e2","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-04-08T17:00:25Z","title_canon_sha256":"8ec806ae1c7047f32d07766d24336996c409c814a3ef20f544ed10592b1872ea"},"schema_version":"1.0","source":{"id":"1204.1746","kind":"arxiv","version":2}},"canonical_sha256":"cb99cd6864c6d93acaad48d013b6853e56f4e8cc60f03100c552c18c423b4ebe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb99cd6864c6d93acaad48d013b6853e56f4e8cc60f03100c552c18c423b4ebe","first_computed_at":"2026-05-18T03:54:15.814129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:15.814129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U/KLyElAVqKaWLQGWvUvV9mPfmq+DjHhrx7S1mnGGYsXGcSfh7z1L6FtwAHglhfcSG1Pi807KDdw3XnY229VDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:15.814600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1746","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3c7cd8a98ef65be3637a8df6e86cf503672816417ca722ab9ec68d5daa6b3ef","sha256:4c5a37c01d7012c2963da99d3e5f0507eb18a6d808c85c2fe592796207e656d7"],"state_sha256":"6b258300cdb617dd7dcd1cbb24fd5b95a44c92c903e2332a15edfea91ff1dab7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cI9rmPMQVTX9xEK8Cq7ShdSusvKB1ERTSxM1ohn291cnZc0bATDhsc+rUkfuBnUh+2r10TGw5JoFtdenXa24Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T14:38:49.764029Z","bundle_sha256":"94717a7900ecb6cfafc2264793b574865d421f9c46980ded3993a9044dbe66ff"}}