{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5NBVKN2VECMPS57Q47JQQLFF2Z","short_pith_number":"pith:5NBVKN2V","canonical_record":{"source":{"id":"1104.0746","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2011-04-05T06:58:39Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"3dc0248f3e3b471e02d83f9f037508f9402eb4f11a58bbc111f5032cd985cfbb","abstract_canon_sha256":"36c340351f5e6be908ae8152b7713f026c2d7e5876224aa11c33303663d216b8"},"schema_version":"1.0"},"canonical_sha256":"eb435537552098f977f0e7d3082ca5d65cc962a37cb737bdef4837ad4fb62fce","source":{"kind":"arxiv","id":"1104.0746","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0746","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0746v1","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0746","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"pith_short_12","alias_value":"5NBVKN2VECMP","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5NBVKN2VECMPS57Q","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5NBVKN2V","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5NBVKN2VECMPS57Q47JQQLFF2Z","target":"record","payload":{"canonical_record":{"source":{"id":"1104.0746","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2011-04-05T06:58:39Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"3dc0248f3e3b471e02d83f9f037508f9402eb4f11a58bbc111f5032cd985cfbb","abstract_canon_sha256":"36c340351f5e6be908ae8152b7713f026c2d7e5876224aa11c33303663d216b8"},"schema_version":"1.0"},"canonical_sha256":"eb435537552098f977f0e7d3082ca5d65cc962a37cb737bdef4837ad4fb62fce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:20.276373Z","signature_b64":"vfxwxf62WsFdWEbxZZrCgbOeSRI+GC72+HO0smDWyc7DCv55Ksi5rF4mgtA5TNO36ouVivrmGgpsCJwUVxYrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb435537552098f977f0e7d3082ca5d65cc962a37cb737bdef4837ad4fb62fce","last_reissued_at":"2026-05-18T00:17:20.275653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:20.275653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.0746","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":"2026-05-18T00:17:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ez6V7jMDMP2IX9GMVp02sE44+3iYRvfWz8mAENmhs5FRcDY7yMBOZ0OJkONEgA2Oyks2z30ENAkyXapZP03bBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T16:44:38.984605Z"},"content_sha256":"4570145226044b3d90aaae930105a2cf55b40262ce2e8139d290e64749f97668","schema_version":"1.0","event_id":"sha256:4570145226044b3d90aaae930105a2cf55b40262ce2e8139d290e64749f97668"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5NBVKN2VECMPS57Q47JQQLFF2Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantifier Elimination over Finite Fields Using Gr\\\"obner Bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.SC","authors_text":"Andr\\'e Platzer, Edmund M. Clarke, Sicun Gao","submitted_at":"2011-04-05T06:58:39Z","abstract_excerpt":"We give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gr\\\"obner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite fields. We analyze the theoretical complexity of the algorithm and show its application in the formal analysis of a biological controller model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0746","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":""},"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":"2026-05-18T00:17:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7aZd5TcJS4okJBXm+LcqzqXmOeByQUvwbZnPuwwWsJ6PChPZxTghtqBQ35SzbESLVwcjmdNcuWHkEK8izTnWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T16:44:38.985285Z"},"content_sha256":"91aa6797c1503399a110d9a766bbc78b9b730577a808907a9a64006f1743feca","schema_version":"1.0","event_id":"sha256:91aa6797c1503399a110d9a766bbc78b9b730577a808907a9a64006f1743feca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NBVKN2VECMPS57Q47JQQLFF2Z/bundle.json","state_url":"https://pith.science/pith/5NBVKN2VECMPS57Q47JQQLFF2Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NBVKN2VECMPS57Q47JQQLFF2Z/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":"2026-05-24T16:44:38Z","links":{"resolver":"https://pith.science/pith/5NBVKN2VECMPS57Q47JQQLFF2Z","bundle":"https://pith.science/pith/5NBVKN2VECMPS57Q47JQQLFF2Z/bundle.json","state":"https://pith.science/pith/5NBVKN2VECMPS57Q47JQQLFF2Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NBVKN2VECMPS57Q47JQQLFF2Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5NBVKN2VECMPS57Q47JQQLFF2Z","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":"36c340351f5e6be908ae8152b7713f026c2d7e5876224aa11c33303663d216b8","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2011-04-05T06:58:39Z","title_canon_sha256":"3dc0248f3e3b471e02d83f9f037508f9402eb4f11a58bbc111f5032cd985cfbb"},"schema_version":"1.0","source":{"id":"1104.0746","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0746","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0746v1","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0746","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"pith_short_12","alias_value":"5NBVKN2VECMP","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5NBVKN2VECMPS57Q","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5NBVKN2V","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:91aa6797c1503399a110d9a766bbc78b9b730577a808907a9a64006f1743feca","target":"graph","created_at":"2026-05-18T00:17:20Z","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 give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gr\\\"obner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite fields. We analyze the theoretical complexity of the algorithm and show its application in the formal analysis of a biological controller model.","authors_text":"Andr\\'e Platzer, Edmund M. Clarke, Sicun Gao","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2011-04-05T06:58:39Z","title":"Quantifier Elimination over Finite Fields Using Gr\\\"obner Bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0746","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":"sha256:4570145226044b3d90aaae930105a2cf55b40262ce2e8139d290e64749f97668","target":"record","created_at":"2026-05-18T00:17:20Z","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":"36c340351f5e6be908ae8152b7713f026c2d7e5876224aa11c33303663d216b8","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2011-04-05T06:58:39Z","title_canon_sha256":"3dc0248f3e3b471e02d83f9f037508f9402eb4f11a58bbc111f5032cd985cfbb"},"schema_version":"1.0","source":{"id":"1104.0746","kind":"arxiv","version":1}},"canonical_sha256":"eb435537552098f977f0e7d3082ca5d65cc962a37cb737bdef4837ad4fb62fce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb435537552098f977f0e7d3082ca5d65cc962a37cb737bdef4837ad4fb62fce","first_computed_at":"2026-05-18T00:17:20.275653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:20.275653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vfxwxf62WsFdWEbxZZrCgbOeSRI+GC72+HO0smDWyc7DCv55Ksi5rF4mgtA5TNO36ouVivrmGgpsCJwUVxYrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:20.276373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0746","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4570145226044b3d90aaae930105a2cf55b40262ce2e8139d290e64749f97668","sha256:91aa6797c1503399a110d9a766bbc78b9b730577a808907a9a64006f1743feca"],"state_sha256":"a18a2c212848a0d80745a2bfc7f3f5fbe15cbdb36f1077a0ad7758a9fe47650e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZPsBIe4c9GBe/FYcXvdpMgzsT49QdCr8fB8vSDfXftCQWFwguwn+P6FXLZrTlPkK5dHPLwBcgkF7xwD4TB+uCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T16:44:38.989257Z","bundle_sha256":"4778a67091cf0ffd47a46aa2693e73870a35d692b403104db6adb41ab5bce959"}}