{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XJXYLL47LCOMMKJ3JAHPVAGGFG","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":"5b6da2eb2d76ba7195bbd3a503b848443978ae051af07561134eb1a776ec9c1d","cross_cats_sorted":["cs.CC","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-09T18:16:08Z","title_canon_sha256":"575bfe1660118dbf727c90d99432e6c6f136ed1f928daf51c4449b16c1e66038"},"schema_version":"1.0","source":{"id":"1609.02879","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02879","created_at":"2026-05-18T00:49:58Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02879v2","created_at":"2026-05-18T00:49:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02879","created_at":"2026-05-18T00:49:58Z"},{"alias_kind":"pith_short_12","alias_value":"XJXYLL47LCOM","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XJXYLL47LCOMMKJ3","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XJXYLL47","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:fe2e8e606765bfecb90eab4123f84be1300562ac8fb6c5ae475714489a4d08d0","target":"graph","created_at":"2026-05-18T00:49:58Z","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 describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In particular, the notion of connected components of semialgebraic sets is not used.","authors_text":"Daniel Perrucci, Marie-Fran\\c{c}oise Roy","cross_cats":["cs.CC","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-09T18:16:08Z","title":"Elementary recursive quantifier elimination based on Thom encoding and sign determination"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02879","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":"sha256:668bd65043036c7b7b4e640608e104a65e456953b258e8d0013b15a023d9e085","target":"record","created_at":"2026-05-18T00:49:58Z","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":"5b6da2eb2d76ba7195bbd3a503b848443978ae051af07561134eb1a776ec9c1d","cross_cats_sorted":["cs.CC","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-09T18:16:08Z","title_canon_sha256":"575bfe1660118dbf727c90d99432e6c6f136ed1f928daf51c4449b16c1e66038"},"schema_version":"1.0","source":{"id":"1609.02879","kind":"arxiv","version":2}},"canonical_sha256":"ba6f85af9f589cc6293b480efa80c62999158bc28cab6b705e46261c86abb742","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba6f85af9f589cc6293b480efa80c62999158bc28cab6b705e46261c86abb742","first_computed_at":"2026-05-18T00:49:58.518060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:58.518060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uhqDRh9ZitpL8V+blAUrDYtTnt+r/wysyL7gtt8b+WLdM3kEP6WFee5osvDqyaZPyU2LToNDguCfxVhwgRkMCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:58.518574Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02879","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:668bd65043036c7b7b4e640608e104a65e456953b258e8d0013b15a023d9e085","sha256:fe2e8e606765bfecb90eab4123f84be1300562ac8fb6c5ae475714489a4d08d0"],"state_sha256":"289240cd71843c7098b4234838a138f50df3ad190a5134cb2d052b9ba225de53"}