{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:WNW5PVVX7GSOFILCTOQN7ID6SP","short_pith_number":"pith:WNW5PVVX","schema_version":"1.0","canonical_sha256":"b36dd7d6b7f9a4e2a1629ba0dfa07e93f506fb1f2cf9b731c80912d1cc7be59c","source":{"kind":"arxiv","id":"2503.21731","version":2},"attestation_state":"computed","paper":{"title":"Cylindrical Algebraic Decomposition in Macaulay2","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.SC","authors_text":"Corin Lee, Hamid Rahkooy, Tereso del R\\'io","submitted_at":"2025-03-27T17:46:24Z","abstract_excerpt":"CylindricalAlgebraicDecomposition.m2 is the first implementation of Cylindrical Algebraic Decomposition (CAD) in Macaulay2. CAD decomposes space into 'cells' where input polynomials are sign-invariant. This package computes an Open CAD (full-dimensional cells only) for sets of real polynomials with rational coefficients, enabling users to solve existential problems involving strict inequalities. With the construction of a full CAD (cells of all dimensions), this tool could be extended to solve any real quantifier elimination problem. The current implementation employs the Lazard projection and"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2503.21731","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SC","submitted_at":"2025-03-27T17:46:24Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"dd1e141beac74abb35c8a555f2617a1c785354dbdeb9f2c7b42bcde185adb23a","abstract_canon_sha256":"2461d0ceabea28a31a7489be6d04685321aaa4c1258c0d32f13a536ff3fa7beb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:41:54.431291Z","signature_b64":"Z3W1fWd3fAmyVvvYUki5drOUoY5MWkjYcuT+z6agb9PfPmnCChZGf+n+lGb50cQapRrHqiolJ285rEIgtpo9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b36dd7d6b7f9a4e2a1629ba0dfa07e93f506fb1f2cf9b731c80912d1cc7be59c","last_reissued_at":"2026-07-05T10:41:54.430828Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:41:54.430828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cylindrical Algebraic Decomposition in Macaulay2","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.SC","authors_text":"Corin Lee, Hamid Rahkooy, Tereso del R\\'io","submitted_at":"2025-03-27T17:46:24Z","abstract_excerpt":"CylindricalAlgebraicDecomposition.m2 is the first implementation of Cylindrical Algebraic Decomposition (CAD) in Macaulay2. CAD decomposes space into 'cells' where input polynomials are sign-invariant. This package computes an Open CAD (full-dimensional cells only) for sets of real polynomials with rational coefficients, enabling users to solve existential problems involving strict inequalities. With the construction of a full CAD (cells of all dimensions), this tool could be extended to solve any real quantifier elimination problem. The current implementation employs the Lazard projection and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.21731","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.21731/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2503.21731","created_at":"2026-07-05T10:41:54.430887+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.21731v2","created_at":"2026-07-05T10:41:54.430887+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.21731","created_at":"2026-07-05T10:41:54.430887+00:00"},{"alias_kind":"pith_short_12","alias_value":"WNW5PVVX7GSO","created_at":"2026-07-05T10:41:54.430887+00:00"},{"alias_kind":"pith_short_16","alias_value":"WNW5PVVX7GSOFILC","created_at":"2026-07-05T10:41:54.430887+00:00"},{"alias_kind":"pith_short_8","alias_value":"WNW5PVVX","created_at":"2026-07-05T10:41:54.430887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WNW5PVVX7GSOFILCTOQN7ID6SP","json":"https://pith.science/pith/WNW5PVVX7GSOFILCTOQN7ID6SP.json","graph_json":"https://pith.science/api/pith-number/WNW5PVVX7GSOFILCTOQN7ID6SP/graph.json","events_json":"https://pith.science/api/pith-number/WNW5PVVX7GSOFILCTOQN7ID6SP/events.json","paper":"https://pith.science/paper/WNW5PVVX"},"agent_actions":{"view_html":"https://pith.science/pith/WNW5PVVX7GSOFILCTOQN7ID6SP","download_json":"https://pith.science/pith/WNW5PVVX7GSOFILCTOQN7ID6SP.json","view_paper":"https://pith.science/paper/WNW5PVVX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.21731&json=true","fetch_graph":"https://pith.science/api/pith-number/WNW5PVVX7GSOFILCTOQN7ID6SP/graph.json","fetch_events":"https://pith.science/api/pith-number/WNW5PVVX7GSOFILCTOQN7ID6SP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WNW5PVVX7GSOFILCTOQN7ID6SP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WNW5PVVX7GSOFILCTOQN7ID6SP/action/storage_attestation","attest_author":"https://pith.science/pith/WNW5PVVX7GSOFILCTOQN7ID6SP/action/author_attestation","sign_citation":"https://pith.science/pith/WNW5PVVX7GSOFILCTOQN7ID6SP/action/citation_signature","submit_replication":"https://pith.science/pith/WNW5PVVX7GSOFILCTOQN7ID6SP/action/replication_record"}},"created_at":"2026-07-05T10:41:54.430887+00:00","updated_at":"2026-07-05T10:41:54.430887+00:00"}