{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7HFYYJW2WL4TBSDODTSAONGOJG","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":"a6959f71ca552de88fdc0cb5f359149d3c8df7950ae1ca0ea69eab721848a80b","cross_cats_sorted":["cs.MS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-02-04T05:52:47Z","title_canon_sha256":"a175f5c12d2aa7b331c49305d26efd415d9f72130b6b4a04c788637846890874"},"schema_version":"1.0","source":{"id":"1402.0622","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0622","created_at":"2026-05-18T03:00:13Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0622v1","created_at":"2026-05-18T03:00:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0622","created_at":"2026-05-18T03:00:13Z"},{"alias_kind":"pith_short_12","alias_value":"7HFYYJW2WL4T","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7HFYYJW2WL4TBSDO","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7HFYYJW2","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:f724a54c87b009a3cc3d9d049bfb6cf1ab6ca7f74723e29b1ce947ce86e3520c","target":"graph","created_at":"2026-05-18T03:00:13Z","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 present a divide-and-conquer version of the Cylindrical Algebraic Decomposition (CAD) algorithm. The algorithm represents the input as a Boolean combination of subformulas, computes cylindrical algebraic decompositions of solution sets of the subformulas, and combines the results. We propose a graph-based heuristic to find a suitable partitioning of the input and present empirical comparison with direct CAD computation.","authors_text":"Adam Strzebonski","cross_cats":["cs.MS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-02-04T05:52:47Z","title":"Divide-And-Conquer Computation of Cylindrical Algebraic Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0622","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":"sha256:3fe8578d24ad07f5ea51c0dcac25e4601167f64043978ad9843d56c174b4f6da","target":"record","created_at":"2026-05-18T03:00:13Z","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":"a6959f71ca552de88fdc0cb5f359149d3c8df7950ae1ca0ea69eab721848a80b","cross_cats_sorted":["cs.MS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-02-04T05:52:47Z","title_canon_sha256":"a175f5c12d2aa7b331c49305d26efd415d9f72130b6b4a04c788637846890874"},"schema_version":"1.0","source":{"id":"1402.0622","kind":"arxiv","version":1}},"canonical_sha256":"f9cb8c26dab2f930c86e1ce40734ce4993d09adbc286965cde719ede01a1cc3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9cb8c26dab2f930c86e1ce40734ce4993d09adbc286965cde719ede01a1cc3b","first_computed_at":"2026-05-18T03:00:13.493137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:13.493137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W0CF00FpVIALAPptOY+aUFm36HHYLyIU+RIv4pzcg/ek5AjgJm6Y9RLw6MMUgAiEZe8k0c+BPZuFsEoYaju7DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:13.493956Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0622","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fe8578d24ad07f5ea51c0dcac25e4601167f64043978ad9843d56c174b4f6da","sha256:f724a54c87b009a3cc3d9d049bfb6cf1ab6ca7f74723e29b1ce947ce86e3520c"],"state_sha256":"5d65fbdff38f26f0a82f8725c2af742b856833e1cbef6cde1cef72ac2d26e2c1"}