{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WJ5MNF6HF7IQO7IEGYQJ2EFLY4","short_pith_number":"pith:WJ5MNF6H","canonical_record":{"source":{"id":"1405.6094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-05-23T15:18:19Z","cross_cats_sorted":[],"title_canon_sha256":"892d961727c48317d3c42f877e1c2af94aa3c7c243ebe81b45b98ec423808c8b","abstract_canon_sha256":"33f85a358aa63676d3421c612a50c6a88153e897716079250952318da756b8bc"},"schema_version":"1.0"},"canonical_sha256":"b27ac697c72fd1077d0436209d10abc722900b4ef91ee42952a3c77e22a052bc","source":{"kind":"arxiv","id":"1405.6094","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6094","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6094v1","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6094","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"pith_short_12","alias_value":"WJ5MNF6HF7IQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WJ5MNF6HF7IQO7IE","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WJ5MNF6H","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WJ5MNF6HF7IQO7IEGYQJ2EFLY4","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-05-23T15:18:19Z","cross_cats_sorted":[],"title_canon_sha256":"892d961727c48317d3c42f877e1c2af94aa3c7c243ebe81b45b98ec423808c8b","abstract_canon_sha256":"33f85a358aa63676d3421c612a50c6a88153e897716079250952318da756b8bc"},"schema_version":"1.0"},"canonical_sha256":"b27ac697c72fd1077d0436209d10abc722900b4ef91ee42952a3c77e22a052bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:08.168893Z","signature_b64":"8p1k6LC8knGxFmO2u+WfEnqfiNcLMLYXF0/PeUvqhl8Mg9SnQWe7CqCtK5d22jGHZn3pSPieiKXIqgIvuysWCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b27ac697c72fd1077d0436209d10abc722900b4ef91ee42952a3c77e22a052bc","last_reissued_at":"2026-05-18T02:44:08.168455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:08.168455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6094","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":"2026-05-18T02:44:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AawTLP4F3L0NA2EqNA0BMh447lclfgjMyCCxhQmr2hJlkSw9mqMl1mjoYD6gtSbno3aCjDpMh1+qtp5hjPVGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:27:15.104269Z"},"content_sha256":"ed9e088357dd3a4c546c4e7be4f570465140b29ec0dbf4ee243f18d7f5982f03","schema_version":"1.0","event_id":"sha256:ed9e088357dd3a4c546c4e7be4f570465140b29ec0dbf4ee243f18d7f5982f03"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WJ5MNF6HF7IQO7IEGYQJ2EFLY4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"David Wilson, James H. Davenport, Matthew England, Russell Bradford","submitted_at":"2014-05-23T15:18:19Z","abstract_excerpt":"Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in complex space. We consider the latest variant of this which builds the complex decomposition incrementally by polynomial and produces CADs on whose cells a sequence of formulae are truth-invariant. Like all CAD algorithms the user must provide a variable ordering which can have a profound impact on the tractability of a problem. We evaluate existing heurist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6094","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":"2026-05-18T02:44:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BOrdlcRinxgc6GIepDwh16xgryYSXFRyFem2nOD9DZTFWx/9Snmrs6JQdo/h12FHAB/Z62U+rb7Stp6t/rQ9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:27:15.104649Z"},"content_sha256":"b5247b7120dbbfb0beca3f3901d0810bc628b8d0f79b51c0d62e712ae6b7a901","schema_version":"1.0","event_id":"sha256:b5247b7120dbbfb0beca3f3901d0810bc628b8d0f79b51c0d62e712ae6b7a901"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WJ5MNF6HF7IQO7IEGYQJ2EFLY4/bundle.json","state_url":"https://pith.science/pith/WJ5MNF6HF7IQO7IEGYQJ2EFLY4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WJ5MNF6HF7IQO7IEGYQJ2EFLY4/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":"2026-06-02T23:27:15Z","links":{"resolver":"https://pith.science/pith/WJ5MNF6HF7IQO7IEGYQJ2EFLY4","bundle":"https://pith.science/pith/WJ5MNF6HF7IQO7IEGYQJ2EFLY4/bundle.json","state":"https://pith.science/pith/WJ5MNF6HF7IQO7IEGYQJ2EFLY4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WJ5MNF6HF7IQO7IEGYQJ2EFLY4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WJ5MNF6HF7IQO7IEGYQJ2EFLY4","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":"33f85a358aa63676d3421c612a50c6a88153e897716079250952318da756b8bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-05-23T15:18:19Z","title_canon_sha256":"892d961727c48317d3c42f877e1c2af94aa3c7c243ebe81b45b98ec423808c8b"},"schema_version":"1.0","source":{"id":"1405.6094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6094","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6094v1","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6094","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"pith_short_12","alias_value":"WJ5MNF6HF7IQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WJ5MNF6HF7IQO7IE","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WJ5MNF6H","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:b5247b7120dbbfb0beca3f3901d0810bc628b8d0f79b51c0d62e712ae6b7a901","target":"graph","created_at":"2026-05-18T02:44:08Z","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":"Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in complex space. We consider the latest variant of this which builds the complex decomposition incrementally by polynomial and produces CADs on whose cells a sequence of formulae are truth-invariant. Like all CAD algorithms the user must provide a variable ordering which can have a profound impact on the tractability of a problem. We evaluate existing heurist","authors_text":"David Wilson, James H. Davenport, Matthew England, Russell Bradford","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-05-23T15:18:19Z","title":"Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6094","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:ed9e088357dd3a4c546c4e7be4f570465140b29ec0dbf4ee243f18d7f5982f03","target":"record","created_at":"2026-05-18T02:44:08Z","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":"33f85a358aa63676d3421c612a50c6a88153e897716079250952318da756b8bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-05-23T15:18:19Z","title_canon_sha256":"892d961727c48317d3c42f877e1c2af94aa3c7c243ebe81b45b98ec423808c8b"},"schema_version":"1.0","source":{"id":"1405.6094","kind":"arxiv","version":1}},"canonical_sha256":"b27ac697c72fd1077d0436209d10abc722900b4ef91ee42952a3c77e22a052bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b27ac697c72fd1077d0436209d10abc722900b4ef91ee42952a3c77e22a052bc","first_computed_at":"2026-05-18T02:44:08.168455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:08.168455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8p1k6LC8knGxFmO2u+WfEnqfiNcLMLYXF0/PeUvqhl8Mg9SnQWe7CqCtK5d22jGHZn3pSPieiKXIqgIvuysWCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:08.168893Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed9e088357dd3a4c546c4e7be4f570465140b29ec0dbf4ee243f18d7f5982f03","sha256:b5247b7120dbbfb0beca3f3901d0810bc628b8d0f79b51c0d62e712ae6b7a901"],"state_sha256":"07609a865376c6508b66364bc0622e153f1f939ec0087cfb15e6736b88f268c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J4+zPJfApmBW/FGUg7m/Df7cu6M3akrz9rgqwxjsk4jNM8j0hYrrLCboutfsXF/nQQWKSMwHsOzJIMdv4M5yDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:27:15.106636Z","bundle_sha256":"cc917d9a8449bb0c9b23b2ff1db74574c9558121663b044f32fabb1257166bd5"}}