{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:IDWBG44A3W6L3H35LATZP6NGRL","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":"4be6e8f42301ff59535fbad777aa7e9c7dcc7792dee72c4f5d54a9e7c212e050","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-06-24T14:54:07Z","title_canon_sha256":"1036ebbe093b95ca6c90516427ab9f2f910c8a07667636fd3d1742174553e641"},"schema_version":"1.0","source":{"id":"0806.3911","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.3911","created_at":"2026-05-18T04:39:00Z"},{"alias_kind":"arxiv_version","alias_value":"0806.3911v1","created_at":"2026-05-18T04:39:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.3911","created_at":"2026-05-18T04:39:00Z"},{"alias_kind":"pith_short_12","alias_value":"IDWBG44A3W6L","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"IDWBG44A3W6L3H35","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"IDWBG44A","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:391280953250ef9a4caba973c26b113392fad327417ca2dced58b7df54638c0e","target":"graph","created_at":"2026-05-18T04:39:00Z","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":"Let $\\R$ be a real closed field, $ {\\mathcal Q} \\subset \\R[Y_1,...,Y_\\ell,X_1,...,X_k], $ with $ \\deg_{Y}(Q) \\leq 2, \\deg_{X}(Q) \\leq d, Q \\in {\\mathcal Q}, #({\\mathcal Q})=m$, and $ {\\mathcal P} \\subset \\R[X_1,...,X_k] $ with $\\deg_{X}(P) \\leq d, P \\in {\\mathcal P}, #({\\mathcal P})=s$. Let $S \\subset \\R^{\\ell+k}$ be a semi-algebraic set defined by a Boolean formula without negations, with atoms $P=0, P \\geq 0, P \\leq 0, P \\in {\\mathcal P} \\cup {\\mathcal Q}$. We describe an algorithm for computing the the Betti numbers of $S$. The complexity of the algorithm is bounded by $(\\ell s m d)^{2^{O(m","authors_text":"Dmitrii V. Pasechnik, Marie-Fran\\c{c}oise Roy, Saugata Basu","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-06-24T14:54:07Z","title":"Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.3911","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":"sha256:9e0b3ee73df0bd05c33e076a16fa962ea23af5f18962f5bc6dc0a4f055e02b19","target":"record","created_at":"2026-05-18T04:39:00Z","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":"4be6e8f42301ff59535fbad777aa7e9c7dcc7792dee72c4f5d54a9e7c212e050","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-06-24T14:54:07Z","title_canon_sha256":"1036ebbe093b95ca6c90516427ab9f2f910c8a07667636fd3d1742174553e641"},"schema_version":"1.0","source":{"id":"0806.3911","kind":"arxiv","version":1}},"canonical_sha256":"40ec137380ddbcbd9f7d582797f9a68aed8caeecfb31f4de59d4487325f79ac6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40ec137380ddbcbd9f7d582797f9a68aed8caeecfb31f4de59d4487325f79ac6","first_computed_at":"2026-05-18T04:39:00.299462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:00.299462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7pA5k0wnoedl5LwrUW+7R6hlt0w85KerA1q4Vt7WBeyo7xOwg1pJIPL+o36iyTT3L5OGiW3rtbldIKFfeuK+Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:00.299961Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.3911","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e0b3ee73df0bd05c33e076a16fa962ea23af5f18962f5bc6dc0a4f055e02b19","sha256:391280953250ef9a4caba973c26b113392fad327417ca2dced58b7df54638c0e"],"state_sha256":"678655c0ac1feb7aad78e79edc855a716ebca6fb74e35ab2f08484437beb62b3"}