{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3CO7XR7GCADFWOCIT6ZVCCRFLI","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":"01b93ebbcc929e97548a57288f52877c25c24fb93b33722502ce4b6fb8458026","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-24T14:14:38Z","title_canon_sha256":"8e4547dbdde2139e317f77ce94b818f46f638bc21b356dfd4e2de09eced5f86b"},"schema_version":"1.0","source":{"id":"1608.06828","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06828","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06828v3","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06828","created_at":"2026-05-18T00:40:28Z"},{"alias_kind":"pith_short_12","alias_value":"3CO7XR7GCADF","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3CO7XR7GCADFWOCI","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3CO7XR7G","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:0bfee06349bb19d5f11983538ee07fcc8ec5809f8ebe4f0eccc12a4655a64399","target":"graph","created_at":"2026-05-18T00:40:28Z","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 $\\mathrm{R}$ be a real closed field and $\\mathrm{D} \\subset \\mathrm{R}$ an ordered domain. We consider the algorithmic problem of computing the generalized Euler-Poincar\\'e characteristic of real algebraic as well as semi-algebraic subsets of $\\mathrm{R}^k$, which are defined by symmetric polynomials with coefficients in $\\mathrm{D}$. We give algorithms for computing the generalized Euler-Poincar\\'e characteristic of such sets, whose complexities measured by the number the number of arithmetic operations in $\\mathrm{D}$, are polynomially bounded in terms of $k$ and the number of polynomial","authors_text":"Cordian Riener, Saugata Basu","cross_cats":["cs.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-24T14:14:38Z","title":"Efficient algorithms for computing the Euler-Poincar\\'e characteristic of symmetric semi-algebraic sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06828","kind":"arxiv","version":3},"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":"sha256:6f277e9560131f6a07350a2ba6340fe71ce3d9e8851ccc905fb8a6af4dd0748f","target":"record","created_at":"2026-05-18T00:40:28Z","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":"01b93ebbcc929e97548a57288f52877c25c24fb93b33722502ce4b6fb8458026","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-24T14:14:38Z","title_canon_sha256":"8e4547dbdde2139e317f77ce94b818f46f638bc21b356dfd4e2de09eced5f86b"},"schema_version":"1.0","source":{"id":"1608.06828","kind":"arxiv","version":3}},"canonical_sha256":"d89dfbc7e610065b38489fb3510a255a09307444be1b0778c4571685ba8a829d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d89dfbc7e610065b38489fb3510a255a09307444be1b0778c4571685ba8a829d","first_computed_at":"2026-05-18T00:40:28.795917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:28.795917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"el5T5pMKWhP6GqoveUmqX+o+T4vi5/j5yerQA3k81948G/kgj13sXgnfPbEBw71Gp4R6sKOb23EqfULeSLE+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:28.796684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06828","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f277e9560131f6a07350a2ba6340fe71ce3d9e8851ccc905fb8a6af4dd0748f","sha256:0bfee06349bb19d5f11983538ee07fcc8ec5809f8ebe4f0eccc12a4655a64399"],"state_sha256":"f83174386421eb958a9a9f1b48d74803ceae52b8a5f7f7430c89bc72b97809cb"}