{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:B7GCETTW7FPI5CPRIUYSIYVEDO","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":"581b20b10d6a8243bed00f6a56607ebbc3dc248e2768b73af6776f71c94eed2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-12T10:27:27Z","title_canon_sha256":"4e1544d5c750055e863745b49e4650d3e7b78a5e8053c984c5c0dde5bc8b9ee0"},"schema_version":"1.0","source":{"id":"1812.04883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04883","created_at":"2026-05-17T23:58:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04883v1","created_at":"2026-05-17T23:58:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04883","created_at":"2026-05-17T23:58:27Z"},{"alias_kind":"pith_short_12","alias_value":"B7GCETTW7FPI","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"B7GCETTW7FPI5CPR","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"B7GCETTW","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:5ea3474f6b1976025d452890fa7d83bbb05ca8452d2b736a12776a4686bfb41d","target":"graph","created_at":"2026-05-17T23:58:27Z","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 $X\\subset \\mathbb{R}^n$ be a compact semialgebraic set and let $f:X\\to \\mathbb{R}$ be a nonzero Nash function. We give a Solern\\'o and D'Acunto-Kurdyka type estimation of the exponent $\\varrho\\in[0,1)$ in the {\\L}ojasiewicz gradient inequality $|\\nabla f(x)|\\ge C|f(x)|^\\varrho$ for $x\\in X$, $|f(x)|<\\varepsilon$ for some constants $C,\\varepsilon>0$, in terms of the degree of a polynomial $P$ such that $P(x,f(x))=0$, $x\\in X$. As a corollary we obtain an estimation of the degree of sufficiency of non-isolated Nash functions singularities","authors_text":"Beata Osi\\'nska-Ulrych, Grzegorz Skalski, Stanis{\\l}aw Spodzieja","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-12T10:27:27Z","title":"Effective {\\L}ojasiewicz gradient inequality and finite determinacy of non-isolated Nash function singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04883","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":"sha256:752209066a6b8e941a79c43bcc1fd9a04983bd615a3a1a72dd344f1e265d47ff","target":"record","created_at":"2026-05-17T23:58:27Z","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":"581b20b10d6a8243bed00f6a56607ebbc3dc248e2768b73af6776f71c94eed2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-12T10:27:27Z","title_canon_sha256":"4e1544d5c750055e863745b49e4650d3e7b78a5e8053c984c5c0dde5bc8b9ee0"},"schema_version":"1.0","source":{"id":"1812.04883","kind":"arxiv","version":1}},"canonical_sha256":"0fcc224e76f95e8e89f145312462a41b933ffcf32ab2f7d4ade07eb6678f5512","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fcc224e76f95e8e89f145312462a41b933ffcf32ab2f7d4ade07eb6678f5512","first_computed_at":"2026-05-17T23:58:27.072901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:27.072901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n9+WM13TYfazyyqPX8ytCRKKlPFtUfPp9j5VTZxyb+ftn0xXQOKE3rgKVql1dYvYw+V/CWtx47H/9U/ID+YaCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:27.073600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.04883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:752209066a6b8e941a79c43bcc1fd9a04983bd615a3a1a72dd344f1e265d47ff","sha256:5ea3474f6b1976025d452890fa7d83bbb05ca8452d2b736a12776a4686bfb41d"],"state_sha256":"f9d7f84f71530f071904850bdc0d919a8fec5e6603b93b4d93b0f2e576b97411"}