{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5GII2QHQS2IUWAUJHBAJTGGHBK","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":"6521a594e143670aea8ce4a0828ace03aab9ed94a4c62f89ccbbc0f70a1c0807","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-01-11T08:50:17Z","title_canon_sha256":"b091944c5948fba562e332227209d0b11a23cbe69a6b8761814cbcd2ab23149f"},"schema_version":"1.0","source":{"id":"1301.2419","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2419","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2419v1","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2419","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"5GII2QHQS2IU","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5GII2QHQS2IUWAUJ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5GII2QHQ","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:eaa0f906c30e7dba8db9e2c4dc6a0ef2fbb1bff49d33314d5066e952b79d29a4","target":"graph","created_at":"2026-05-18T03:36:37Z","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 prove a Lojasiewicz type inequality for a system of polynomial equations with coefficients in the ring of formal power series in two variables. This result is an effective version of the Strong Artin Approximation Theorem. From this result we deduce a bound of Artin functions of isolated singularities.","authors_text":"Guillaume Rond","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-01-11T08:50:17Z","title":"Lojasiewicz inequality over the ring of power series in two variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2419","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:d616ee31c890d798ccdf858cb2add923c04fa755cd4d050c767953cc28ba4bb5","target":"record","created_at":"2026-05-18T03:36:37Z","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":"6521a594e143670aea8ce4a0828ace03aab9ed94a4c62f89ccbbc0f70a1c0807","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-01-11T08:50:17Z","title_canon_sha256":"b091944c5948fba562e332227209d0b11a23cbe69a6b8761814cbcd2ab23149f"},"schema_version":"1.0","source":{"id":"1301.2419","kind":"arxiv","version":1}},"canonical_sha256":"e9908d40f096914b028938409998c70ab4bf7736a8d7c126b1d199e1778b4a25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9908d40f096914b028938409998c70ab4bf7736a8d7c126b1d199e1778b4a25","first_computed_at":"2026-05-18T03:36:37.986036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:37.986036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MMT0creHK/EqdfnhZ6esiKhCjrnnNX3kUT0BZ6jTt+B3PLV+Q8MEWbXtlj2jB8cI9ldtEdIUpRgRQrEGzD4TDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:37.986628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2419","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d616ee31c890d798ccdf858cb2add923c04fa755cd4d050c767953cc28ba4bb5","sha256:eaa0f906c30e7dba8db9e2c4dc6a0ef2fbb1bff49d33314d5066e952b79d29a4"],"state_sha256":"9ee69f3f613d0218310f32140ccc3fc9fdcf590ada87983109abbc9ad0712cbd"}