{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:N6KKKUPKYTIEFNVTZZAHMQY4LW","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":"6211f00c6233b1ececec802d7e3a243c446637e11ec0fa60007344370421569e","cross_cats_sorted":["math.CA","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-04T20:23:41Z","title_canon_sha256":"7fba68bb05c5e35a0431c14766d542a2e57b9d27bf76bce0d3044bdd7a1400e3"},"schema_version":"1.0","source":{"id":"1605.01425","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01425","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01425v2","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01425","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"N6KKKUPKYTIE","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N6KKKUPKYTIEFNVT","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N6KKKUPK","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:144b234e88b96bf20573ce62d7403a3b644c9553476c94c9858d563397f48751","target":"graph","created_at":"2026-05-18T00:41:13Z","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":"The article develops techniques for solving equations G(x,y)=0, where G(x,y)=G(x_1,...,x_n,y) is a function in a given quasianalytic class (for example, a quasianalytic Denjoy-Carleman class, or the class of infinitely differentiable functions definable in a polynomially-bounded o-minimal structure). We show that, if G(x,y)=0 has a formal power series solution y=H(x) at some point a, then H is the Taylor expansion at a of a quasianalytic solution y=h(x), where h(x) is allowed to have a certain controlled loss of regularity, depending on G. Several important questions on quasianalytic functions","authors_text":"Andre Belotto da Silva, Edward Bierstone, Iwo Biborski","cross_cats":["math.CA","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-04T20:23:41Z","title":"Solutions of quasianalytic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01425","kind":"arxiv","version":2},"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":"sha256:52c7393afd81d88793886e79a4c458b6b849b3ebb397fb911fae5676c2e50aa8","target":"record","created_at":"2026-05-18T00:41:13Z","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":"6211f00c6233b1ececec802d7e3a243c446637e11ec0fa60007344370421569e","cross_cats_sorted":["math.CA","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-04T20:23:41Z","title_canon_sha256":"7fba68bb05c5e35a0431c14766d542a2e57b9d27bf76bce0d3044bdd7a1400e3"},"schema_version":"1.0","source":{"id":"1605.01425","kind":"arxiv","version":2}},"canonical_sha256":"6f94a551eac4d042b6b3ce4076431c5da1e0fc518d2beab3c114cfdca77b3015","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f94a551eac4d042b6b3ce4076431c5da1e0fc518d2beab3c114cfdca77b3015","first_computed_at":"2026-05-18T00:41:13.034559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:13.034559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aioJGtxGBeSZtEPYegwhhpRLhsIS7yd9IDUDzN6YQFB04WGKvhdm4FPH8PlAP8fJUYKI/Q5oeYmry2G8jHpoBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:13.035300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01425","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52c7393afd81d88793886e79a4c458b6b849b3ebb397fb911fae5676c2e50aa8","sha256:144b234e88b96bf20573ce62d7403a3b644c9553476c94c9858d563397f48751"],"state_sha256":"6e91a5515492e8ca83e84e3e994489ed503c1b3370171096730898f2a90fcc54"}