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Given a family y=\\phi_{s}(t,x)=sb_{1}(x)t+b_{2}(x)t^{2}+... of analytic curves in C\\timesC^{n} passing through the origin, Conv_{\\phi}(f) of a formal power series f(y,t,x)\\inC[[y,t,x]] is defined to be the set of all s\\inC for which the power series f(\\phi_{s}(t,x),t,x) converges as a series in (t,x). We prove that for a subset E\\subsetC there exists a divergent formal power series f(y,t,x)\\inC[[y,t,x]] such that E=Conv_{\\phi}(f) if and only if E is a F_{{\\sigma}} set of zero ca"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1104.1778","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-04-10T15:35:53Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"377d7d69ed87ac3e3fd954786e9956a07833f73d925bc571bf3944974a849cf9","abstract_canon_sha256":"2505136b9c3bff7855835305cccafacd0f081574569baaaad0e405ab1d3acaed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:03.964629Z","signature_b64":"PN/ldzysJCWPkcWhRhk0S+ic4uio1sMBH3wlqPeMKUEpZcdC8OZh3ucddvggA1qdEnNw4Y70XMtmpA42CwYlBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac06fda7d30024e1ba7072c329aab426e93b317190a971f3b7ef56cee2e21960","last_reissued_at":"2026-05-18T04:15:03.963924Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:03.963924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear Convergence Sets of Divergent Power Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Buma L. Fridman, Daowei Ma, Tejinder Neelon","submitted_at":"2011-04-10T15:35:53Z","abstract_excerpt":"A nonlinear generalization of convergence sets of formal power series, in the sense of Abhyankar-Moh, is introduced. Given a family y=\\phi_{s}(t,x)=sb_{1}(x)t+b_{2}(x)t^{2}+... of analytic curves in C\\timesC^{n} passing through the origin, Conv_{\\phi}(f) of a formal power series f(y,t,x)\\inC[[y,t,x]] is defined to be the set of all s\\inC for which the power series f(\\phi_{s}(t,x),t,x) converges as a series in (t,x). We prove that for a subset E\\subsetC there exists a divergent formal power series f(y,t,x)\\inC[[y,t,x]] such that E=Conv_{\\phi}(f) if and only if E is a F_{{\\sigma}} set of zero ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1778","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1104.1778","created_at":"2026-05-18T04:15:03.964011+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.1778v5","created_at":"2026-05-18T04:15:03.964011+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1778","created_at":"2026-05-18T04:15:03.964011+00:00"},{"alias_kind":"pith_short_12","alias_value":"VQDP3J6TAASO","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"VQDP3J6TAASODOTQ","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"VQDP3J6T","created_at":"2026-05-18T12:26:44.992195+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VQDP3J6TAASODOTQOLBSTKVUE3","json":"https://pith.science/pith/VQDP3J6TAASODOTQOLBSTKVUE3.json","graph_json":"https://pith.science/api/pith-number/VQDP3J6TAASODOTQOLBSTKVUE3/graph.json","events_json":"https://pith.science/api/pith-number/VQDP3J6TAASODOTQOLBSTKVUE3/events.json","paper":"https://pith.science/paper/VQDP3J6T"},"agent_actions":{"view_html":"https://pith.science/pith/VQDP3J6TAASODOTQOLBSTKVUE3","download_json":"https://pith.science/pith/VQDP3J6TAASODOTQOLBSTKVUE3.json","view_paper":"https://pith.science/paper/VQDP3J6T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.1778&json=true","fetch_graph":"https://pith.science/api/pith-number/VQDP3J6TAASODOTQOLBSTKVUE3/graph.json","fetch_events":"https://pith.science/api/pith-number/VQDP3J6TAASODOTQOLBSTKVUE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VQDP3J6TAASODOTQOLBSTKVUE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VQDP3J6TAASODOTQOLBSTKVUE3/action/storage_attestation","attest_author":"https://pith.science/pith/VQDP3J6TAASODOTQOLBSTKVUE3/action/author_attestation","sign_citation":"https://pith.science/pith/VQDP3J6TAASODOTQOLBSTKVUE3/action/citation_signature","submit_replication":"https://pith.science/pith/VQDP3J6TAASODOTQOLBSTKVUE3/action/replication_record"}},"created_at":"2026-05-18T04:15:03.964011+00:00","updated_at":"2026-05-18T04:15:03.964011+00:00"}