{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7TUR6QU4ZVROINJRY3RYXOYL2Z","short_pith_number":"pith:7TUR6QU4","schema_version":"1.0","canonical_sha256":"fce91f429ccd62e43531c6e38bbb0bd649d13737b67ba9e40a12744d00c9cf59","source":{"kind":"arxiv","id":"1103.2559","version":2},"attestation_state":"computed","paper":{"title":"The Abhyankar-Jung Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Adam Parusinski, Guillaume Rond","submitted_at":"2011-03-13T22:20:14Z","abstract_excerpt":"We show that every quasi-ordinary Weierstrass polynomial $P(Z) = Z^d+a_1 (X) Z^{d-1}+...+a_d(X) \\in \\K[[X]][Z] $, $X=(X_1,..., X_n)$, over an algebraically closed field of characterisic zero $\\K$, and satisfying $a_1=0$, is $\\nu$-quasi-ordinary. That means that if the discriminant $\\Delta_P \\in \\K[[X]]$ is equal to a monomial times a unit then the ideal $(a_i^{d!/i}(X))_{i=2,...,d}$ is principal and generated by a monomial. We use this result to give a constructive proof of the Abhyankar-Jung Theorem that works for any Henselian local subring of $\\K[[X]]$ and the function germs of quasi-analyt"},"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":"1103.2559","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-03-13T22:20:14Z","cross_cats_sorted":[],"title_canon_sha256":"4925534e198860c4cb742a60445f3d649ea05e2d6175d9c82f75bc0804b788f0","abstract_canon_sha256":"d69a8819768d05c5eeb6feed242ec1830d3efb1dead7c4c000f353e6c71ae7ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:02.919118Z","signature_b64":"XiQd5B/1UDPsOp04Rr8WbZdf0NcEAgIplqhbwaYL1UAbQEqtZxJoCW0NpHAxZ1PWvV0Ybc7irUhNDgnfeevjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fce91f429ccd62e43531c6e38bbb0bd649d13737b67ba9e40a12744d00c9cf59","last_reissued_at":"2026-05-18T03:55:02.918630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:02.918630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Abhyankar-Jung Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Adam Parusinski, Guillaume Rond","submitted_at":"2011-03-13T22:20:14Z","abstract_excerpt":"We show that every quasi-ordinary Weierstrass polynomial $P(Z) = Z^d+a_1 (X) Z^{d-1}+...+a_d(X) \\in \\K[[X]][Z] $, $X=(X_1,..., X_n)$, over an algebraically closed field of characterisic zero $\\K$, and satisfying $a_1=0$, is $\\nu$-quasi-ordinary. That means that if the discriminant $\\Delta_P \\in \\K[[X]]$ is equal to a monomial times a unit then the ideal $(a_i^{d!/i}(X))_{i=2,...,d}$ is principal and generated by a monomial. We use this result to give a constructive proof of the Abhyankar-Jung Theorem that works for any Henselian local subring of $\\K[[X]]$ and the function germs of quasi-analyt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2559","kind":"arxiv","version":2},"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":"1103.2559","created_at":"2026-05-18T03:55:02.918706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.2559v2","created_at":"2026-05-18T03:55:02.918706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2559","created_at":"2026-05-18T03:55:02.918706+00:00"},{"alias_kind":"pith_short_12","alias_value":"7TUR6QU4ZVRO","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7TUR6QU4ZVROINJR","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7TUR6QU4","created_at":"2026-05-18T12:26:22.705136+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/7TUR6QU4ZVROINJRY3RYXOYL2Z","json":"https://pith.science/pith/7TUR6QU4ZVROINJRY3RYXOYL2Z.json","graph_json":"https://pith.science/api/pith-number/7TUR6QU4ZVROINJRY3RYXOYL2Z/graph.json","events_json":"https://pith.science/api/pith-number/7TUR6QU4ZVROINJRY3RYXOYL2Z/events.json","paper":"https://pith.science/paper/7TUR6QU4"},"agent_actions":{"view_html":"https://pith.science/pith/7TUR6QU4ZVROINJRY3RYXOYL2Z","download_json":"https://pith.science/pith/7TUR6QU4ZVROINJRY3RYXOYL2Z.json","view_paper":"https://pith.science/paper/7TUR6QU4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.2559&json=true","fetch_graph":"https://pith.science/api/pith-number/7TUR6QU4ZVROINJRY3RYXOYL2Z/graph.json","fetch_events":"https://pith.science/api/pith-number/7TUR6QU4ZVROINJRY3RYXOYL2Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7TUR6QU4ZVROINJRY3RYXOYL2Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7TUR6QU4ZVROINJRY3RYXOYL2Z/action/storage_attestation","attest_author":"https://pith.science/pith/7TUR6QU4ZVROINJRY3RYXOYL2Z/action/author_attestation","sign_citation":"https://pith.science/pith/7TUR6QU4ZVROINJRY3RYXOYL2Z/action/citation_signature","submit_replication":"https://pith.science/pith/7TUR6QU4ZVROINJRY3RYXOYL2Z/action/replication_record"}},"created_at":"2026-05-18T03:55:02.918706+00:00","updated_at":"2026-05-18T03:55:02.918706+00:00"}