{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:EYUGADEMC3ZRGMRMBKQHTYFS6S","short_pith_number":"pith:EYUGADEM","schema_version":"1.0","canonical_sha256":"2628600c8c16f313322c0aa079e0b2f494c63e4af53e69bff1553073d1d756b2","source":{"kind":"arxiv","id":"1510.03480","version":2},"attestation_state":"computed","paper":{"title":"Singular implicit and inverse function theorems. Strong resolution with normally flat centers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Jaroslaw Wlodarczyk","submitted_at":"2015-10-12T23:00:14Z","abstract_excerpt":"Building upon ideas of Hironaka, Bierstone-Milman, Malgrange and others we generalize the inverse and implicit function theorem (in differential, analytic and algebraic setting) to sets of functions of larger multiplicities (or ideals). This allows one to describe singularities given by a finite set of generators or by ideals in a simpler form. In the special Cohen-Macaulay case we obtain a singular analog of the inverse function theorem. The singular implicit function theorem is closely related to a (proven here) extended version of the Weierstrass-Hironaka-Malgrange division and preparation "},"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":"1510.03480","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-12T23:00:14Z","cross_cats_sorted":["math.AC","math.CV","math.DG"],"title_canon_sha256":"30a000a035348cc38170055a7d85c43d4291e4524f2d51bab6dc2af38f4a0700","abstract_canon_sha256":"e96b91ea1b006866a5df1701540ebd935663fbe3e6a5de6545449474bc5ff9b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:00.861928Z","signature_b64":"CGj1wNx83+LDlu3/UTuEG4K4rQE1+hurqKW8re1Ap67DwAdZc4DdLR+3gNHpeHm+OKjNzScisO+HgOMdZcV3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2628600c8c16f313322c0aa079e0b2f494c63e4af53e69bff1553073d1d756b2","last_reissued_at":"2026-05-18T01:21:00.861398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:00.861398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singular implicit and inverse function theorems. Strong resolution with normally flat centers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Jaroslaw Wlodarczyk","submitted_at":"2015-10-12T23:00:14Z","abstract_excerpt":"Building upon ideas of Hironaka, Bierstone-Milman, Malgrange and others we generalize the inverse and implicit function theorem (in differential, analytic and algebraic setting) to sets of functions of larger multiplicities (or ideals). This allows one to describe singularities given by a finite set of generators or by ideals in a simpler form. In the special Cohen-Macaulay case we obtain a singular analog of the inverse function theorem. The singular implicit function theorem is closely related to a (proven here) extended version of the Weierstrass-Hironaka-Malgrange division and preparation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03480","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":"1510.03480","created_at":"2026-05-18T01:21:00.861492+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.03480v2","created_at":"2026-05-18T01:21:00.861492+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03480","created_at":"2026-05-18T01:21:00.861492+00:00"},{"alias_kind":"pith_short_12","alias_value":"EYUGADEMC3ZR","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"EYUGADEMC3ZRGMRM","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"EYUGADEM","created_at":"2026-05-18T12:29:19.899920+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/EYUGADEMC3ZRGMRMBKQHTYFS6S","json":"https://pith.science/pith/EYUGADEMC3ZRGMRMBKQHTYFS6S.json","graph_json":"https://pith.science/api/pith-number/EYUGADEMC3ZRGMRMBKQHTYFS6S/graph.json","events_json":"https://pith.science/api/pith-number/EYUGADEMC3ZRGMRMBKQHTYFS6S/events.json","paper":"https://pith.science/paper/EYUGADEM"},"agent_actions":{"view_html":"https://pith.science/pith/EYUGADEMC3ZRGMRMBKQHTYFS6S","download_json":"https://pith.science/pith/EYUGADEMC3ZRGMRMBKQHTYFS6S.json","view_paper":"https://pith.science/paper/EYUGADEM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.03480&json=true","fetch_graph":"https://pith.science/api/pith-number/EYUGADEMC3ZRGMRMBKQHTYFS6S/graph.json","fetch_events":"https://pith.science/api/pith-number/EYUGADEMC3ZRGMRMBKQHTYFS6S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EYUGADEMC3ZRGMRMBKQHTYFS6S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EYUGADEMC3ZRGMRMBKQHTYFS6S/action/storage_attestation","attest_author":"https://pith.science/pith/EYUGADEMC3ZRGMRMBKQHTYFS6S/action/author_attestation","sign_citation":"https://pith.science/pith/EYUGADEMC3ZRGMRMBKQHTYFS6S/action/citation_signature","submit_replication":"https://pith.science/pith/EYUGADEMC3ZRGMRMBKQHTYFS6S/action/replication_record"}},"created_at":"2026-05-18T01:21:00.861492+00:00","updated_at":"2026-05-18T01:21:00.861492+00:00"}