{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:ZWDNUEAGKL6ZAQFN7K73F2YV6V","short_pith_number":"pith:ZWDNUEAG","schema_version":"1.0","canonical_sha256":"cd86da100652fd9040adfabfb2eb15f56f3852430c28d04564815680148e33cc","source":{"kind":"arxiv","id":"1007.0170","version":2},"attestation_state":"computed","paper":{"title":"Normal Forms of Hypersurface Singularities in Positive Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Gert-Martin Greuel, Thomas Markwig, Yousra Boubakri","submitted_at":"2010-07-01T14:00:15Z","abstract_excerpt":"The main purpose of this article is to lay the foundations for a classification of isolated hypersurface singularities in positive characteristic. Although our article is in the spirit of Arnol'd who classified real an complex hypersurfaces in the 1970's with respect to right equivalence, several new phenomena occur in positive characteristic. Already the notion of isolated singularity is different for right resp. contact equivalence over fields of characteristic other than zero. The heart of this paper consists of the study of different notions of non-degeneracy and the associated piecewise f"},"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":"1007.0170","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-01T14:00:15Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"0fcb29238929ab01b25095a2be724588c389ce57aa9e2b4e2df93be8be5ea989","abstract_canon_sha256":"115d094f7b001cb7ed6f9a734cb74587f7fe5ee40fead12ed68c48fa37f4356e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:47.671995Z","signature_b64":"9J9YHzAOq6ZWGkJG041xmB/+Odn1SvCrwGNRj9wurBdiSe38LFZVMQ5frvsY8v6BktrQQvlIceFDSO4+ZH7HDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd86da100652fd9040adfabfb2eb15f56f3852430c28d04564815680148e33cc","last_reissued_at":"2026-05-18T04:35:47.671499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:47.671499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Normal Forms of Hypersurface Singularities in Positive Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Gert-Martin Greuel, Thomas Markwig, Yousra Boubakri","submitted_at":"2010-07-01T14:00:15Z","abstract_excerpt":"The main purpose of this article is to lay the foundations for a classification of isolated hypersurface singularities in positive characteristic. Although our article is in the spirit of Arnol'd who classified real an complex hypersurfaces in the 1970's with respect to right equivalence, several new phenomena occur in positive characteristic. Already the notion of isolated singularity is different for right resp. contact equivalence over fields of characteristic other than zero. The heart of this paper consists of the study of different notions of non-degeneracy and the associated piecewise f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0170","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":"1007.0170","created_at":"2026-05-18T04:35:47.671584+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.0170v2","created_at":"2026-05-18T04:35:47.671584+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0170","created_at":"2026-05-18T04:35:47.671584+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZWDNUEAGKL6Z","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZWDNUEAGKL6ZAQFN","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZWDNUEAG","created_at":"2026-05-18T12:26:18.847500+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/ZWDNUEAGKL6ZAQFN7K73F2YV6V","json":"https://pith.science/pith/ZWDNUEAGKL6ZAQFN7K73F2YV6V.json","graph_json":"https://pith.science/api/pith-number/ZWDNUEAGKL6ZAQFN7K73F2YV6V/graph.json","events_json":"https://pith.science/api/pith-number/ZWDNUEAGKL6ZAQFN7K73F2YV6V/events.json","paper":"https://pith.science/paper/ZWDNUEAG"},"agent_actions":{"view_html":"https://pith.science/pith/ZWDNUEAGKL6ZAQFN7K73F2YV6V","download_json":"https://pith.science/pith/ZWDNUEAGKL6ZAQFN7K73F2YV6V.json","view_paper":"https://pith.science/paper/ZWDNUEAG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.0170&json=true","fetch_graph":"https://pith.science/api/pith-number/ZWDNUEAGKL6ZAQFN7K73F2YV6V/graph.json","fetch_events":"https://pith.science/api/pith-number/ZWDNUEAGKL6ZAQFN7K73F2YV6V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZWDNUEAGKL6ZAQFN7K73F2YV6V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZWDNUEAGKL6ZAQFN7K73F2YV6V/action/storage_attestation","attest_author":"https://pith.science/pith/ZWDNUEAGKL6ZAQFN7K73F2YV6V/action/author_attestation","sign_citation":"https://pith.science/pith/ZWDNUEAGKL6ZAQFN7K73F2YV6V/action/citation_signature","submit_replication":"https://pith.science/pith/ZWDNUEAGKL6ZAQFN7K73F2YV6V/action/replication_record"}},"created_at":"2026-05-18T04:35:47.671584+00:00","updated_at":"2026-05-18T04:35:47.671584+00:00"}