{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:TK4U6M7PQQ3FICBJ4XKHLC34O4","short_pith_number":"pith:TK4U6M7P","schema_version":"1.0","canonical_sha256":"9ab94f33ef8436540829e5d4758b7c773d7de03f55825730dc6f1c715f32968b","source":{"kind":"arxiv","id":"2606.22587","version":1},"attestation_state":"computed","paper":{"title":"Jacobian algebras and variation of hyperplane sections","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abbas Nasrollah Nejad, Giovanna Ilardi, Saeed Tafazolian","submitted_at":"2026-06-21T16:49:57Z","abstract_excerpt":"We study the variation in moduli of hyperplane sections of a hypersurface $V(f)\\subseteq \\mathbf P^n$ with at most isolated singularities. Using the Milnor algebra $M(f)$, we give an infinitesimal quotient criterion for the hyperplane-section map $\\Phi(f):(\\mathbf P^n)^*\\dashrightarrow M(d,n-1)$ to be generically finite onto its image. The passage from the infinitesimal quotient to the coarse moduli space is justified by a local GIT slice argument. Our approach gives a Jacobian-algebraic extension of the Beauville--Patel--Riedl--Tseng theory from smooth hypersurfaces to hypersurfaces with isol"},"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":"2606.22587","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-21T16:49:57Z","cross_cats_sorted":[],"title_canon_sha256":"5c2d82f13f2d3bc67fdaf80f25371060611ce56b1d4e4aadab4ab0bb34fc3658","abstract_canon_sha256":"3d17e8f80457fe6adedba56a9613a7464d8ae50cdbf9d5782049ced5e80ad37d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:42.255717Z","signature_b64":"UjTOZbVrsmlsg/ViOBf/Tj3bI8Y/u+sX6Nrg1NIF078lLY/MsWgFe3nfYNq+/x9wdMDDEommX8SF67vLRd1JBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ab94f33ef8436540829e5d4758b7c773d7de03f55825730dc6f1c715f32968b","last_reissued_at":"2026-06-23T02:13:42.255335Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:42.255335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Jacobian algebras and variation of hyperplane sections","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abbas Nasrollah Nejad, Giovanna Ilardi, Saeed Tafazolian","submitted_at":"2026-06-21T16:49:57Z","abstract_excerpt":"We study the variation in moduli of hyperplane sections of a hypersurface $V(f)\\subseteq \\mathbf P^n$ with at most isolated singularities. Using the Milnor algebra $M(f)$, we give an infinitesimal quotient criterion for the hyperplane-section map $\\Phi(f):(\\mathbf P^n)^*\\dashrightarrow M(d,n-1)$ to be generically finite onto its image. The passage from the infinitesimal quotient to the coarse moduli space is justified by a local GIT slice argument. Our approach gives a Jacobian-algebraic extension of the Beauville--Patel--Riedl--Tseng theory from smooth hypersurfaces to hypersurfaces with isol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22587","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22587/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.22587","created_at":"2026-06-23T02:13:42.255406+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.22587v1","created_at":"2026-06-23T02:13:42.255406+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22587","created_at":"2026-06-23T02:13:42.255406+00:00"},{"alias_kind":"pith_short_12","alias_value":"TK4U6M7PQQ3F","created_at":"2026-06-23T02:13:42.255406+00:00"},{"alias_kind":"pith_short_16","alias_value":"TK4U6M7PQQ3FICBJ","created_at":"2026-06-23T02:13:42.255406+00:00"},{"alias_kind":"pith_short_8","alias_value":"TK4U6M7P","created_at":"2026-06-23T02:13:42.255406+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/TK4U6M7PQQ3FICBJ4XKHLC34O4","json":"https://pith.science/pith/TK4U6M7PQQ3FICBJ4XKHLC34O4.json","graph_json":"https://pith.science/api/pith-number/TK4U6M7PQQ3FICBJ4XKHLC34O4/graph.json","events_json":"https://pith.science/api/pith-number/TK4U6M7PQQ3FICBJ4XKHLC34O4/events.json","paper":"https://pith.science/paper/TK4U6M7P"},"agent_actions":{"view_html":"https://pith.science/pith/TK4U6M7PQQ3FICBJ4XKHLC34O4","download_json":"https://pith.science/pith/TK4U6M7PQQ3FICBJ4XKHLC34O4.json","view_paper":"https://pith.science/paper/TK4U6M7P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.22587&json=true","fetch_graph":"https://pith.science/api/pith-number/TK4U6M7PQQ3FICBJ4XKHLC34O4/graph.json","fetch_events":"https://pith.science/api/pith-number/TK4U6M7PQQ3FICBJ4XKHLC34O4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TK4U6M7PQQ3FICBJ4XKHLC34O4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TK4U6M7PQQ3FICBJ4XKHLC34O4/action/storage_attestation","attest_author":"https://pith.science/pith/TK4U6M7PQQ3FICBJ4XKHLC34O4/action/author_attestation","sign_citation":"https://pith.science/pith/TK4U6M7PQQ3FICBJ4XKHLC34O4/action/citation_signature","submit_replication":"https://pith.science/pith/TK4U6M7PQQ3FICBJ4XKHLC34O4/action/replication_record"}},"created_at":"2026-06-23T02:13:42.255406+00:00","updated_at":"2026-06-23T02:13:42.255406+00:00"}