{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:LXTM47SAIR4UX3276Q3MOQTV3H","short_pith_number":"pith:LXTM47SA","schema_version":"1.0","canonical_sha256":"5de6ce7e4044794bef5ff436c74275d9ce1f40df5e60490c3df843e5bed00fb0","source":{"kind":"arxiv","id":"1908.04819","version":2},"attestation_state":"computed","paper":{"title":"Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Austyn Simpson, Rankeya Datta","submitted_at":"2019-08-13T18:47:26Z","abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic $p > 0$. We show that if $X\\subseteq\\mathbb{P}^n_k$ is an equidimensional subscheme with Hilbert--Kunz multiplicity less than $\\lambda$ at all points $x\\in X$, then for a general hyperplane $H\\subseteq\\mathbb{P}^n_k$, the Hilbert--Kunz multiplicity of $X\\cap H$ is less than $\\lambda$ at all points $x\\in X\\cap H$. This answers a conjecture and generalizes a result of Carvajal-Rojas, Schwede and Tucker, whose conclusion is the same as ours when $X\\subseteq\\mathbb{P}^n_k$ is normal. In the process, we substantially generalize certain unif"},"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":"1908.04819","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-13T18:47:26Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"6b0d283b68f3547744a636aa665db1aaeb65baba665a2e0bb998a70ce3d20988","abstract_canon_sha256":"d2bfc12575128f6d1006942df8f9e5b85524f8987d8ca0cfe512a4e2a4b660c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:49:37.603247Z","signature_b64":"tF2xKZ4Xtw+AkwKXePeeYK8MURNVAIiyoJDqDiKr1+ssWAuOnFRiGPw7EXniwOV/8GhanFFdYOilajWqdSKtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5de6ce7e4044794bef5ff436c74275d9ce1f40df5e60490c3df843e5bed00fb0","last_reissued_at":"2026-07-05T00:49:37.602776Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:49:37.602776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Austyn Simpson, Rankeya Datta","submitted_at":"2019-08-13T18:47:26Z","abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic $p > 0$. We show that if $X\\subseteq\\mathbb{P}^n_k$ is an equidimensional subscheme with Hilbert--Kunz multiplicity less than $\\lambda$ at all points $x\\in X$, then for a general hyperplane $H\\subseteq\\mathbb{P}^n_k$, the Hilbert--Kunz multiplicity of $X\\cap H$ is less than $\\lambda$ at all points $x\\in X\\cap H$. This answers a conjecture and generalizes a result of Carvajal-Rojas, Schwede and Tucker, whose conclusion is the same as ours when $X\\subseteq\\mathbb{P}^n_k$ is normal. In the process, we substantially generalize certain unif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04819","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04819/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":"1908.04819","created_at":"2026-07-05T00:49:37.602836+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.04819v2","created_at":"2026-07-05T00:49:37.602836+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04819","created_at":"2026-07-05T00:49:37.602836+00:00"},{"alias_kind":"pith_short_12","alias_value":"LXTM47SAIR4U","created_at":"2026-07-05T00:49:37.602836+00:00"},{"alias_kind":"pith_short_16","alias_value":"LXTM47SAIR4UX327","created_at":"2026-07-05T00:49:37.602836+00:00"},{"alias_kind":"pith_short_8","alias_value":"LXTM47SA","created_at":"2026-07-05T00:49:37.602836+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/LXTM47SAIR4UX3276Q3MOQTV3H","json":"https://pith.science/pith/LXTM47SAIR4UX3276Q3MOQTV3H.json","graph_json":"https://pith.science/api/pith-number/LXTM47SAIR4UX3276Q3MOQTV3H/graph.json","events_json":"https://pith.science/api/pith-number/LXTM47SAIR4UX3276Q3MOQTV3H/events.json","paper":"https://pith.science/paper/LXTM47SA"},"agent_actions":{"view_html":"https://pith.science/pith/LXTM47SAIR4UX3276Q3MOQTV3H","download_json":"https://pith.science/pith/LXTM47SAIR4UX3276Q3MOQTV3H.json","view_paper":"https://pith.science/paper/LXTM47SA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.04819&json=true","fetch_graph":"https://pith.science/api/pith-number/LXTM47SAIR4UX3276Q3MOQTV3H/graph.json","fetch_events":"https://pith.science/api/pith-number/LXTM47SAIR4UX3276Q3MOQTV3H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LXTM47SAIR4UX3276Q3MOQTV3H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LXTM47SAIR4UX3276Q3MOQTV3H/action/storage_attestation","attest_author":"https://pith.science/pith/LXTM47SAIR4UX3276Q3MOQTV3H/action/author_attestation","sign_citation":"https://pith.science/pith/LXTM47SAIR4UX3276Q3MOQTV3H/action/citation_signature","submit_replication":"https://pith.science/pith/LXTM47SAIR4UX3276Q3MOQTV3H/action/replication_record"}},"created_at":"2026-07-05T00:49:37.602836+00:00","updated_at":"2026-07-05T00:49:37.602836+00:00"}