{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:HRAR54QNC2XQSIAXKHSPE5HWA3","short_pith_number":"pith:HRAR54QN","schema_version":"1.0","canonical_sha256":"3c411ef20d16af09201751e4f274f606ced292c8ad28d5c98a21dfbf039184a2","source":{"kind":"arxiv","id":"2606.09693","version":1},"attestation_state":"computed","paper":{"title":"Bertini theorems for Hilbert-Samuel multiplicity over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"math.AG","authors_text":"Matthew Bertucci, Rahul Ajit","submitted_at":"2026-06-08T16:10:57Z","abstract_excerpt":"Let $X\\subseteq \\mathbb{P}^n_{\\mathbb{F}_q}$ be a reduced, equidimensional, quasiprojective scheme. We prove that there exists a positive-density set of hypersurfaces $H_f$ such that for every closed point $P\\in X\\cap H_f$, one has $\\mathrm{ord}_P(f)=1$ and $e_P(X\\cap H_f)=e_P(X)$."},"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":"2606.09693","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-08T16:10:57Z","cross_cats_sorted":["math.AC","math.NT"],"title_canon_sha256":"83fc3decf6a9bebf96d752a5eb560163b043ac7abc7bd5a3545bc20d35396ea9","abstract_canon_sha256":"acbeaac1849b7b38eade67d70caa89cd48b8000167924ef080b050bb9ab14ab2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:09:04.180158Z","signature_b64":"/myW/hudEMAS4EUJXdwYPERkw+XccY8ExVHDoFSOm+nuQk+8e2oQymEqPxeL2JBBBLvRmS2vbsdCvDPJni9fBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c411ef20d16af09201751e4f274f606ced292c8ad28d5c98a21dfbf039184a2","last_reissued_at":"2026-06-09T02:09:04.179471Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:09:04.179471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bertini theorems for Hilbert-Samuel multiplicity over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"math.AG","authors_text":"Matthew Bertucci, Rahul Ajit","submitted_at":"2026-06-08T16:10:57Z","abstract_excerpt":"Let $X\\subseteq \\mathbb{P}^n_{\\mathbb{F}_q}$ be a reduced, equidimensional, quasiprojective scheme. We prove that there exists a positive-density set of hypersurfaces $H_f$ such that for every closed point $P\\in X\\cap H_f$, one has $\\mathrm{ord}_P(f)=1$ and $e_P(X\\cap H_f)=e_P(X)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09693","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/2606.09693/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":"2606.09693","created_at":"2026-06-09T02:09:04.179593+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.09693v1","created_at":"2026-06-09T02:09:04.179593+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09693","created_at":"2026-06-09T02:09:04.179593+00:00"},{"alias_kind":"pith_short_12","alias_value":"HRAR54QNC2XQ","created_at":"2026-06-09T02:09:04.179593+00:00"},{"alias_kind":"pith_short_16","alias_value":"HRAR54QNC2XQSIAX","created_at":"2026-06-09T02:09:04.179593+00:00"},{"alias_kind":"pith_short_8","alias_value":"HRAR54QN","created_at":"2026-06-09T02:09:04.179593+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/HRAR54QNC2XQSIAXKHSPE5HWA3","json":"https://pith.science/pith/HRAR54QNC2XQSIAXKHSPE5HWA3.json","graph_json":"https://pith.science/api/pith-number/HRAR54QNC2XQSIAXKHSPE5HWA3/graph.json","events_json":"https://pith.science/api/pith-number/HRAR54QNC2XQSIAXKHSPE5HWA3/events.json","paper":"https://pith.science/paper/HRAR54QN"},"agent_actions":{"view_html":"https://pith.science/pith/HRAR54QNC2XQSIAXKHSPE5HWA3","download_json":"https://pith.science/pith/HRAR54QNC2XQSIAXKHSPE5HWA3.json","view_paper":"https://pith.science/paper/HRAR54QN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.09693&json=true","fetch_graph":"https://pith.science/api/pith-number/HRAR54QNC2XQSIAXKHSPE5HWA3/graph.json","fetch_events":"https://pith.science/api/pith-number/HRAR54QNC2XQSIAXKHSPE5HWA3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HRAR54QNC2XQSIAXKHSPE5HWA3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HRAR54QNC2XQSIAXKHSPE5HWA3/action/storage_attestation","attest_author":"https://pith.science/pith/HRAR54QNC2XQSIAXKHSPE5HWA3/action/author_attestation","sign_citation":"https://pith.science/pith/HRAR54QNC2XQSIAXKHSPE5HWA3/action/citation_signature","submit_replication":"https://pith.science/pith/HRAR54QNC2XQSIAXKHSPE5HWA3/action/replication_record"}},"created_at":"2026-06-09T02:09:04.179593+00:00","updated_at":"2026-06-09T02:09:04.179593+00:00"}