{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6HMELZZAQESFGBNMDZ72MYOCKE","short_pith_number":"pith:6HMELZZA","schema_version":"1.0","canonical_sha256":"f1d845e72081245305ac1e7fa661c2512014f7cb4530f1eab78489959fa2d59f","source":{"kind":"arxiv","id":"2606.30160","version":1},"attestation_state":"computed","paper":{"title":"On Property $N_p$ of line bundles on smooth projective toric varieties","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.AG","authors_text":"Huanqi Wen, Lei Song","submitted_at":"2026-06-29T11:36:23Z","abstract_excerpt":"We establish a criterion for Property $N_p$ for line bundles on a class of smooth projective toric varieties. More precisely, we prove that if a smooth projective toric variety $X$ of dimension $n\\ge2$ satisfies the uniform unimodularity condition and the Thomsen stratification intersection-number condition, then any line bundle $L$ on $X$ with $L\\cdot C\\ge n-1+p$ for every $T$-invariant curve $C$ satisfies Property $N_p$. We also show that these two conditions hold for several families of toric varieties and are preserved under finite products."},"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":"2606.30160","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-29T11:36:23Z","cross_cats_sorted":["math.AC","math.CO"],"title_canon_sha256":"356081f951034dd0fb97b03103e9e466b817902b236dd3cc7b3f264de052abeb","abstract_canon_sha256":"7e163bb2ee5edba311d6e1b4993eb483599e72e9fba104ca0a060049b23658ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:52.018724Z","signature_b64":"IK/H1o16wCPrqVyAfWhqjMyeAfa0k2+xr1gD6nb8S45RausO35H+6ysxjTseoNZn6eXMY2EyysafznFFHhXnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1d845e72081245305ac1e7fa661c2512014f7cb4530f1eab78489959fa2d59f","last_reissued_at":"2026-06-30T02:17:52.018155Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:52.018155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Property $N_p$ of line bundles on smooth projective toric varieties","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.AG","authors_text":"Huanqi Wen, Lei Song","submitted_at":"2026-06-29T11:36:23Z","abstract_excerpt":"We establish a criterion for Property $N_p$ for line bundles on a class of smooth projective toric varieties. More precisely, we prove that if a smooth projective toric variety $X$ of dimension $n\\ge2$ satisfies the uniform unimodularity condition and the Thomsen stratification intersection-number condition, then any line bundle $L$ on $X$ with $L\\cdot C\\ge n-1+p$ for every $T$-invariant curve $C$ satisfies Property $N_p$. We also show that these two conditions hold for several families of toric varieties and are preserved under finite products."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30160","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/2606.30160/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":"2606.30160","created_at":"2026-06-30T02:17:52.018245+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.30160v1","created_at":"2026-06-30T02:17:52.018245+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30160","created_at":"2026-06-30T02:17:52.018245+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HMELZZAQESF","created_at":"2026-06-30T02:17:52.018245+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HMELZZAQESFGBNM","created_at":"2026-06-30T02:17:52.018245+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HMELZZA","created_at":"2026-06-30T02:17:52.018245+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/6HMELZZAQESFGBNMDZ72MYOCKE","json":"https://pith.science/pith/6HMELZZAQESFGBNMDZ72MYOCKE.json","graph_json":"https://pith.science/api/pith-number/6HMELZZAQESFGBNMDZ72MYOCKE/graph.json","events_json":"https://pith.science/api/pith-number/6HMELZZAQESFGBNMDZ72MYOCKE/events.json","paper":"https://pith.science/paper/6HMELZZA"},"agent_actions":{"view_html":"https://pith.science/pith/6HMELZZAQESFGBNMDZ72MYOCKE","download_json":"https://pith.science/pith/6HMELZZAQESFGBNMDZ72MYOCKE.json","view_paper":"https://pith.science/paper/6HMELZZA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.30160&json=true","fetch_graph":"https://pith.science/api/pith-number/6HMELZZAQESFGBNMDZ72MYOCKE/graph.json","fetch_events":"https://pith.science/api/pith-number/6HMELZZAQESFGBNMDZ72MYOCKE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HMELZZAQESFGBNMDZ72MYOCKE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HMELZZAQESFGBNMDZ72MYOCKE/action/storage_attestation","attest_author":"https://pith.science/pith/6HMELZZAQESFGBNMDZ72MYOCKE/action/author_attestation","sign_citation":"https://pith.science/pith/6HMELZZAQESFGBNMDZ72MYOCKE/action/citation_signature","submit_replication":"https://pith.science/pith/6HMELZZAQESFGBNMDZ72MYOCKE/action/replication_record"}},"created_at":"2026-06-30T02:17:52.018245+00:00","updated_at":"2026-06-30T02:17:52.018245+00:00"}