{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:R7SW2A3IAEFZFXWPCWMTEVWRVY","short_pith_number":"pith:R7SW2A3I","schema_version":"1.0","canonical_sha256":"8fe56d0368010b92decf15993256d1ae02a1b8bda101ea8feb934f17ab2ea081","source":{"kind":"arxiv","id":"2501.05720","version":2},"attestation_state":"computed","paper":{"title":"Khovanskii bases of subalgebras arising from finite distributive lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Akihiro Higashitani, Koichiro Tani, Koji Matsushita","submitted_at":"2025-01-10T05:38:29Z","abstract_excerpt":"The notion of Khovanskii bases was introduced by Kaveh and Manon. It is a generalization of the notion of SAGBI bases for a subalgebra of polynomials. The notion of SAGBI bases was introduced by Robbiano and Sweedler as an analogue of Gr\\\"{o}bner bases in the context of subalgebras. A Hibi ideal is an ideal of a polynomial ring that arises from a distributive lattice. For the development of an analogy of the theory of Hibi ideals and Gr\\\"{o}bner bases within the framework of subalgebras, in this paper, we investigate when the set of the polynomials associated with a distributive lattice forms "},"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":"2501.05720","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-01-10T05:38:29Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"422b446efa94d877e07a0ff3f44be7a7bc49e607c993b878591cedb85d001d5b","abstract_canon_sha256":"378866896ffc6bd309d2082b0b705d2545c5622e85ff45ceccec4b9aff9759ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:02:09.430346Z","signature_b64":"hD3aMRys6VviZcyQIOTdZHZIeg8eIkIZ8kExt2Cg+4j3evzrjOX7tMPXdB1zVuIsdDIEa16WEBBxWu0t/WuQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fe56d0368010b92decf15993256d1ae02a1b8bda101ea8feb934f17ab2ea081","last_reissued_at":"2026-07-05T10:02:09.429903Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:02:09.429903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Khovanskii bases of subalgebras arising from finite distributive lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Akihiro Higashitani, Koichiro Tani, Koji Matsushita","submitted_at":"2025-01-10T05:38:29Z","abstract_excerpt":"The notion of Khovanskii bases was introduced by Kaveh and Manon. It is a generalization of the notion of SAGBI bases for a subalgebra of polynomials. The notion of SAGBI bases was introduced by Robbiano and Sweedler as an analogue of Gr\\\"{o}bner bases in the context of subalgebras. A Hibi ideal is an ideal of a polynomial ring that arises from a distributive lattice. For the development of an analogy of the theory of Hibi ideals and Gr\\\"{o}bner bases within the framework of subalgebras, in this paper, we investigate when the set of the polynomials associated with a distributive lattice forms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05720","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/2501.05720/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":"2501.05720","created_at":"2026-07-05T10:02:09.429962+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.05720v2","created_at":"2026-07-05T10:02:09.429962+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.05720","created_at":"2026-07-05T10:02:09.429962+00:00"},{"alias_kind":"pith_short_12","alias_value":"R7SW2A3IAEFZ","created_at":"2026-07-05T10:02:09.429962+00:00"},{"alias_kind":"pith_short_16","alias_value":"R7SW2A3IAEFZFXWP","created_at":"2026-07-05T10:02:09.429962+00:00"},{"alias_kind":"pith_short_8","alias_value":"R7SW2A3I","created_at":"2026-07-05T10:02:09.429962+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/R7SW2A3IAEFZFXWPCWMTEVWRVY","json":"https://pith.science/pith/R7SW2A3IAEFZFXWPCWMTEVWRVY.json","graph_json":"https://pith.science/api/pith-number/R7SW2A3IAEFZFXWPCWMTEVWRVY/graph.json","events_json":"https://pith.science/api/pith-number/R7SW2A3IAEFZFXWPCWMTEVWRVY/events.json","paper":"https://pith.science/paper/R7SW2A3I"},"agent_actions":{"view_html":"https://pith.science/pith/R7SW2A3IAEFZFXWPCWMTEVWRVY","download_json":"https://pith.science/pith/R7SW2A3IAEFZFXWPCWMTEVWRVY.json","view_paper":"https://pith.science/paper/R7SW2A3I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.05720&json=true","fetch_graph":"https://pith.science/api/pith-number/R7SW2A3IAEFZFXWPCWMTEVWRVY/graph.json","fetch_events":"https://pith.science/api/pith-number/R7SW2A3IAEFZFXWPCWMTEVWRVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R7SW2A3IAEFZFXWPCWMTEVWRVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R7SW2A3IAEFZFXWPCWMTEVWRVY/action/storage_attestation","attest_author":"https://pith.science/pith/R7SW2A3IAEFZFXWPCWMTEVWRVY/action/author_attestation","sign_citation":"https://pith.science/pith/R7SW2A3IAEFZFXWPCWMTEVWRVY/action/citation_signature","submit_replication":"https://pith.science/pith/R7SW2A3IAEFZFXWPCWMTEVWRVY/action/replication_record"}},"created_at":"2026-07-05T10:02:09.429962+00:00","updated_at":"2026-07-05T10:02:09.429962+00:00"}