{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:KEFGR3VKNA5DRE7U2URZXHXIGD","short_pith_number":"pith:KEFGR3VK","schema_version":"1.0","canonical_sha256":"510a68eeaa683a3893f4d5239b9ee830d2e30d95b249107196b9dcaffa0200ce","source":{"kind":"arxiv","id":"2502.04146","version":2},"attestation_state":"computed","paper":{"title":"On the $E$-base of Finite Lattices: Semidistributive, Modular, and Geometric Lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Kira Adaricheva, Simon Vilmin","submitted_at":"2025-02-06T15:28:32Z","abstract_excerpt":"Implicational bases are a well-known representation of closure spaces and their closure lattices. This representation is not unique, though, and a closure space usually admits multiple bases. Among these, the canonical base, the canonical direct base as well as the $D$-base aroused significant attention due to their structural and algorithmic properties. Recently, a new base has emerged from the study of free lattices: the $E$-base. It is a refinement of the $D$-base that, unlike the aforementioned implicational bases, does not always accurately represent its associated closure space. This lea"},"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":"2502.04146","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-06T15:28:32Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"8f0b2faa2a3c46d50784b219f56e20f887ca25c245d037e6f75a66691427cfbd","abstract_canon_sha256":"980c8ecd0d447d08d7296f84007b5b450fc8341513867baccf12c1beb82b6d8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:01:57.356956Z","signature_b64":"uM4E6cmcBF5p2AVSkY9tYZ4D3XXv0XB8eiaC8sn5u+0MyhaA06Bi9ig5OAhHBODqpZyx+1yZfJ426G2hTQJ/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"510a68eeaa683a3893f4d5239b9ee830d2e30d95b249107196b9dcaffa0200ce","last_reissued_at":"2026-07-05T12:01:57.356421Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:01:57.356421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the $E$-base of Finite Lattices: Semidistributive, Modular, and Geometric Lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Kira Adaricheva, Simon Vilmin","submitted_at":"2025-02-06T15:28:32Z","abstract_excerpt":"Implicational bases are a well-known representation of closure spaces and their closure lattices. This representation is not unique, though, and a closure space usually admits multiple bases. Among these, the canonical base, the canonical direct base as well as the $D$-base aroused significant attention due to their structural and algorithmic properties. Recently, a new base has emerged from the study of free lattices: the $E$-base. It is a refinement of the $D$-base that, unlike the aforementioned implicational bases, does not always accurately represent its associated closure space. This lea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.04146","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/2502.04146/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":"2502.04146","created_at":"2026-07-05T12:01:57.356483+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.04146v2","created_at":"2026-07-05T12:01:57.356483+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.04146","created_at":"2026-07-05T12:01:57.356483+00:00"},{"alias_kind":"pith_short_12","alias_value":"KEFGR3VKNA5D","created_at":"2026-07-05T12:01:57.356483+00:00"},{"alias_kind":"pith_short_16","alias_value":"KEFGR3VKNA5DRE7U","created_at":"2026-07-05T12:01:57.356483+00:00"},{"alias_kind":"pith_short_8","alias_value":"KEFGR3VK","created_at":"2026-07-05T12:01:57.356483+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/KEFGR3VKNA5DRE7U2URZXHXIGD","json":"https://pith.science/pith/KEFGR3VKNA5DRE7U2URZXHXIGD.json","graph_json":"https://pith.science/api/pith-number/KEFGR3VKNA5DRE7U2URZXHXIGD/graph.json","events_json":"https://pith.science/api/pith-number/KEFGR3VKNA5DRE7U2URZXHXIGD/events.json","paper":"https://pith.science/paper/KEFGR3VK"},"agent_actions":{"view_html":"https://pith.science/pith/KEFGR3VKNA5DRE7U2URZXHXIGD","download_json":"https://pith.science/pith/KEFGR3VKNA5DRE7U2URZXHXIGD.json","view_paper":"https://pith.science/paper/KEFGR3VK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.04146&json=true","fetch_graph":"https://pith.science/api/pith-number/KEFGR3VKNA5DRE7U2URZXHXIGD/graph.json","fetch_events":"https://pith.science/api/pith-number/KEFGR3VKNA5DRE7U2URZXHXIGD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KEFGR3VKNA5DRE7U2URZXHXIGD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KEFGR3VKNA5DRE7U2URZXHXIGD/action/storage_attestation","attest_author":"https://pith.science/pith/KEFGR3VKNA5DRE7U2URZXHXIGD/action/author_attestation","sign_citation":"https://pith.science/pith/KEFGR3VKNA5DRE7U2URZXHXIGD/action/citation_signature","submit_replication":"https://pith.science/pith/KEFGR3VKNA5DRE7U2URZXHXIGD/action/replication_record"}},"created_at":"2026-07-05T12:01:57.356483+00:00","updated_at":"2026-07-05T12:01:57.356483+00:00"}