{"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"}