{"paper":{"title":"Computing Projective Implicit Representations from Poset Towers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Florian Russold, Tamal K. Dey","submitted_at":"2025-05-13T17:17:13Z","abstract_excerpt":"A family of simplicial complexes connected by simplicial maps and indexed by a finite poset $P$ is called a poset tower. Poset towers subsume multi-parameter filtrations, zigzag filtrations, and one-parameter simplicial towers, while allowing arbitrary finite posets and simplicial maps. The homology of a poset tower is a $P$-persistence module. To compute it globally over $P$, we consider the chain complex segment of $P$-persistence modules $C_{\\ell-1}\\xleftarrow{\\partial_{\\ell}}C_\\ell \\xleftarrow{\\partial_{\\ell+1}}C_{\\ell+1}$ induced by the simplices of the tower. Unlike in one-critical multi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.08755","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/2505.08755/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"}