{"paper":{"title":"Exact Uniform L1 Spacing for Solow-Polasky Diversity on Lines and Ordered Pareto Fronts","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","cs.NE"],"primary_cat":"math.OC","authors_text":"Jes\\'us Guillermo Falc\\'on Cardona, Mahboubeh Nezhadmoghaddam, Michael T. M. Emmerich","submitted_at":"2026-05-21T02:46:52Z","abstract_excerpt":"We study fixed-cardinality maximization of the inverse-matrix Solow--Polasky diversity, equivalently finite metric magnitude for the exponential kernel, on one-dimensional and ordered metric sets. The analysis starts from the known finite-line gap formula for the exponential kernel, which writes the excess inverse-matrix diversity as a sum of functions of consecutive gaps. Building on this formula, the main interval theorem proves that, for every $k\\geq 2$, the unique maximizing $k$-point subset of $[0,1]$ is the equally spaced set. Thus the objective selects a uniform gap representation on th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21922","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/2605.21922/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"}