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We frame this as a mode-selection scoring problem: each mode receives a score that ranks it as true or spurious; any hard selection (threshold or clustering) is a downstream choice. We show that mode selection in DC-DMD is fundamentally a problem of subspace geometry. True modes are characterized by concentration within a low-dimensional signal subspace, whereas spurious modes tend to retain non-negligible components outside any moderate overestimate of that subspace. This geometric distinction defines true and spurious modes and motivates fully data-driven robust scoring criteria. The framework yields two complementary scores. The first uses a data-driven proxy of the signal subspace to compute a residual. The second comes from a new operator-theoretic analysis of delay embedding: using a block-companion formulation, we show that all modes exhibit a Kronecker\u2013Vandermonde structure, with true modes distinguished by the degree of conformity to it. This deviation is governed by the geometric residual. Our analysis further explains the empirical behavior of magnitude- and norm-based heuristics and clarifies when and why they fail under delay coordinates. Numerical experiments, evaluated by precision-recall area under the curve (PR-AUC) of true-vs-spurious ranking, show that the proposed scores outperform the tested baselines across most of the small-spatial-dimension regime.<\/jats:p>","DOI":"10.1063\/5.0333317","type":"journal-article","created":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T12:56:19Z","timestamp":1785761779000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Geometric mode-selection scores for delay-coordinates dynamic mode decomposition"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8172-5895","authenticated-orcid":false,"given":"Yoav","family":"Harris","sequence":"first","affiliation":[{"name":"Viterbi Faculty of Electrical and Computer Engineering, Technion\u2014Israel Institute of Technology 1 , Haifa 3200003,","place":["Israel"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6308-2267","authenticated-orcid":false,"given":"Hadas","family":"Benisty","sequence":"additional","affiliation":[{"name":"Rappaport Faculty of Medicine, Technion\u2014Israel Institute of Technology 2 , Haifa 3200003,","place":["Israel"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6838-1423","authenticated-orcid":false,"given":"Ronen","family":"Talmon","sequence":"additional","affiliation":[{"name":"Viterbi Faculty of Electrical and Computer Engineering, Technion\u2014Israel Institute of Technology 1 , Haifa 3200003,","place":["Israel"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,8,3]]},"reference":[{"key":"2026080308561037000_c1","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1017\/S0022112010001217","volume":"656","year":"2010","journal-title":"J. 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