{"paper":{"title":"Prism: Structural Symmetry Scanning via Duality-Constrained Laplacian Projection","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.SI","authors_text":"Jiatong Xie","submitted_at":"2026-05-18T04:20:05Z","abstract_excerpt":"We introduce \\textbf{Prism}, a framework for structural symmetry diagnosis in complex networks. Given a graph Laplacian $L$ and a duality operator $P$ (a symmetric involution), Prism computes the \\emph{duality defect} $\\delta(L,P) = \\|LP - PL\\|_F / \\|L\\|_F$ -- a scalar measuring how far the network deviates from structural self-consistency. When $P$ encodes the network's true symmetry, $\\delta$ starts near zero and rises monotonically as structure degrades; an arbitrary $P$ gives noise. We prove that the optimal $L'$ satisfying $[L', P] = 0$ is given by a closed-form block-diagonal projection,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20245","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/2605.20245/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"}