{"paper":{"title":"Endpoint Koopman Spectral Computation: $L^1$ Residual Bounds, $L^\\infty$ Instability, and Point-Spectral SCI Calibration Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DS","math.NA","math.SP"],"primary_cat":"math.LO","authors_text":"Christopher Sorg","submitted_at":"2026-01-17T13:17:21Z","abstract_excerpt":"We study endpoint Koopman spectral computation from the viewpoint of the Solvability Complexity Index (SCI). Let \\((\\mathcal X,d)\\) be a compact metric space with finite Borel measure \\(\\omega\\), and let \\(\\mathcal K_F\\) be the Koopman operator associated with a continuous nonsingular map \\(F:\\mathcal X\\to\\mathcal X\\).\n  First, on \\(L^1(\\mathcal X,\\omega)\\), we record the endpoint residual upper-bound in the target-split form. The regularized compact fixed-\\(\\varepsilon\\) target $R_{\\mathrm{ap},\\varepsilon}(\\mathcal K_F)$ is separated from the closed fixed-\\(\\varepsilon\\) target $C_{\\mathrm{ap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.12044","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/2601.12044/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"}