{"paper":{"title":"Preparation geometry and slow-sector routing in driven Kerr resonators: an operational spectral theory of Liouvillians","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kilian Seibold","submitted_at":"2026-08-05T16:57:05Z","abstract_excerpt":"Liouvillian eigenvalues determine decay rates and oscillation frequencies, but not how the corresponding modes are excited, propagated, and detected in a chosen protocol. We develop an operational spectral theory based on matched left and right eigenoperators. Left eigenoperators determine excitation by an input or source; right eigenoperators determine the propagated density deformation and readout overlap; their product is a gauge-invariant modal weight. For bosonic systems, coherent preparations turn left eigenoperators into phase-space excitation maps whose zeros identify mode-selective su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05046","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/2608.05046/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-08-06T01:48:06.382554Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"fe74e75678eec12c8d83cda649821171c769a2a6b16afe6cf1cf8b6df429ab56"},"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"}