{"paper":{"title":"Algebraic Structure of Three-Flavor Neutrino Oscillations in Constant-Density Matter: Cayley--Hamilton Evolution, DMP Resummation, and Closed-Form Uncertainty Propagation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Aaryan Chaulagain, Anju Dhakal, Daya Nidhi Chhatkuli","submitted_at":"2026-07-08T09:54:06Z","abstract_excerpt":"For three-flavor neutrino oscillations in constant-density matter, the Cayley--Hamilton theorem forces the evolution operator into a quadratic polynomial in $\\hat{H}$, with coefficients determined by the three real eigenvalues through a Vandermonde system we write out explicitly. The eigenvalues follow from Cardano's trigonometric formula, recovering the Zaglauer--Schwarzer expressions. The Denton--Minakata--Parke (DMP) approximation achieves fractional accuracy better than $10^{-4}$ because its $1$--$3$ rotation is a resummation: it removes the near-degeneracy that makes the naive expansion d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07213","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/2607.07213/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"}