{"paper":{"title":"K3 atoms of the cubic fourfold and the BPS structure of the Painlev\\'e I determinant line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Mark Raugas","submitted_at":"2026-08-12T15:46:19Z","abstract_excerpt":"The compatibility of the semiorthogonal decomposition of a cubic fourfold with Bridgeland stability beyond a generic point is the missing ingredient in the conjectured dynamical protection of the K3 atom $\\AX$. We analyze it in the exactly solvable models of the noncommutative minimal model program. In the uncoupled Fano models ($\\PP^1$; $\\PP^1 \\times \\PP^1$ at resonance) the quantum cohomology path exits the geometric chamber at an explicit finite time, enters the selection region of the gluing, and never leaves; perturbing the resonance shows the $\\varepsilon$-crossover is not a wall. The $A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12191","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/2608.12191/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"}