{"paper":{"title":"A Borodin-Okounkov-Geronimo-Case identity for tilted Toeplitz minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.FA","authors_text":"Leonid Petrov","submitted_at":"2026-05-24T10:14:14Z","abstract_excerpt":"We prove a Fredholm determinantal identity for the tilted Toeplitz minor $$ D_{N}^{\\xi,\\theta}(\\varphi):= \\det\\bigl[(\\theta_{i}\\xi_{j}\\varphi)_{i-j}\\bigr]_{i,j=1}^{N}, $$ generalizing the Borodin-Okounkov-Geronimo-Case (BOGC) identity to oblique splittings of the Hardy space. The tilts $\\xi_{j},\\theta_{i}$ enter only through an oblique projection that multiplies the trace-class kernel $K$ inside the Fredholm determinant; the BOGC operator $A=I-K$ constructed from $\\varphi$ is unchanged.\n  Baik-Liao-Liu (arXiv:2603.01964) and Liu-Tripathi (arXiv:2604.24747) have recently shown that the same til"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24976","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/2605.24976/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"}