{"paper":{"title":"On Conservative Matrix Fields: Continuous Asymptotics and Arithmetic","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.SC","math.CO","math.RA"],"primary_cat":"math.NT","authors_text":"Elyasheev Leibtag, Ido Kaminer, Michael Shalyt, Rotem Kalisch, Shachar Weinbaum","submitted_at":"2025-07-10T19:56:14Z","abstract_excerpt":"Ratios of D-finite sequences and their limits -- known as Ap\\'ery limits -- have driven much of the work on irrationality proofs since Ap\\'ery's 1979 breakthrough proof of the irrationality of $\\zeta(3)$. We extend ratios of D-finite sequences to a high-dimensional setting by introducing the Conservative Matrix Field (CMF). We demonstrate how classical Ap\\'ery limits are included by this object as special cases. A useful construction of CMFs is provided, drawing a connection to gauge transformations and to representations of shift operators in finite dimensional modules of Ore algebras. Finall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.08138","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/2507.08138/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"}