{"paper":{"title":"Infinite Belligerent Jump Inversion and Computable Scott Analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Gonzalez, Hongyu Zhu, Uri Andrews","submitted_at":"2026-07-12T21:54:06Z","abstract_excerpt":"Scott analysis provides two fundamental tools for studying countable structures: Scott sentences, which characterize structures up to isomorphism, and back-and-forth relations, which measure structural similarity. A recurring phenomenon in computable structure theory is that many notions naturally associated with level $\\alpha$ of Scott analysis have effective complexity at approximately $2\\alpha$ jumps. This discrepancy appears both in the complexity of the back-and-forth relations and in the passage from arbitrary infinitary formulas to computable infinitary formulas.\n  We develop two new co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10935","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/2607.10935/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"}