{"paper":{"title":"Alpay Algebra V: Multi-Layered Semantic Games and Transfinite Fixed-Point Simulation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.CL","authors_text":"Bugra Kilictas, Faruk Alpay","submitted_at":"2025-07-10T15:48:23Z","abstract_excerpt":"This paper extends the self-referential framework of Alpay Algebra into a multi-layered semantic game architecture where transfinite fixed-point convergence encompasses hierarchical sub-games at each iteration level. Building upon Alpay Algebra IV's empathetic embedding concept, we introduce a nested game-theoretic structure where the alignment process between AI systems and documents becomes a meta-game containing embedded decision problems. We formalize this through a composite operator $\\phi(\\cdot, \\gamma(\\cdot))$ where $\\phi$ drives the main semantic convergence while $\\gamma$ resolves loc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07868","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/2507.07868/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"}