{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ESWJ5T53N2YZP4SVKASMDD2ILB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"aadf71ca092ff2cfe1462a7405ccc51fd9af49c8ba3fad928d072ccb1acca144","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2025-07-10T15:48:23Z","title_canon_sha256":"ec45a4d33b34fded8209e6f7387c654aa838182a27e01066cb8318fe4114e31a"},"schema_version":"1.0","source":{"id":"2507.07868","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.07868","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"2507.07868v1","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.07868","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"ESWJ5T53N2YZ","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"pith_short_16","alias_value":"ESWJ5T53N2YZP4SV","created_at":"2026-07-05T11:35:06Z"},{"alias_kind":"pith_short_8","alias_value":"ESWJ5T53","created_at":"2026-07-05T11:35:06Z"}],"graph_snapshots":[{"event_id":"sha256:8161ee77dce75211bb0bbd4d44d236471b8c77569f78c2c84b1af62afbe78a7c","target":"graph","created_at":"2026-07-05T11:35:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.07868/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Bugra Kilictas, Faruk Alpay","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2025-07-10T15:48:23Z","title":"Alpay Algebra V: Multi-Layered Semantic Games and Transfinite Fixed-Point Simulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07868","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:800f5dbf99aa97e8e3ade3924094cf07d0e563fd3cfb225af4b09f4eee41300a","target":"record","created_at":"2026-07-05T11:35:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"aadf71ca092ff2cfe1462a7405ccc51fd9af49c8ba3fad928d072ccb1acca144","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2025-07-10T15:48:23Z","title_canon_sha256":"ec45a4d33b34fded8209e6f7387c654aa838182a27e01066cb8318fe4114e31a"},"schema_version":"1.0","source":{"id":"2507.07868","kind":"arxiv","version":1}},"canonical_sha256":"24ac9ecfbb6eb197f2555024c18f48584940b8fb86976cecf9c9b662917a47c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24ac9ecfbb6eb197f2555024c18f48584940b8fb86976cecf9c9b662917a47c5","first_computed_at":"2026-07-05T11:35:06.401074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:35:06.401074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AevWOGAmbixbSiMCA1qcTQhiOh2wQRq0lfB5O5Af5pKJGfY2bqsVX7j0oSxpEZvjlqnyPThWnSknBQatMbu9Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:35:06.401539Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.07868","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:800f5dbf99aa97e8e3ade3924094cf07d0e563fd3cfb225af4b09f4eee41300a","sha256:8161ee77dce75211bb0bbd4d44d236471b8c77569f78c2c84b1af62afbe78a7c"],"state_sha256":"3bfd5e826b4210d4176256894a165dd8c76cc80cec8e62ccdd90ceae06d94d75"}