{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:IWNCCX23DPMF5UXBYVSUDTQRWS","short_pith_number":"pith:IWNCCX23","schema_version":"1.0","canonical_sha256":"459a215f5b1bd85ed2e1c56541ce11b480ebb7d03079b02b8217eafaff83c313","source":{"kind":"arxiv","id":"2507.16620","version":1},"attestation_state":"computed","paper":{"title":"Transordinal Fixed-Point Operators and Self-Referential Games: A Categorical Framework for Reflective Semantic Convergence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Faruk Alpay, Hamdi Al Alakkad","submitted_at":"2025-07-22T14:15:11Z","abstract_excerpt":"We present a new theoretical framework that unifies category-theoretic fixed-point constructions, transfinite recursion, and game-based semantics to model how interpretations of language can stabilize through unlimited self-reference. By iterating a meaning-refinement operator across all ordinal stages, we isolate a unique \"transordinal\" fixed point and show, via a hierarchy of reflective games, that this same object is the sole equilibrium of an infinite dialogue between a text and its interpreter. The result delivers a mathematically rigorous account of semantic convergence without resorting"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.16620","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-07-22T14:15:11Z","cross_cats_sorted":[],"title_canon_sha256":"d6ef5b5b6ce15cd5c7c33c3a1fba9ca853b24117e238296fc02256d052b57b86","abstract_canon_sha256":"adaeabdfb02f2fe09143b3bbe14418ea5b6928d4695bcd96dd3a3d4d5e59a163"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:41:27.757436Z","signature_b64":"k2n6WUI6qoAgEwLQKrm7/ygLDtvqYv6VplpzcJo/tEKdOj6nSiHTfRVJUmR22wraQ7PtaLqX7wz8ROi+W5F6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"459a215f5b1bd85ed2e1c56541ce11b480ebb7d03079b02b8217eafaff83c313","last_reissued_at":"2026-07-05T11:41:27.756882Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:41:27.756882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transordinal Fixed-Point Operators and Self-Referential Games: A Categorical Framework for Reflective Semantic Convergence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Faruk Alpay, Hamdi Al Alakkad","submitted_at":"2025-07-22T14:15:11Z","abstract_excerpt":"We present a new theoretical framework that unifies category-theoretic fixed-point constructions, transfinite recursion, and game-based semantics to model how interpretations of language can stabilize through unlimited self-reference. By iterating a meaning-refinement operator across all ordinal stages, we isolate a unique \"transordinal\" fixed point and show, via a hierarchy of reflective games, that this same object is the sole equilibrium of an infinite dialogue between a text and its interpreter. The result delivers a mathematically rigorous account of semantic convergence without resorting"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.16620","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/2507.16620/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.16620","created_at":"2026-07-05T11:41:27.756960+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.16620v1","created_at":"2026-07-05T11:41:27.756960+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.16620","created_at":"2026-07-05T11:41:27.756960+00:00"},{"alias_kind":"pith_short_12","alias_value":"IWNCCX23DPMF","created_at":"2026-07-05T11:41:27.756960+00:00"},{"alias_kind":"pith_short_16","alias_value":"IWNCCX23DPMF5UXB","created_at":"2026-07-05T11:41:27.756960+00:00"},{"alias_kind":"pith_short_8","alias_value":"IWNCCX23","created_at":"2026-07-05T11:41:27.756960+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.19245","citing_title":"Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IWNCCX23DPMF5UXBYVSUDTQRWS","json":"https://pith.science/pith/IWNCCX23DPMF5UXBYVSUDTQRWS.json","graph_json":"https://pith.science/api/pith-number/IWNCCX23DPMF5UXBYVSUDTQRWS/graph.json","events_json":"https://pith.science/api/pith-number/IWNCCX23DPMF5UXBYVSUDTQRWS/events.json","paper":"https://pith.science/paper/IWNCCX23"},"agent_actions":{"view_html":"https://pith.science/pith/IWNCCX23DPMF5UXBYVSUDTQRWS","download_json":"https://pith.science/pith/IWNCCX23DPMF5UXBYVSUDTQRWS.json","view_paper":"https://pith.science/paper/IWNCCX23","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.16620&json=true","fetch_graph":"https://pith.science/api/pith-number/IWNCCX23DPMF5UXBYVSUDTQRWS/graph.json","fetch_events":"https://pith.science/api/pith-number/IWNCCX23DPMF5UXBYVSUDTQRWS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IWNCCX23DPMF5UXBYVSUDTQRWS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IWNCCX23DPMF5UXBYVSUDTQRWS/action/storage_attestation","attest_author":"https://pith.science/pith/IWNCCX23DPMF5UXBYVSUDTQRWS/action/author_attestation","sign_citation":"https://pith.science/pith/IWNCCX23DPMF5UXBYVSUDTQRWS/action/citation_signature","submit_replication":"https://pith.science/pith/IWNCCX23DPMF5UXBYVSUDTQRWS/action/replication_record"}},"created_at":"2026-07-05T11:41:27.756960+00:00","updated_at":"2026-07-05T11:41:27.756960+00:00"}