{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:MLVGCAGNOSNYBBNDYW5VMG3M46","short_pith_number":"pith:MLVGCAGN","canonical_record":{"source":{"id":"2507.19245","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-07-25T13:12:55Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"000ba42433a0c7a9e7fde170ebd8bd9778ddd9867e9504aa6af07305885c3d6f","abstract_canon_sha256":"b942245c1c09ba59423028f00fe212dd9b41ecd2cc10f49203d8d6e55a78dacb"},"schema_version":"1.0"},"canonical_sha256":"62ea6100cd749b8085a3c5bb561b6ce78749731915ba441439df485464feabba","source":{"kind":"arxiv","id":"2507.19245","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.19245","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"arxiv_version","alias_value":"2507.19245v1","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19245","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"pith_short_12","alias_value":"MLVGCAGNOSNY","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"pith_short_16","alias_value":"MLVGCAGNOSNYBBND","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"pith_short_8","alias_value":"MLVGCAGN","created_at":"2026-07-05T11:43:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:MLVGCAGNOSNYBBNDYW5VMG3M46","target":"record","payload":{"canonical_record":{"source":{"id":"2507.19245","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-07-25T13:12:55Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"000ba42433a0c7a9e7fde170ebd8bd9778ddd9867e9504aa6af07305885c3d6f","abstract_canon_sha256":"b942245c1c09ba59423028f00fe212dd9b41ecd2cc10f49203d8d6e55a78dacb"},"schema_version":"1.0"},"canonical_sha256":"62ea6100cd749b8085a3c5bb561b6ce78749731915ba441439df485464feabba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:22.221648Z","signature_b64":"t+yQ83/Vn3v3G1GoGfc6BLt0nu8MPn0bKEKFOGKK6j9lR2lh4siut56chIxy7plprStHg9SaaA6KzeZCpHYmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62ea6100cd749b8085a3c5bb561b6ce78749731915ba441439df485464feabba","last_reissued_at":"2026-07-05T11:43:22.221088Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:22.221088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.19245","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:43:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y7tk0DxzNTC5WEUF6qiLmlI40s91RY+O4wh31Ltc90MmQcJj7bOYDokSF58ZyFXOuseSVd88nWThw5vOo1YkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T01:05:21.930454Z"},"content_sha256":"47133affbd2c14b0a91575b4d2879ae1e3d85a1c1dc21480c2277ddf841fa994","schema_version":"1.0","event_id":"sha256:47133affbd2c14b0a91575b4d2879ae1e3d85a1c1dc21480c2277ddf841fa994"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:MLVGCAGNOSNYBBNDYW5VMG3M46","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LO","authors_text":"Bugra Kilictas, Faruk Alpay, Taylan Alpay","submitted_at":"2025-07-25T13:12:55Z","abstract_excerpt":"This paper contributes to the Alpay Algebra by demonstrating that the stable outcome of a self referential process, obtained by iterating a transformation through all ordinal stages, is identical to the unique equilibrium of an unbounded revision dialogue between a system and its environment. The analysis initially elucidates how classical fixed point theorems guarantee such convergence in finite settings and subsequently extends the argument to the transfinite domain, relying upon well founded induction and principles of order theoretic continuity.\n  Furthermore, the resulting transordinal fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19245","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/2507.19245/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:43:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fO/CakS4EtNx+cl+OhgJHmoqx6Mjsl8Zq0+PGzNPOGbgHC39oVYXJrmbQ007OSt1xtJMdpS7yhk/VQ26jjuBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T01:05:21.933035Z"},"content_sha256":"f402379f298134206b8e69808a8f39973e975331d5a304ee699a1d55f94c12cf","schema_version":"1.0","event_id":"sha256:f402379f298134206b8e69808a8f39973e975331d5a304ee699a1d55f94c12cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MLVGCAGNOSNYBBNDYW5VMG3M46/bundle.json","state_url":"https://pith.science/pith/MLVGCAGNOSNYBBNDYW5VMG3M46/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MLVGCAGNOSNYBBNDYW5VMG3M46/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-18T01:05:21Z","links":{"resolver":"https://pith.science/pith/MLVGCAGNOSNYBBNDYW5VMG3M46","bundle":"https://pith.science/pith/MLVGCAGNOSNYBBNDYW5VMG3M46/bundle.json","state":"https://pith.science/pith/MLVGCAGNOSNYBBNDYW5VMG3M46/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MLVGCAGNOSNYBBNDYW5VMG3M46/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MLVGCAGNOSNYBBNDYW5VMG3M46","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":"b942245c1c09ba59423028f00fe212dd9b41ecd2cc10f49203d8d6e55a78dacb","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-07-25T13:12:55Z","title_canon_sha256":"000ba42433a0c7a9e7fde170ebd8bd9778ddd9867e9504aa6af07305885c3d6f"},"schema_version":"1.0","source":{"id":"2507.19245","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.19245","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"arxiv_version","alias_value":"2507.19245v1","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19245","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"pith_short_12","alias_value":"MLVGCAGNOSNY","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"pith_short_16","alias_value":"MLVGCAGNOSNYBBND","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"pith_short_8","alias_value":"MLVGCAGN","created_at":"2026-07-05T11:43:22Z"}],"graph_snapshots":[{"event_id":"sha256:f402379f298134206b8e69808a8f39973e975331d5a304ee699a1d55f94c12cf","target":"graph","created_at":"2026-07-05T11:43:22Z","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/2507.19245/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper contributes to the Alpay Algebra by demonstrating that the stable outcome of a self referential process, obtained by iterating a transformation through all ordinal stages, is identical to the unique equilibrium of an unbounded revision dialogue between a system and its environment. The analysis initially elucidates how classical fixed point theorems guarantee such convergence in finite settings and subsequently extends the argument to the transfinite domain, relying upon well founded induction and principles of order theoretic continuity.\n  Furthermore, the resulting transordinal fi","authors_text":"Bugra Kilictas, Faruk Alpay, Taylan Alpay","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-07-25T13:12:55Z","title":"Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19245","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":"sha256:47133affbd2c14b0a91575b4d2879ae1e3d85a1c1dc21480c2277ddf841fa994","target":"record","created_at":"2026-07-05T11:43:22Z","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":"b942245c1c09ba59423028f00fe212dd9b41ecd2cc10f49203d8d6e55a78dacb","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2025-07-25T13:12:55Z","title_canon_sha256":"000ba42433a0c7a9e7fde170ebd8bd9778ddd9867e9504aa6af07305885c3d6f"},"schema_version":"1.0","source":{"id":"2507.19245","kind":"arxiv","version":1}},"canonical_sha256":"62ea6100cd749b8085a3c5bb561b6ce78749731915ba441439df485464feabba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62ea6100cd749b8085a3c5bb561b6ce78749731915ba441439df485464feabba","first_computed_at":"2026-07-05T11:43:22.221088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:43:22.221088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t+yQ83/Vn3v3G1GoGfc6BLt0nu8MPn0bKEKFOGKK6j9lR2lh4siut56chIxy7plprStHg9SaaA6KzeZCpHYmDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:43:22.221648Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.19245","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47133affbd2c14b0a91575b4d2879ae1e3d85a1c1dc21480c2277ddf841fa994","sha256:f402379f298134206b8e69808a8f39973e975331d5a304ee699a1d55f94c12cf"],"state_sha256":"1f9d1efdf7d48d24befd957b0a1c211c29e3c25accb8ecc03edd36591a0662d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"25zZxGPmJGyTLyHnTwvfSs55OcOz3+HDFbFDbFTynDjDT0uLHmlKEUVZLpeZgZDX08gOeOm+HQzaJ1wue5rmAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T01:05:22.031591Z","bundle_sha256":"314b6e64d3dd1a5363a3b37848fa67034a59ec5b8739461deff0967c4c3f8885"}}