{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:5NSLF7MAEOW3NNGNZ2UPFRPA24","short_pith_number":"pith:5NSLF7MA","canonical_record":{"source":{"id":"2203.13069","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-03-24T13:47:45Z","cross_cats_sorted":["cs.LO","math.CO"],"title_canon_sha256":"2addb1b657ff0cc004c3de501056bfad575158ea1af641efe2b4671a81529dbc","abstract_canon_sha256":"245d8ea2094a37e2fe4bf9a215c5dba1e91bc498c2016d5a01d9a7809d442138"},"schema_version":"1.0"},"canonical_sha256":"eb64b2fd8023adb6b4cdcea8f2c5e0d70454d6acfc1a023ea847dbdf64cf2cca","source":{"kind":"arxiv","id":"2203.13069","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.13069","created_at":"2026-07-05T04:08:20Z"},{"alias_kind":"arxiv_version","alias_value":"2203.13069v1","created_at":"2026-07-05T04:08:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.13069","created_at":"2026-07-05T04:08:20Z"},{"alias_kind":"pith_short_12","alias_value":"5NSLF7MAEOW3","created_at":"2026-07-05T04:08:20Z"},{"alias_kind":"pith_short_16","alias_value":"5NSLF7MAEOW3NNGN","created_at":"2026-07-05T04:08:20Z"},{"alias_kind":"pith_short_8","alias_value":"5NSLF7MA","created_at":"2026-07-05T04:08:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:5NSLF7MAEOW3NNGNZ2UPFRPA24","target":"record","payload":{"canonical_record":{"source":{"id":"2203.13069","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-03-24T13:47:45Z","cross_cats_sorted":["cs.LO","math.CO"],"title_canon_sha256":"2addb1b657ff0cc004c3de501056bfad575158ea1af641efe2b4671a81529dbc","abstract_canon_sha256":"245d8ea2094a37e2fe4bf9a215c5dba1e91bc498c2016d5a01d9a7809d442138"},"schema_version":"1.0"},"canonical_sha256":"eb64b2fd8023adb6b4cdcea8f2c5e0d70454d6acfc1a023ea847dbdf64cf2cca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:08:20.241873Z","signature_b64":"eoYrL1QEg0B7f1hng3loebZQdNMPoeyeiipX8RNyYjGO3fkKZwqfQ7mdy50hGO6gif1qAHcpn/2eh9IxnCVmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb64b2fd8023adb6b4cdcea8f2c5e0d70454d6acfc1a023ea847dbdf64cf2cca","last_reissued_at":"2026-07-05T04:08:20.241391Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:08:20.241391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.13069","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":"2026-07-05T04:08:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7INTcYQcfKv5u2Ex530gzo8sVeWNF2G/+K3+B7e+zqMeq4eUPC9gbq9DDoEVEo+f+L2Dts8LQrKyIb0IKskwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T06:54:30.440174Z"},"content_sha256":"00ee6ab8e03c794f01cf8696c6a3f051926739a39dfecfc80ee42c959ef766d9","schema_version":"1.0","event_id":"sha256:00ee6ab8e03c794f01cf8696c6a3f051926739a39dfecfc80ee42c959ef766d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:5NSLF7MAEOW3NNGNZ2UPFRPA24","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Game semantics of universes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO","math.CO"],"primary_cat":"math.LO","authors_text":"Norihiro Yamada","submitted_at":"2022-03-24T13:47:45Z","abstract_excerpt":"This work extends the present author's computational game semantics of Martin-L\\\"{o}f type theory to the cumulative hierarchy of universes. This extension completes game semantics of all standard types of Martin-L\\\"{o}f type theory for the first time in the 30 years history of modern game semantics. As a result, the powerful combinatorial reasoning of game semantics becomes available for the study of universes and types generated by them. A main challenge in achieving game semantics of universes comes from a conflict between identity types and universes: Naive game semantics of the encoding of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.13069","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/2203.13069/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":"2026-07-05T04:08:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5rDaMnMed6Gn6WQ+Irxq4JcbIcT0M8I+tINq5M3vyHDpU1ddzOs33ECYxWrPHSk+TA+LPmMeDgquBfugHuggDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T06:54:30.441091Z"},"content_sha256":"045b4856d6af3562725a8a50666e1d0fe04e5e15ce64a4ba9b5efae35c8b2ef2","schema_version":"1.0","event_id":"sha256:045b4856d6af3562725a8a50666e1d0fe04e5e15ce64a4ba9b5efae35c8b2ef2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NSLF7MAEOW3NNGNZ2UPFRPA24/bundle.json","state_url":"https://pith.science/pith/5NSLF7MAEOW3NNGNZ2UPFRPA24/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NSLF7MAEOW3NNGNZ2UPFRPA24/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":"2026-08-18T06:54:30Z","links":{"resolver":"https://pith.science/pith/5NSLF7MAEOW3NNGNZ2UPFRPA24","bundle":"https://pith.science/pith/5NSLF7MAEOW3NNGNZ2UPFRPA24/bundle.json","state":"https://pith.science/pith/5NSLF7MAEOW3NNGNZ2UPFRPA24/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NSLF7MAEOW3NNGNZ2UPFRPA24/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:5NSLF7MAEOW3NNGNZ2UPFRPA24","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":"245d8ea2094a37e2fe4bf9a215c5dba1e91bc498c2016d5a01d9a7809d442138","cross_cats_sorted":["cs.LO","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-03-24T13:47:45Z","title_canon_sha256":"2addb1b657ff0cc004c3de501056bfad575158ea1af641efe2b4671a81529dbc"},"schema_version":"1.0","source":{"id":"2203.13069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.13069","created_at":"2026-07-05T04:08:20Z"},{"alias_kind":"arxiv_version","alias_value":"2203.13069v1","created_at":"2026-07-05T04:08:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.13069","created_at":"2026-07-05T04:08:20Z"},{"alias_kind":"pith_short_12","alias_value":"5NSLF7MAEOW3","created_at":"2026-07-05T04:08:20Z"},{"alias_kind":"pith_short_16","alias_value":"5NSLF7MAEOW3NNGN","created_at":"2026-07-05T04:08:20Z"},{"alias_kind":"pith_short_8","alias_value":"5NSLF7MA","created_at":"2026-07-05T04:08:20Z"}],"graph_snapshots":[{"event_id":"sha256:045b4856d6af3562725a8a50666e1d0fe04e5e15ce64a4ba9b5efae35c8b2ef2","target":"graph","created_at":"2026-07-05T04:08:20Z","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/2203.13069/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work extends the present author's computational game semantics of Martin-L\\\"{o}f type theory to the cumulative hierarchy of universes. This extension completes game semantics of all standard types of Martin-L\\\"{o}f type theory for the first time in the 30 years history of modern game semantics. As a result, the powerful combinatorial reasoning of game semantics becomes available for the study of universes and types generated by them. A main challenge in achieving game semantics of universes comes from a conflict between identity types and universes: Naive game semantics of the encoding of","authors_text":"Norihiro Yamada","cross_cats":["cs.LO","math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-03-24T13:47:45Z","title":"Game semantics of universes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.13069","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":"sha256:00ee6ab8e03c794f01cf8696c6a3f051926739a39dfecfc80ee42c959ef766d9","target":"record","created_at":"2026-07-05T04:08:20Z","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":"245d8ea2094a37e2fe4bf9a215c5dba1e91bc498c2016d5a01d9a7809d442138","cross_cats_sorted":["cs.LO","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-03-24T13:47:45Z","title_canon_sha256":"2addb1b657ff0cc004c3de501056bfad575158ea1af641efe2b4671a81529dbc"},"schema_version":"1.0","source":{"id":"2203.13069","kind":"arxiv","version":1}},"canonical_sha256":"eb64b2fd8023adb6b4cdcea8f2c5e0d70454d6acfc1a023ea847dbdf64cf2cca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb64b2fd8023adb6b4cdcea8f2c5e0d70454d6acfc1a023ea847dbdf64cf2cca","first_computed_at":"2026-07-05T04:08:20.241391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:08:20.241391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eoYrL1QEg0B7f1hng3loebZQdNMPoeyeiipX8RNyYjGO3fkKZwqfQ7mdy50hGO6gif1qAHcpn/2eh9IxnCVmAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:08:20.241873Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.13069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00ee6ab8e03c794f01cf8696c6a3f051926739a39dfecfc80ee42c959ef766d9","sha256:045b4856d6af3562725a8a50666e1d0fe04e5e15ce64a4ba9b5efae35c8b2ef2"],"state_sha256":"a9ec25f7b9fa81469ac33d0d379294647909586af0920a197d87f410d32cc898"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HoMf/4AU3/1LMroAE3ux81Fs2++dzdqwuKnY+5F8nJpdSattsj0EsApTuaBlfE3IFF8T384GgJUplhAvKvcfCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T06:54:30.447034Z","bundle_sha256":"9cbc6ce6fba5a0352f028f0fe1bd7b7b449d1aac72075f849837fb3a5e4a373f"}}