{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:GSJYM5FB3PLHS7765CFSWT2AST","short_pith_number":"pith:GSJYM5FB","canonical_record":{"source":{"id":"1904.06538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-04-13T12:54:57Z","cross_cats_sorted":[],"title_canon_sha256":"63d1bf6ddcfc5b27e8228e1b8142aea5ae44b7b1728ac32508fc6ff49ca1fcbc","abstract_canon_sha256":"94f7f4e2f90503c29e8150e7cb15b41094e6552f6bb6edb7fa9091c82998cb6b"},"schema_version":"1.0"},"canonical_sha256":"34938674a1dbd6797ffee88b2b4f4094cef22af74797e1b7c90c091e44ba8a8f","source":{"kind":"arxiv","id":"1904.06538","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06538","created_at":"2026-05-17T23:48:38Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06538v1","created_at":"2026-05-17T23:48:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06538","created_at":"2026-05-17T23:48:38Z"},{"alias_kind":"pith_short_12","alias_value":"GSJYM5FB3PLH","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GSJYM5FB3PLHS776","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GSJYM5FB","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:GSJYM5FB3PLHS7765CFSWT2AST","target":"record","payload":{"canonical_record":{"source":{"id":"1904.06538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-04-13T12:54:57Z","cross_cats_sorted":[],"title_canon_sha256":"63d1bf6ddcfc5b27e8228e1b8142aea5ae44b7b1728ac32508fc6ff49ca1fcbc","abstract_canon_sha256":"94f7f4e2f90503c29e8150e7cb15b41094e6552f6bb6edb7fa9091c82998cb6b"},"schema_version":"1.0"},"canonical_sha256":"34938674a1dbd6797ffee88b2b4f4094cef22af74797e1b7c90c091e44ba8a8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:38.900449Z","signature_b64":"CfhdbwfALjcoIOrAGMPSNM4MFwx2Q+c9r+WOVihI5DclsQo02MojV/v5GKnjl1D1Gvj4slkHGt5/BBwLpJHFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34938674a1dbd6797ffee88b2b4f4094cef22af74797e1b7c90c091e44ba8a8f","last_reissued_at":"2026-05-17T23:48:38.899818Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:38.899818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.06538","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":"2026-05-17T23:48:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5rIfDkpnKlTr3IgQeto9tv8QL8SZDDgb/PG8yO1NCCHovibLToZczuuwqmbzMk7ITD3YycuXrxpnYwPf2ah/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:47:02.493538Z"},"content_sha256":"1746dbf20691ba3e810299b274d91fee72190a56fe166e454fd3eb570546eac9","schema_version":"1.0","event_id":"sha256:1746dbf20691ba3e810299b274d91fee72190a56fe166e454fd3eb570546eac9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:GSJYM5FB3PLHS7765CFSWT2AST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A type theory for cartesian closed bicategories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Marcelo Fiore, Philip Saville","submitted_at":"2019-04-13T12:54:57Z","abstract_excerpt":"We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal property, thereby lifting the Curry-Howard-Lambek correspondence to the bicategorical setting. Our approach is principled and practical. Weak substitution structure is constructed using a bicategorification of the notion of abstract clone from universal algebra, and the rules for products and exponentials are synthesised from semantic considerations. The result is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06538","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":""},"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":"2026-05-17T23:48:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qA0TlCaIWauWeSQ6eP/j7yA0DJpSGLohq0mVAxRbN6qX5SBQEg3936rf37Bw86wp+p//zYK9UIn66/D3/6FtCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:47:02.494217Z"},"content_sha256":"290a19a68d446952daac05dd8ea6f7128668815687654fef67cc98d3b2c48172","schema_version":"1.0","event_id":"sha256:290a19a68d446952daac05dd8ea6f7128668815687654fef67cc98d3b2c48172"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GSJYM5FB3PLHS7765CFSWT2AST/bundle.json","state_url":"https://pith.science/pith/GSJYM5FB3PLHS7765CFSWT2AST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GSJYM5FB3PLHS7765CFSWT2AST/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":"2026-06-08T01:47:02Z","links":{"resolver":"https://pith.science/pith/GSJYM5FB3PLHS7765CFSWT2AST","bundle":"https://pith.science/pith/GSJYM5FB3PLHS7765CFSWT2AST/bundle.json","state":"https://pith.science/pith/GSJYM5FB3PLHS7765CFSWT2AST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GSJYM5FB3PLHS7765CFSWT2AST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GSJYM5FB3PLHS7765CFSWT2AST","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":"94f7f4e2f90503c29e8150e7cb15b41094e6552f6bb6edb7fa9091c82998cb6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-04-13T12:54:57Z","title_canon_sha256":"63d1bf6ddcfc5b27e8228e1b8142aea5ae44b7b1728ac32508fc6ff49ca1fcbc"},"schema_version":"1.0","source":{"id":"1904.06538","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06538","created_at":"2026-05-17T23:48:38Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06538v1","created_at":"2026-05-17T23:48:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06538","created_at":"2026-05-17T23:48:38Z"},{"alias_kind":"pith_short_12","alias_value":"GSJYM5FB3PLH","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GSJYM5FB3PLHS776","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GSJYM5FB","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:290a19a68d446952daac05dd8ea6f7128668815687654fef67cc98d3b2c48172","target":"graph","created_at":"2026-05-17T23:48:38Z","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"},"paper":{"abstract_excerpt":"We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal property, thereby lifting the Curry-Howard-Lambek correspondence to the bicategorical setting. Our approach is principled and practical. Weak substitution structure is constructed using a bicategorification of the notion of abstract clone from universal algebra, and the rules for products and exponentials are synthesised from semantic considerations. The result is ","authors_text":"Marcelo Fiore, Philip Saville","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-04-13T12:54:57Z","title":"A type theory for cartesian closed bicategories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06538","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":"sha256:1746dbf20691ba3e810299b274d91fee72190a56fe166e454fd3eb570546eac9","target":"record","created_at":"2026-05-17T23:48:38Z","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":"94f7f4e2f90503c29e8150e7cb15b41094e6552f6bb6edb7fa9091c82998cb6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-04-13T12:54:57Z","title_canon_sha256":"63d1bf6ddcfc5b27e8228e1b8142aea5ae44b7b1728ac32508fc6ff49ca1fcbc"},"schema_version":"1.0","source":{"id":"1904.06538","kind":"arxiv","version":1}},"canonical_sha256":"34938674a1dbd6797ffee88b2b4f4094cef22af74797e1b7c90c091e44ba8a8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34938674a1dbd6797ffee88b2b4f4094cef22af74797e1b7c90c091e44ba8a8f","first_computed_at":"2026-05-17T23:48:38.899818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:38.899818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CfhdbwfALjcoIOrAGMPSNM4MFwx2Q+c9r+WOVihI5DclsQo02MojV/v5GKnjl1D1Gvj4slkHGt5/BBwLpJHFDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:38.900449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.06538","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1746dbf20691ba3e810299b274d91fee72190a56fe166e454fd3eb570546eac9","sha256:290a19a68d446952daac05dd8ea6f7128668815687654fef67cc98d3b2c48172"],"state_sha256":"4920fb26ef384bc1c124bb4046078cdee578e8c0b58d81aaa3a26b0cba11e655"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"exHasfkYgUay8RAs9mEt5SoTcwkgmLadpPCqRpR9HiOcfF3PDkduaMQFglBRIKfh3xwT5akVqCStzja+5ej1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T01:47:02.498048Z","bundle_sha256":"1ff7aa6a7f4144637b3d9b69d1f7c5333b64db0281ef3e0be8cc8b5a91e9cf7f"}}