{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2AZ63TFOIYVV6V3V2I7X4D37UW","short_pith_number":"pith:2AZ63TFO","canonical_record":{"source":{"id":"1802.00997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-02-03T16:58:00Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"d8b88fc3b54031910f680c15da5901a54139ad21fcf463fc2bc38d3fa4935a7d","abstract_canon_sha256":"c58557ed77df301ea40766cf9960fa9830e7b979bff1e6643359300c52e0ed58"},"schema_version":"1.0"},"canonical_sha256":"d033edccae462b5f5775d23f7e0f7fa5807d2d94f7e294732f4c52978c028232","source":{"kind":"arxiv","id":"1802.00997","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00997","created_at":"2026-05-18T00:24:27Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00997v1","created_at":"2026-05-18T00:24:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00997","created_at":"2026-05-18T00:24:27Z"},{"alias_kind":"pith_short_12","alias_value":"2AZ63TFOIYVV","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2AZ63TFOIYVV6V3V","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2AZ63TFO","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2AZ63TFOIYVV6V3V2I7X4D37UW","target":"record","payload":{"canonical_record":{"source":{"id":"1802.00997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-02-03T16:58:00Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"d8b88fc3b54031910f680c15da5901a54139ad21fcf463fc2bc38d3fa4935a7d","abstract_canon_sha256":"c58557ed77df301ea40766cf9960fa9830e7b979bff1e6643359300c52e0ed58"},"schema_version":"1.0"},"canonical_sha256":"d033edccae462b5f5775d23f7e0f7fa5807d2d94f7e294732f4c52978c028232","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:27.666719Z","signature_b64":"1WuyeCget7CuE8yDlx5qPBW4p8TATVRjrDJotfJExrcGYnJo1eti5rRXA4dOL0gp4ZkqcaaKzgBUIawfLOIZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d033edccae462b5f5775d23f7e0f7fa5807d2d94f7e294732f4c52978c028232","last_reissued_at":"2026-05-18T00:24:27.666221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:27.666221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.00997","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":"2026-05-18T00:24:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ltk8F5wEx6zATXeCkOQHGAxbwMk/Zn8qrRmeFJCEUz2cxmI4XCN1Dr+4fBLerNT9P2LfrY99q3pbVsjXZmTpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:25:23.367687Z"},"content_sha256":"3a5680170353a0179eded5417caeff96d3ed168baa40560135e0b8750db7d4f5","schema_version":"1.0","event_id":"sha256:3a5680170353a0179eded5417caeff96d3ed168baa40560135e0b8750db7d4f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2AZ63TFOIYVV6V3V2I7X4D37UW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial pseudomonads and dependent type theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CT","authors_text":"Clive Newstead, Steve Awodey","submitted_at":"2018-02-03T16:58:00Z","abstract_excerpt":"We assemble polynomials in a locally cartesian closed category into a tricategory, allowing us to define the notion of a polynomial pseudomonad and polynomial pseudoalgebra. Working in the context of natural models of type theory, we prove that dependent type theories admitting a unit type and dependent sum types give rise to polynomial pseudomonads, and that those admitting dependent product types give rise to polynomial pseudoalgebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00997","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":"2026-05-18T00:24:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kZPmtrQ7AJ9hzPTk44cMXD/V0cqEvUqfcFEMrKllYXiPMuSx27um1PkyUlGV8djhsEJrL13Ehon/lB1/cdpJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:25:23.374678Z"},"content_sha256":"b35d9d49ed5def762a6855b7c6b771c09fb8e36ad8c4bb6ecd344f1f1efbb680","schema_version":"1.0","event_id":"sha256:b35d9d49ed5def762a6855b7c6b771c09fb8e36ad8c4bb6ecd344f1f1efbb680"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2AZ63TFOIYVV6V3V2I7X4D37UW/bundle.json","state_url":"https://pith.science/pith/2AZ63TFOIYVV6V3V2I7X4D37UW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2AZ63TFOIYVV6V3V2I7X4D37UW/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":"2026-08-18T18:25:23Z","links":{"resolver":"https://pith.science/pith/2AZ63TFOIYVV6V3V2I7X4D37UW","bundle":"https://pith.science/pith/2AZ63TFOIYVV6V3V2I7X4D37UW/bundle.json","state":"https://pith.science/pith/2AZ63TFOIYVV6V3V2I7X4D37UW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2AZ63TFOIYVV6V3V2I7X4D37UW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2AZ63TFOIYVV6V3V2I7X4D37UW","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":"c58557ed77df301ea40766cf9960fa9830e7b979bff1e6643359300c52e0ed58","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-02-03T16:58:00Z","title_canon_sha256":"d8b88fc3b54031910f680c15da5901a54139ad21fcf463fc2bc38d3fa4935a7d"},"schema_version":"1.0","source":{"id":"1802.00997","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00997","created_at":"2026-05-18T00:24:27Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00997v1","created_at":"2026-05-18T00:24:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00997","created_at":"2026-05-18T00:24:27Z"},{"alias_kind":"pith_short_12","alias_value":"2AZ63TFOIYVV","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2AZ63TFOIYVV6V3V","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2AZ63TFO","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:b35d9d49ed5def762a6855b7c6b771c09fb8e36ad8c4bb6ecd344f1f1efbb680","target":"graph","created_at":"2026-05-18T00:24:27Z","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 assemble polynomials in a locally cartesian closed category into a tricategory, allowing us to define the notion of a polynomial pseudomonad and polynomial pseudoalgebra. Working in the context of natural models of type theory, we prove that dependent type theories admitting a unit type and dependent sum types give rise to polynomial pseudomonads, and that those admitting dependent product types give rise to polynomial pseudoalgebras.","authors_text":"Clive Newstead, Steve Awodey","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-02-03T16:58:00Z","title":"Polynomial pseudomonads and dependent type theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00997","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":"sha256:3a5680170353a0179eded5417caeff96d3ed168baa40560135e0b8750db7d4f5","target":"record","created_at":"2026-05-18T00:24:27Z","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":"c58557ed77df301ea40766cf9960fa9830e7b979bff1e6643359300c52e0ed58","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-02-03T16:58:00Z","title_canon_sha256":"d8b88fc3b54031910f680c15da5901a54139ad21fcf463fc2bc38d3fa4935a7d"},"schema_version":"1.0","source":{"id":"1802.00997","kind":"arxiv","version":1}},"canonical_sha256":"d033edccae462b5f5775d23f7e0f7fa5807d2d94f7e294732f4c52978c028232","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d033edccae462b5f5775d23f7e0f7fa5807d2d94f7e294732f4c52978c028232","first_computed_at":"2026-05-18T00:24:27.666221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:27.666221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1WuyeCget7CuE8yDlx5qPBW4p8TATVRjrDJotfJExrcGYnJo1eti5rRXA4dOL0gp4ZkqcaaKzgBUIawfLOIZAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:27.666719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.00997","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a5680170353a0179eded5417caeff96d3ed168baa40560135e0b8750db7d4f5","sha256:b35d9d49ed5def762a6855b7c6b771c09fb8e36ad8c4bb6ecd344f1f1efbb680"],"state_sha256":"3b46f08cb9c7cd43acc0c615e2e91edce2837c8cbb98d83f42224693e251b7c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wjYnrcY4i+kVw4B5JcZ7EajsOyqwR+NC2mAQkRX8gaWrL/yelo4xggELydlOyqrTf051U8SLgYm1zpGYmoKLDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T18:25:23.383439Z","bundle_sha256":"58e29ba5f4cdb8b4bb5531b05b84fffee84b6b2efeff0063ea7f60ec0c5ff2c4"}}