{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:M547YLCPCCGGPCC6NQCFD7BDGL","short_pith_number":"pith:M547YLCP","schema_version":"1.0","canonical_sha256":"6779fc2c4f108c67885e6c0451fc2332ee35da9cc57f4d1a2fd064574e33dab4","source":{"kind":"arxiv","id":"2101.10491","version":1},"attestation_state":"computed","paper":{"title":"Categorical semantics of a simple differential programming language","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"math.CT","authors_text":"Dorette Pronk, Geoffrey Cruttwell, Jonathan Gallagher","submitted_at":"2021-01-26T00:08:48Z","abstract_excerpt":"With the increased interest in machine learning, and deep learning in particular,  the use of automatic differentiation has become more wide-spread in computation.  There have been two recent developments to provide the theoretical support for this types of structure.  One approach, due to Abadi and Plotkin, provides a simple differential programming language.  Another approach is the notion of a reverse differential category.  In the present paper we bring these two approaches together.  In particular, we show how an extension of reverse derivative categories models Abadi and Plotkin's langua"},"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":"2101.10491","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2021-01-26T00:08:48Z","cross_cats_sorted":["cs.PL"],"title_canon_sha256":"046fa83c6fca86cb40a6c2b7b5a0174be1f61ef405981d0698cb7b9f58e935ba","abstract_canon_sha256":"521dccc805a89a1f443069a4a38731fb432a910c91e804991fc2dd7020a2ebb1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:09:59.087357Z","signature_b64":"ZZXTqPhAzeHph4kTnmnZ+tAJkO/Sn+yN7EBe4giiJHevzRp53rC5u5QX6PwBm47KomN1MyWl2fHquXLXNAH+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6779fc2c4f108c67885e6c0451fc2332ee35da9cc57f4d1a2fd064574e33dab4","last_reissued_at":"2026-07-05T02:09:59.086973Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:09:59.086973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Categorical semantics of a simple differential programming language","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"math.CT","authors_text":"Dorette Pronk, Geoffrey Cruttwell, Jonathan Gallagher","submitted_at":"2021-01-26T00:08:48Z","abstract_excerpt":"With the increased interest in machine learning, and deep learning in particular,  the use of automatic differentiation has become more wide-spread in computation.  There have been two recent developments to provide the theoretical support for this types of structure.  One approach, due to Abadi and Plotkin, provides a simple differential programming language.  Another approach is the notion of a reverse differential category.  In the present paper we bring these two approaches together.  In particular, we show how an extension of reverse derivative categories models Abadi and Plotkin's langua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.10491","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/2101.10491/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":"2101.10491","created_at":"2026-07-05T02:09:59.087030+00:00"},{"alias_kind":"arxiv_version","alias_value":"2101.10491v1","created_at":"2026-07-05T02:09:59.087030+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.10491","created_at":"2026-07-05T02:09:59.087030+00:00"},{"alias_kind":"pith_short_12","alias_value":"M547YLCPCCGG","created_at":"2026-07-05T02:09:59.087030+00:00"},{"alias_kind":"pith_short_16","alias_value":"M547YLCPCCGGPCC6","created_at":"2026-07-05T02:09:59.087030+00:00"},{"alias_kind":"pith_short_8","alias_value":"M547YLCP","created_at":"2026-07-05T02:09:59.087030+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M547YLCPCCGGPCC6NQCFD7BDGL","json":"https://pith.science/pith/M547YLCPCCGGPCC6NQCFD7BDGL.json","graph_json":"https://pith.science/api/pith-number/M547YLCPCCGGPCC6NQCFD7BDGL/graph.json","events_json":"https://pith.science/api/pith-number/M547YLCPCCGGPCC6NQCFD7BDGL/events.json","paper":"https://pith.science/paper/M547YLCP"},"agent_actions":{"view_html":"https://pith.science/pith/M547YLCPCCGGPCC6NQCFD7BDGL","download_json":"https://pith.science/pith/M547YLCPCCGGPCC6NQCFD7BDGL.json","view_paper":"https://pith.science/paper/M547YLCP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2101.10491&json=true","fetch_graph":"https://pith.science/api/pith-number/M547YLCPCCGGPCC6NQCFD7BDGL/graph.json","fetch_events":"https://pith.science/api/pith-number/M547YLCPCCGGPCC6NQCFD7BDGL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M547YLCPCCGGPCC6NQCFD7BDGL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M547YLCPCCGGPCC6NQCFD7BDGL/action/storage_attestation","attest_author":"https://pith.science/pith/M547YLCPCCGGPCC6NQCFD7BDGL/action/author_attestation","sign_citation":"https://pith.science/pith/M547YLCPCCGGPCC6NQCFD7BDGL/action/citation_signature","submit_replication":"https://pith.science/pith/M547YLCPCCGGPCC6NQCFD7BDGL/action/replication_record"}},"created_at":"2026-07-05T02:09:59.087030+00:00","updated_at":"2026-07-05T02:09:59.087030+00:00"}