{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PS5QQL2CKYWMBDJQB3DVVFOCNH","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":"b1361fb9a2893cd0ba0f39f136fc54716da114451f9735c473126c7bf1057444","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-11-29T04:43:22Z","title_canon_sha256":"cf3f0ca5099893bcfff689f23e81d8f0011c97a494fb49faa6fb0a421813893d"},"schema_version":"1.0","source":{"id":"1811.11961","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.11961","created_at":"2026-05-17T23:51:52Z"},{"alias_kind":"arxiv_version","alias_value":"1811.11961v2","created_at":"2026-05-17T23:51:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11961","created_at":"2026-05-17T23:51:52Z"},{"alias_kind":"pith_short_12","alias_value":"PS5QQL2CKYWM","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PS5QQL2CKYWMBDJQ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PS5QQL2C","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:5a8497831298919f9925e8dc73dfed3a4282e4e5b56f782c72c22d229623ab60","target":"graph","created_at":"2026-05-17T23:51:52Z","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":"In the categorical setting, histomorphisms model a course-of-value recursion scheme that allows functions to be defined using arbitrary previously computed values. In this paper, we use the Calculus of Dependent Lambda Eliminations (CDLE) to derive a lambda-encoding of inductive datatypes that admits course-of-value induction. Similar to course-of-value recursion, course-of-value induction gives access to inductive hypotheses at arbitrary depth of the inductive arguments of a function. We show that the derived course-of-value datatypes are well-behaved by proving Lambek's lemma and characteriz","authors_text":"Aaron Stump, Christopher Jenkins, Denis Firsov, Larry Diehl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-11-29T04:43:22Z","title":"Course-of-Value Induction in Cedille"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11961","kind":"arxiv","version":2},"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":"sha256:623c1d8fa2f6ba7cebbca1a9983719788c5963b2da935aeb7c87f8c60fa9985b","target":"record","created_at":"2026-05-17T23:51:52Z","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":"b1361fb9a2893cd0ba0f39f136fc54716da114451f9735c473126c7bf1057444","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-11-29T04:43:22Z","title_canon_sha256":"cf3f0ca5099893bcfff689f23e81d8f0011c97a494fb49faa6fb0a421813893d"},"schema_version":"1.0","source":{"id":"1811.11961","kind":"arxiv","version":2}},"canonical_sha256":"7cbb082f42562cc08d300ec75a95c269d7cb29c5f90646831bd6d4d640262d71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cbb082f42562cc08d300ec75a95c269d7cb29c5f90646831bd6d4d640262d71","first_computed_at":"2026-05-17T23:51:52.259590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:52.259590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9rifwzBvNOOUOBsJbT8CKBC2yv860lmw6DRdL0r3GhjmOF20sN/hFstSGd8QwNBGpJhdZrkmsjaRS1mZ5NnXBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:52.260286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.11961","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:623c1d8fa2f6ba7cebbca1a9983719788c5963b2da935aeb7c87f8c60fa9985b","sha256:5a8497831298919f9925e8dc73dfed3a4282e4e5b56f782c72c22d229623ab60"],"state_sha256":"1934314fac6948e08b436197b597b92d41493bb9bb846c097ea45e46b71c67c9"}