{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2O5DRWFPJHCI7MU6553A5VYCYI","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":"c318e357e7de884f6d9268b932176823cec4d0298409417ef89398b876093a99","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-01-06T11:58:48Z","title_canon_sha256":"3bdcaac8a44465eaf194ae710f1841a9f461f946f0609838f0f982927f8578a8"},"schema_version":"1.0","source":{"id":"1401.1053","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1053","created_at":"2026-05-18T02:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1053v2","created_at":"2026-05-18T02:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1053","created_at":"2026-05-18T02:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"2O5DRWFPJHCI","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2O5DRWFPJHCI7MU6","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2O5DRWFP","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:0ff415fe2f9a12a1d1f21c6da132a834be00c5264dc2674c95f217eff0d5282d","target":"graph","created_at":"2026-05-18T02:53:40Z","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 this work, we study the notions of relative comonad and comodule over a relative comonad, and use these notions to give a terminal coalgebra semantics for the coinductive type families of streams and of infinite triangular matrices, respectively, in intensional Martin-L\\\"of type theory. Our results are mechanized in the proof assistant Coq.","authors_text":"Benedikt Ahrens, R\\'egis Spadotti","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-01-06T11:58:48Z","title":"Terminal semantics for codata types in intensional Martin-L\\\"of type theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1053","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":"sha256:367c3dae255b1c2383decb21b61ef847fd5d61354a552ed736139676d4308583","target":"record","created_at":"2026-05-18T02:53:40Z","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":"c318e357e7de884f6d9268b932176823cec4d0298409417ef89398b876093a99","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-01-06T11:58:48Z","title_canon_sha256":"3bdcaac8a44465eaf194ae710f1841a9f461f946f0609838f0f982927f8578a8"},"schema_version":"1.0","source":{"id":"1401.1053","kind":"arxiv","version":2}},"canonical_sha256":"d3ba38d8af49c48fb29eef760ed702c2151549f149b4e02c351530d684be505b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3ba38d8af49c48fb29eef760ed702c2151549f149b4e02c351530d684be505b","first_computed_at":"2026-05-18T02:53:40.220911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:40.220911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LCt9qH+H+A+14Qp0bgz9mllhPTYsfxV2O8g2MC6gT+xZRr1yj+GHFesAQ6nbpx7rmwYYHh9TKAMWniwNtOIUDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:40.221392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1053","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:367c3dae255b1c2383decb21b61ef847fd5d61354a552ed736139676d4308583","sha256:0ff415fe2f9a12a1d1f21c6da132a834be00c5264dc2674c95f217eff0d5282d"],"state_sha256":"315395dd5249b5089cb706b872b0a44f6fdc78be7775b3c85ed77399a1ad51f3"}