{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XU2IZ5EZLGNRYOGDSEITE2BLJZ","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":"87aaf7ee171c2d1ba802f94e1fd0e62802e76fa5e5f279e9407f6579dcc80ece","cross_cats_sorted":["cs.LO","cs.PL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2020-04-09T13:15:06Z","title_canon_sha256":"f63ae35f583aa5a9fab8e1209dc6070dd0e1b6d41540cf4a3816417d0edc3b09"},"schema_version":"1.0","source":{"id":"2004.04526","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.04526","created_at":"2026-07-05T03:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"2004.04526v5","created_at":"2026-07-05T03:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.04526","created_at":"2026-07-05T03:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"XU2IZ5EZLGNR","created_at":"2026-07-05T03:58:32Z"},{"alias_kind":"pith_short_16","alias_value":"XU2IZ5EZLGNRYOGD","created_at":"2026-07-05T03:58:32Z"},{"alias_kind":"pith_short_8","alias_value":"XU2IZ5EZ","created_at":"2026-07-05T03:58:32Z"}],"graph_snapshots":[{"event_id":"sha256:ddb07270b59ad2d372a0ed0c1f96ba624d5b65165fdce78861fd8abd53763124","target":"graph","created_at":"2026-07-05T03:58:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2004.04526/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Morphisms in a monoidal category are usually interpreted as processes, and graphically depicted as square boxes. In practice, we are faced with the problem of interpreting what non-square boxes ought to represent in terms of the monoidal category and, more importantly, how should they be composed. Examples of this situation include lenses or learners. We propose a description of these non-square boxes, which we call open diagrams, using the monoidal bicategory of profunctors. A graphical coend calculus can then be used to reason about open diagrams and their compositions.","authors_text":"Mario Rom\\'an (Tallinn University of Technology)","cross_cats":["cs.LO","cs.PL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2020-04-09T13:15:06Z","title":"Open Diagrams via Coend Calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.04526","kind":"arxiv","version":5},"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":"sha256:4579b7bc33b4c6f36565755d29ebd6998835c248ab6619eccbcc0fddbee002a2","target":"record","created_at":"2026-07-05T03:58:32Z","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":"87aaf7ee171c2d1ba802f94e1fd0e62802e76fa5e5f279e9407f6579dcc80ece","cross_cats_sorted":["cs.LO","cs.PL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2020-04-09T13:15:06Z","title_canon_sha256":"f63ae35f583aa5a9fab8e1209dc6070dd0e1b6d41540cf4a3816417d0edc3b09"},"schema_version":"1.0","source":{"id":"2004.04526","kind":"arxiv","version":5}},"canonical_sha256":"bd348cf499599b1c38c3911132682b4e4a1064cb218101d8cfc7d0417752a6d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd348cf499599b1c38c3911132682b4e4a1064cb218101d8cfc7d0417752a6d8","first_computed_at":"2026-07-05T03:58:32.329848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:58:32.329848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HEyOvctEvhDJfNEhnlnKMlmSfy8kTR6SVKMhTxNvHstH7WPXxB2lyCT395WeOOz39QJtExhvhcFspKFXzbA/AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:58:32.330312Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.04526","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4579b7bc33b4c6f36565755d29ebd6998835c248ab6619eccbcc0fddbee002a2","sha256:ddb07270b59ad2d372a0ed0c1f96ba624d5b65165fdce78861fd8abd53763124"],"state_sha256":"29cbb718d088ba995e7ef1fdb8ea1066d74c3cad21df0933545453a0cf281970"}