{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:BWR7AREMYO734K6RHJB2YQRICU","short_pith_number":"pith:BWR7AREM","canonical_record":{"source":{"id":"2003.06214","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2020-03-13T12:03:04Z","cross_cats_sorted":[],"title_canon_sha256":"d3b8735e635e6017595a223e87ba30bbb77043422aa57426c97e2f4d7e92580d","abstract_canon_sha256":"2bc5151b4e61acc3e16182b0f8afd1c970257a282667ae414ce345dc40131fcc"},"schema_version":"1.0"},"canonical_sha256":"0da3f0448cc3bfbe2bd13a43ac4228152edf9920e712f08a692730085bf58fa7","source":{"kind":"arxiv","id":"2003.06214","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.06214","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"arxiv_version","alias_value":"2003.06214v1","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.06214","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"pith_short_12","alias_value":"BWR7AREMYO73","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"pith_short_16","alias_value":"BWR7AREMYO734K6R","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"pith_short_8","alias_value":"BWR7AREM","created_at":"2026-07-05T00:47:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:BWR7AREMYO734K6RHJB2YQRICU","target":"record","payload":{"canonical_record":{"source":{"id":"2003.06214","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2020-03-13T12:03:04Z","cross_cats_sorted":[],"title_canon_sha256":"d3b8735e635e6017595a223e87ba30bbb77043422aa57426c97e2f4d7e92580d","abstract_canon_sha256":"2bc5151b4e61acc3e16182b0f8afd1c970257a282667ae414ce345dc40131fcc"},"schema_version":"1.0"},"canonical_sha256":"0da3f0448cc3bfbe2bd13a43ac4228152edf9920e712f08a692730085bf58fa7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:47:44.714121Z","signature_b64":"ghhIYlIca9LXDtJfMasW+ubH1ZnOEp2YKEDoufSP8XTCcZZTqArKSoo97crEs/VMIdPKOQiQWfLqwLw4iQZsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0da3f0448cc3bfbe2bd13a43ac4228152edf9920e712f08a692730085bf58fa7","last_reissued_at":"2026-07-05T00:47:44.713744Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:47:44.713744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2003.06214","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":"2026-07-05T00:47:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Om5X7F1FrtIBsQrwiZyiqBJI8s1/tuW1FPsvK1zS/FgItmJwMUAauhFkDptk8v2Mj545hssjcjtkBvtvBZv4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T04:46:13.220577Z"},"content_sha256":"284bdc4b8f2d15f61104026f4965c9a77319e64862644cf2ae77b7e1085f0d23","schema_version":"1.0","event_id":"sha256:284bdc4b8f2d15f61104026f4965c9a77319e64862644cf2ae77b7e1085f0d23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:BWR7AREMYO734K6RHJB2YQRICU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comb Diagrams for Discrete-Time Feedback","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Mario Rom\\'an","submitted_at":"2020-03-13T12:03:04Z","abstract_excerpt":"The data for many useful bidirectional constructions in applied category theory (optics, learners, games, quantum combs) can be expressed in terms of diagrams containing \"holes\" or \"incomplete parts\", sometimes known as comb diagrams. We give a possible formalization of what these circuits with incomplete parts represent in terms of symmetric monoidal categories, using the dinaturality equivalence relations arising from a coend. Our main idea is to extend this formal description to allow for infinite circuits with holes indexed by the natural numbers. We show how infinite combs over an arbitra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.06214","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/2003.06214/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:47:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l39SWwjzrET6vLkF7DvBC9NRpqhiIaA65U5nUYYHAqet5Yv2H9hkAHOP30rdzXQ7q/Io1v04NhNTwSl2GwCZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T04:46:13.221113Z"},"content_sha256":"057229de91ca3602cba7b5bfbe952a34e35e6673de77fc04bde162b264638f3b","schema_version":"1.0","event_id":"sha256:057229de91ca3602cba7b5bfbe952a34e35e6673de77fc04bde162b264638f3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BWR7AREMYO734K6RHJB2YQRICU/bundle.json","state_url":"https://pith.science/pith/BWR7AREMYO734K6RHJB2YQRICU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BWR7AREMYO734K6RHJB2YQRICU/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":"2026-08-07T04:46:13Z","links":{"resolver":"https://pith.science/pith/BWR7AREMYO734K6RHJB2YQRICU","bundle":"https://pith.science/pith/BWR7AREMYO734K6RHJB2YQRICU/bundle.json","state":"https://pith.science/pith/BWR7AREMYO734K6RHJB2YQRICU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BWR7AREMYO734K6RHJB2YQRICU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:BWR7AREMYO734K6RHJB2YQRICU","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":"2bc5151b4e61acc3e16182b0f8afd1c970257a282667ae414ce345dc40131fcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2020-03-13T12:03:04Z","title_canon_sha256":"d3b8735e635e6017595a223e87ba30bbb77043422aa57426c97e2f4d7e92580d"},"schema_version":"1.0","source":{"id":"2003.06214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.06214","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"arxiv_version","alias_value":"2003.06214v1","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.06214","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"pith_short_12","alias_value":"BWR7AREMYO73","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"pith_short_16","alias_value":"BWR7AREMYO734K6R","created_at":"2026-07-05T00:47:44Z"},{"alias_kind":"pith_short_8","alias_value":"BWR7AREM","created_at":"2026-07-05T00:47:44Z"}],"graph_snapshots":[{"event_id":"sha256:057229de91ca3602cba7b5bfbe952a34e35e6673de77fc04bde162b264638f3b","target":"graph","created_at":"2026-07-05T00:47:44Z","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/2003.06214/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The data for many useful bidirectional constructions in applied category theory (optics, learners, games, quantum combs) can be expressed in terms of diagrams containing \"holes\" or \"incomplete parts\", sometimes known as comb diagrams. We give a possible formalization of what these circuits with incomplete parts represent in terms of symmetric monoidal categories, using the dinaturality equivalence relations arising from a coend. Our main idea is to extend this formal description to allow for infinite circuits with holes indexed by the natural numbers. We show how infinite combs over an arbitra","authors_text":"Mario Rom\\'an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2020-03-13T12:03:04Z","title":"Comb Diagrams for Discrete-Time Feedback"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.06214","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":"sha256:284bdc4b8f2d15f61104026f4965c9a77319e64862644cf2ae77b7e1085f0d23","target":"record","created_at":"2026-07-05T00:47:44Z","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":"2bc5151b4e61acc3e16182b0f8afd1c970257a282667ae414ce345dc40131fcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2020-03-13T12:03:04Z","title_canon_sha256":"d3b8735e635e6017595a223e87ba30bbb77043422aa57426c97e2f4d7e92580d"},"schema_version":"1.0","source":{"id":"2003.06214","kind":"arxiv","version":1}},"canonical_sha256":"0da3f0448cc3bfbe2bd13a43ac4228152edf9920e712f08a692730085bf58fa7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0da3f0448cc3bfbe2bd13a43ac4228152edf9920e712f08a692730085bf58fa7","first_computed_at":"2026-07-05T00:47:44.713744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:47:44.713744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ghhIYlIca9LXDtJfMasW+ubH1ZnOEp2YKEDoufSP8XTCcZZTqArKSoo97crEs/VMIdPKOQiQWfLqwLw4iQZsBA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:47:44.714121Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.06214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:284bdc4b8f2d15f61104026f4965c9a77319e64862644cf2ae77b7e1085f0d23","sha256:057229de91ca3602cba7b5bfbe952a34e35e6673de77fc04bde162b264638f3b"],"state_sha256":"cdbb781ef7dab9e29e10dcd538826c3062b413f5dceb7f8bf1a5682895346f97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WpFLQzHzmALKGksr1xyEFEyubVhjhfWdoHHwO7pI3/0rskpIj2SXKvSBakXVl0x1x5hfMie5XBu6oy2fy/3XCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T04:46:13.226014Z","bundle_sha256":"62a5b9641ead15ddb9ea59454552d5b73d4649fcb69503743489d1cfe85d2ad6"}}