{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:JNFX3O2ZQ6VCDAEYMIESYIO5GX","short_pith_number":"pith:JNFX3O2Z","canonical_record":{"source":{"id":"2305.01041","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CT","submitted_at":"2023-05-01T19:02:20Z","cross_cats_sorted":["cs.PL"],"title_canon_sha256":"785574a5e8eaba2d6e7c5fbc4b35167aa68c0b26a028862adee08c925b06d4ac","abstract_canon_sha256":"8b65320e6ee74d897247b65001f2b418389efa4fc0b65c006f7b9e50a4087686"},"schema_version":"1.0"},"canonical_sha256":"4b4b7dbb5987aa21809862092c21dd35e7104b1436630b267f9fd32bd11c4336","source":{"kind":"arxiv","id":"2305.01041","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.01041","created_at":"2026-07-05T06:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"2305.01041v1","created_at":"2026-07-05T06:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.01041","created_at":"2026-07-05T06:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"JNFX3O2ZQ6VC","created_at":"2026-07-05T06:06:20Z"},{"alias_kind":"pith_short_16","alias_value":"JNFX3O2ZQ6VCDAEY","created_at":"2026-07-05T06:06:20Z"},{"alias_kind":"pith_short_8","alias_value":"JNFX3O2Z","created_at":"2026-07-05T06:06:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:JNFX3O2ZQ6VCDAEYMIESYIO5GX","target":"record","payload":{"canonical_record":{"source":{"id":"2305.01041","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CT","submitted_at":"2023-05-01T19:02:20Z","cross_cats_sorted":["cs.PL"],"title_canon_sha256":"785574a5e8eaba2d6e7c5fbc4b35167aa68c0b26a028862adee08c925b06d4ac","abstract_canon_sha256":"8b65320e6ee74d897247b65001f2b418389efa4fc0b65c006f7b9e50a4087686"},"schema_version":"1.0"},"canonical_sha256":"4b4b7dbb5987aa21809862092c21dd35e7104b1436630b267f9fd32bd11c4336","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:06:20.904826Z","signature_b64":"1LIArfGNarPsK8xGiUnixJWAjad4Z7Xf3LBo58I1k1thVMy/wzuM9crEAm47U4fmzlp7kDwFRpNIsWKATwkrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b4b7dbb5987aa21809862092c21dd35e7104b1436630b267f9fd32bd11c4336","last_reissued_at":"2026-07-05T06:06:20.904262Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:06:20.904262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.01041","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":"2026-07-05T06:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rjd/qGqvIKdrkwc7dvO621G8yI+6oRPkB3CTmf+z4OnVPg7yuNSHYpqzkOzSltds1vfZaaseprFQymBN/aV/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:43:50.954826Z"},"content_sha256":"eb7c35a86bce305f25eabffcd521d974ec180224db05aae89fc1d00d0802f34a","schema_version":"1.0","event_id":"sha256:eb7c35a86bce305f25eabffcd521d974ec180224db05aae89fc1d00d0802f34a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:JNFX3O2ZQ6VCDAEYMIESYIO5GX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Data-Parallel Algorithms for String Diagrams","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"math.CT","authors_text":"Fabio Zanasi, Paul Wilson","submitted_at":"2023-05-01T19:02:20Z","abstract_excerpt":"We give parallel algorithms for string diagrams represented as structured cospans of ACSets. Specifically, we give linear (sequential) and logarithmic (parallel) time algorithms for composition, tensor product, construction of diagrams from arbitrary $\\Sigma$-terms, and application of functors to diagrams. Our datastructure can represent morphisms of both the free symmetric monoidal category over an arbitrary signature as well as those with a chosen Special Frobenius structure. We show how this additional (hypergraph) structure can be used to map diagrams to diagrams of optics. This leads to a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.01041","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/2305.01041/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":"2026-07-05T06:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Tum4hYJfyTjXgYwdfyMQZPkcEKvGrZdfv9gyW5Wg+X09qhsv5bVCV2UolkSVGUEj5aElpQj/sNEYfrQDdISAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:43:50.955335Z"},"content_sha256":"48ec8d68e8580a27105fa5c66c29b3ff477514fd21a30cab14ad7e329363aea6","schema_version":"1.0","event_id":"sha256:48ec8d68e8580a27105fa5c66c29b3ff477514fd21a30cab14ad7e329363aea6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX/bundle.json","state_url":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX/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":"2026-08-12T14:43:50Z","links":{"resolver":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX","bundle":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX/bundle.json","state":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:JNFX3O2ZQ6VCDAEYMIESYIO5GX","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":"8b65320e6ee74d897247b65001f2b418389efa4fc0b65c006f7b9e50a4087686","cross_cats_sorted":["cs.PL"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CT","submitted_at":"2023-05-01T19:02:20Z","title_canon_sha256":"785574a5e8eaba2d6e7c5fbc4b35167aa68c0b26a028862adee08c925b06d4ac"},"schema_version":"1.0","source":{"id":"2305.01041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.01041","created_at":"2026-07-05T06:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"2305.01041v1","created_at":"2026-07-05T06:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.01041","created_at":"2026-07-05T06:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"JNFX3O2ZQ6VC","created_at":"2026-07-05T06:06:20Z"},{"alias_kind":"pith_short_16","alias_value":"JNFX3O2ZQ6VCDAEY","created_at":"2026-07-05T06:06:20Z"},{"alias_kind":"pith_short_8","alias_value":"JNFX3O2Z","created_at":"2026-07-05T06:06:20Z"}],"graph_snapshots":[{"event_id":"sha256:48ec8d68e8580a27105fa5c66c29b3ff477514fd21a30cab14ad7e329363aea6","target":"graph","created_at":"2026-07-05T06:06:20Z","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/2305.01041/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give parallel algorithms for string diagrams represented as structured cospans of ACSets. Specifically, we give linear (sequential) and logarithmic (parallel) time algorithms for composition, tensor product, construction of diagrams from arbitrary $\\Sigma$-terms, and application of functors to diagrams. Our datastructure can represent morphisms of both the free symmetric monoidal category over an arbitrary signature as well as those with a chosen Special Frobenius structure. We show how this additional (hypergraph) structure can be used to map diagrams to diagrams of optics. This leads to a","authors_text":"Fabio Zanasi, Paul Wilson","cross_cats":["cs.PL"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CT","submitted_at":"2023-05-01T19:02:20Z","title":"Data-Parallel Algorithms for String Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.01041","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:eb7c35a86bce305f25eabffcd521d974ec180224db05aae89fc1d00d0802f34a","target":"record","created_at":"2026-07-05T06:06:20Z","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":"8b65320e6ee74d897247b65001f2b418389efa4fc0b65c006f7b9e50a4087686","cross_cats_sorted":["cs.PL"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CT","submitted_at":"2023-05-01T19:02:20Z","title_canon_sha256":"785574a5e8eaba2d6e7c5fbc4b35167aa68c0b26a028862adee08c925b06d4ac"},"schema_version":"1.0","source":{"id":"2305.01041","kind":"arxiv","version":1}},"canonical_sha256":"4b4b7dbb5987aa21809862092c21dd35e7104b1436630b267f9fd32bd11c4336","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b4b7dbb5987aa21809862092c21dd35e7104b1436630b267f9fd32bd11c4336","first_computed_at":"2026-07-05T06:06:20.904262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:06:20.904262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1LIArfGNarPsK8xGiUnixJWAjad4Z7Xf3LBo58I1k1thVMy/wzuM9crEAm47U4fmzlp7kDwFRpNIsWKATwkrBg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:06:20.904826Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.01041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb7c35a86bce305f25eabffcd521d974ec180224db05aae89fc1d00d0802f34a","sha256:48ec8d68e8580a27105fa5c66c29b3ff477514fd21a30cab14ad7e329363aea6"],"state_sha256":"6f358160fb45895e61ce158bbe8d07e526b5dc2afcc2a05949ad6eb1dad2a259"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0R0UgltPv7VWFHxxytzGLT80MjmnoBFewSUi34gdL7Zro14g6yHWYb0hPTUa2Bgevga7dedTLGEx7WZxsg2OBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T14:43:50.960241Z","bundle_sha256":"3cc7b488c19a046813d84b2f4ed3680e63d5faca76cf67b30d347b1f11ed881a"}}