{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:JNFX3O2ZQ6VCDAEYMIESYIO5GX","short_pith_number":"pith:JNFX3O2Z","schema_version":"1.0","canonical_sha256":"4b4b7dbb5987aa21809862092c21dd35e7104b1436630b267f9fd32bd11c4336","source":{"kind":"arxiv","id":"2305.01041","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2305.01041","created_at":"2026-07-05T06:06:20.904346+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.01041v1","created_at":"2026-07-05T06:06:20.904346+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.01041","created_at":"2026-07-05T06:06:20.904346+00:00"},{"alias_kind":"pith_short_12","alias_value":"JNFX3O2ZQ6VC","created_at":"2026-07-05T06:06:20.904346+00:00"},{"alias_kind":"pith_short_16","alias_value":"JNFX3O2ZQ6VCDAEY","created_at":"2026-07-05T06:06:20.904346+00:00"},{"alias_kind":"pith_short_8","alias_value":"JNFX3O2Z","created_at":"2026-07-05T06:06:20.904346+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.25321","citing_title":"Fixed-parameter tractable inference for discrete probabilistic programs, via string diagram algebraisation","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2604.08331","citing_title":"Metacat: a categorical framework for formal systems","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX","json":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX.json","graph_json":"https://pith.science/api/pith-number/JNFX3O2ZQ6VCDAEYMIESYIO5GX/graph.json","events_json":"https://pith.science/api/pith-number/JNFX3O2ZQ6VCDAEYMIESYIO5GX/events.json","paper":"https://pith.science/paper/JNFX3O2Z"},"agent_actions":{"view_html":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX","download_json":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX.json","view_paper":"https://pith.science/paper/JNFX3O2Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.01041&json=true","fetch_graph":"https://pith.science/api/pith-number/JNFX3O2ZQ6VCDAEYMIESYIO5GX/graph.json","fetch_events":"https://pith.science/api/pith-number/JNFX3O2ZQ6VCDAEYMIESYIO5GX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX/action/storage_attestation","attest_author":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX/action/author_attestation","sign_citation":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX/action/citation_signature","submit_replication":"https://pith.science/pith/JNFX3O2ZQ6VCDAEYMIESYIO5GX/action/replication_record"}},"created_at":"2026-07-05T06:06:20.904346+00:00","updated_at":"2026-07-05T06:06:20.904346+00:00"}