{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CCNQSYP24QS6AHXTS2OKDXI2RO","short_pith_number":"pith:CCNQSYP2","schema_version":"1.0","canonical_sha256":"109b0961fae425e01ef3969ca1dd1a8bb1c77254aadf970024e498cf188a40a4","source":{"kind":"arxiv","id":"1505.00048","version":1},"attestation_state":"computed","paper":{"title":"PROPs for Linear Systems","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Nick Woods, Simon Wadsley","submitted_at":"2015-04-30T22:19:16Z","abstract_excerpt":"A PROP is a symmetric monoidal category whose objects are the nonnegative integers and whose tensor product on objects is addition. A morphism from $m$ to $n$ in a PROP can be visualized as a string diagram with $m$ input wires and $n$ output wires. For a field $k$, the PROP $\\mathrm{FinVect}_k$ where morphisms are $k$-linear maps is used by Baez and Erbele to study signal-flow diagrams. We aim to generalize their result characterizing this PROP in terms of generators and relations by looking at the PROP $\\mathrm{Mat}(R)$ of matrices of values in $R$, where $R$ is a commutative rig (that is, 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":"1505.00048","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CT","submitted_at":"2015-04-30T22:19:16Z","cross_cats_sorted":[],"title_canon_sha256":"62c30be3a2ae8a657f60837d8ae6dc2aaf026b1897ae965928e373000cd24e8e","abstract_canon_sha256":"b46380008b3c215003e69fcb7ad4682d0320e98caa411c771ad146fe628ca77b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:13.735919Z","signature_b64":"iZ8jhtL0ahFaCUWnrajgj6C5+bLqugxgg38MgxXQ8m8tRtN915FJllthFvXnsqeaFyR0+h+/sJExkRyneNFZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"109b0961fae425e01ef3969ca1dd1a8bb1c77254aadf970024e498cf188a40a4","last_reissued_at":"2026-05-18T02:17:13.735194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:13.735194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"PROPs for Linear Systems","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Nick Woods, Simon Wadsley","submitted_at":"2015-04-30T22:19:16Z","abstract_excerpt":"A PROP is a symmetric monoidal category whose objects are the nonnegative integers and whose tensor product on objects is addition. A morphism from $m$ to $n$ in a PROP can be visualized as a string diagram with $m$ input wires and $n$ output wires. For a field $k$, the PROP $\\mathrm{FinVect}_k$ where morphisms are $k$-linear maps is used by Baez and Erbele to study signal-flow diagrams. We aim to generalize their result characterizing this PROP in terms of generators and relations by looking at the PROP $\\mathrm{Mat}(R)$ of matrices of values in $R$, where $R$ is a commutative rig (that is, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00048","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":""},"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":"1505.00048","created_at":"2026-05-18T02:17:13.735288+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.00048v1","created_at":"2026-05-18T02:17:13.735288+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00048","created_at":"2026-05-18T02:17:13.735288+00:00"},{"alias_kind":"pith_short_12","alias_value":"CCNQSYP24QS6","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"CCNQSYP24QS6AHXT","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"CCNQSYP2","created_at":"2026-05-18T12:29:14.074870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CCNQSYP24QS6AHXTS2OKDXI2RO","json":"https://pith.science/pith/CCNQSYP24QS6AHXTS2OKDXI2RO.json","graph_json":"https://pith.science/api/pith-number/CCNQSYP24QS6AHXTS2OKDXI2RO/graph.json","events_json":"https://pith.science/api/pith-number/CCNQSYP24QS6AHXTS2OKDXI2RO/events.json","paper":"https://pith.science/paper/CCNQSYP2"},"agent_actions":{"view_html":"https://pith.science/pith/CCNQSYP24QS6AHXTS2OKDXI2RO","download_json":"https://pith.science/pith/CCNQSYP24QS6AHXTS2OKDXI2RO.json","view_paper":"https://pith.science/paper/CCNQSYP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.00048&json=true","fetch_graph":"https://pith.science/api/pith-number/CCNQSYP24QS6AHXTS2OKDXI2RO/graph.json","fetch_events":"https://pith.science/api/pith-number/CCNQSYP24QS6AHXTS2OKDXI2RO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CCNQSYP24QS6AHXTS2OKDXI2RO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CCNQSYP24QS6AHXTS2OKDXI2RO/action/storage_attestation","attest_author":"https://pith.science/pith/CCNQSYP24QS6AHXTS2OKDXI2RO/action/author_attestation","sign_citation":"https://pith.science/pith/CCNQSYP24QS6AHXTS2OKDXI2RO/action/citation_signature","submit_replication":"https://pith.science/pith/CCNQSYP24QS6AHXTS2OKDXI2RO/action/replication_record"}},"created_at":"2026-05-18T02:17:13.735288+00:00","updated_at":"2026-05-18T02:17:13.735288+00:00"}