{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5XJRQSUSWE3QSNFEBY22ZYAFEA","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":"30125beffbda49b1d4863621fb88caf79d145d0cc8d2d360c566d20e6a528eb7","cross_cats_sorted":["math.QA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-05-27T12:15:54Z","title_canon_sha256":"d8f4dda00cdef0d56c396d8138271b64a9c0069a44439e06e9ffb4e213a8b7e8"},"schema_version":"1.0","source":{"id":"1405.6881","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6881","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6881v3","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6881","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"pith_short_12","alias_value":"5XJRQSUSWE3Q","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5XJRQSUSWE3QSNFE","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5XJRQSUS","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:b914c7ff7a4f5a62b56aee4eaa94887575dadf452c0a39d2caba0566390f95bc","target":"graph","created_at":"2026-05-18T00:37:49Z","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"},"paper":{"abstract_excerpt":"Control theory uses \"signal-flow diagrams\" to describe processes where real-valued functions of time are added, multiplied by scalars, differentiated and integrated, duplicated and deleted. These diagrams can be seen as string diagrams for the symmetric monoidal category FinVect_k of finite-dimensional vector spaces over the field of rational functions k = R(s), where the variable s acts as differentiation and the monoidal structure is direct sum rather than the usual tensor product of vector spaces. For any field k we give a presentation of FinVect_k in terms of the generators used in signal ","authors_text":"Jason Erbele, John C. Baez","cross_cats":["math.QA","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-05-27T12:15:54Z","title":"Categories in Control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6881","kind":"arxiv","version":3},"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":"sha256:7d211db0e0e75d62bfb5f96fabd252e24a288e1825c9d549824eb91193ef7e80","target":"record","created_at":"2026-05-18T00:37:49Z","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":"30125beffbda49b1d4863621fb88caf79d145d0cc8d2d360c566d20e6a528eb7","cross_cats_sorted":["math.QA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-05-27T12:15:54Z","title_canon_sha256":"d8f4dda00cdef0d56c396d8138271b64a9c0069a44439e06e9ffb4e213a8b7e8"},"schema_version":"1.0","source":{"id":"1405.6881","kind":"arxiv","version":3}},"canonical_sha256":"edd3184a92b1370934a40e35ace0052035e1e79669789f3fc1ef65b9fedc139e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edd3184a92b1370934a40e35ace0052035e1e79669789f3fc1ef65b9fedc139e","first_computed_at":"2026-05-18T00:37:49.067413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:49.067413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/pMfNspoH0SXzU/5BfLgfypUzIsio5jV8BHod3SfCpUqSTrfsyBtyfCVo9MgwP7/pTg9gCMDBBF/gmGc8qB4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:49.067989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6881","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d211db0e0e75d62bfb5f96fabd252e24a288e1825c9d549824eb91193ef7e80","sha256:b914c7ff7a4f5a62b56aee4eaa94887575dadf452c0a39d2caba0566390f95bc"],"state_sha256":"a7fa7e3e53b15f70c729dbe273b928b7713795729ed68ba64fa0c4760a7c9fd2"}