{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:5C7TNUYEQROHHQEUD3XYJ75Q7R","short_pith_number":"pith:5C7TNUYE","schema_version":"1.0","canonical_sha256":"e8bf36d304845c73c0941eef84ffb0fc7ca41a500f681fcaa488c43874b4ecc3","source":{"kind":"arxiv","id":"1107.6019","version":1},"attestation_state":"computed","paper":{"title":"Causal categories: relativistically interacting processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","quant-ph"],"primary_cat":"gr-qc","authors_text":"Bob Coecke, Raymond Lal","submitted_at":"2011-07-29T16:52:03Z","abstract_excerpt":"A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces"},"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":"1107.6019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-07-29T16:52:03Z","cross_cats_sorted":["math.CT","quant-ph"],"title_canon_sha256":"93306f7d9ad1ab45406296f5954fb02e0273e6e0219670d0b66f7f3b0796645e","abstract_canon_sha256":"788573f19aa66737b7360df7d04a0a0a25b57a8df7c1526888c4a3d1aaf9c4d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:05.571009Z","signature_b64":"061IMSl1MvijAG3GWf9njm/P1IEFBJIFynX6KSlKHpSxphNFsDyEnweTJlLnH7H5zQ9VScyYHFlNWwzlqnPsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8bf36d304845c73c0941eef84ffb0fc7ca41a500f681fcaa488c43874b4ecc3","last_reissued_at":"2026-05-18T02:01:05.570328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:05.570328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Causal categories: relativistically interacting processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","quant-ph"],"primary_cat":"gr-qc","authors_text":"Bob Coecke, Raymond Lal","submitted_at":"2011-07-29T16:52:03Z","abstract_excerpt":"A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.6019","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":"1107.6019","created_at":"2026-05-18T02:01:05.570436+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.6019v1","created_at":"2026-05-18T02:01:05.570436+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.6019","created_at":"2026-05-18T02:01:05.570436+00:00"},{"alias_kind":"pith_short_12","alias_value":"5C7TNUYEQROH","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"5C7TNUYEQROHHQEU","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"5C7TNUYE","created_at":"2026-05-18T12:26:20.644004+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/5C7TNUYEQROHHQEUD3XYJ75Q7R","json":"https://pith.science/pith/5C7TNUYEQROHHQEUD3XYJ75Q7R.json","graph_json":"https://pith.science/api/pith-number/5C7TNUYEQROHHQEUD3XYJ75Q7R/graph.json","events_json":"https://pith.science/api/pith-number/5C7TNUYEQROHHQEUD3XYJ75Q7R/events.json","paper":"https://pith.science/paper/5C7TNUYE"},"agent_actions":{"view_html":"https://pith.science/pith/5C7TNUYEQROHHQEUD3XYJ75Q7R","download_json":"https://pith.science/pith/5C7TNUYEQROHHQEUD3XYJ75Q7R.json","view_paper":"https://pith.science/paper/5C7TNUYE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.6019&json=true","fetch_graph":"https://pith.science/api/pith-number/5C7TNUYEQROHHQEUD3XYJ75Q7R/graph.json","fetch_events":"https://pith.science/api/pith-number/5C7TNUYEQROHHQEUD3XYJ75Q7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5C7TNUYEQROHHQEUD3XYJ75Q7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5C7TNUYEQROHHQEUD3XYJ75Q7R/action/storage_attestation","attest_author":"https://pith.science/pith/5C7TNUYEQROHHQEUD3XYJ75Q7R/action/author_attestation","sign_citation":"https://pith.science/pith/5C7TNUYEQROHHQEUD3XYJ75Q7R/action/citation_signature","submit_replication":"https://pith.science/pith/5C7TNUYEQROHHQEUD3XYJ75Q7R/action/replication_record"}},"created_at":"2026-05-18T02:01:05.570436+00:00","updated_at":"2026-05-18T02:01:05.570436+00:00"}