{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:PT5DVMPHFCFTLHIGGBAW3QB5NR","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":"550b436d1d48b88b92766962cc9287d71a488ee24df8f37a27613223da8a560d","cross_cats_sorted":["cs.LO","math.CT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-06-25T15:58:11Z","title_canon_sha256":"f1e0ec1a37dc2eeda0b2c17a32571da7dd9749a122887855b351b03f50f4c404"},"schema_version":"1.0","source":{"id":"0906.4725","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.4725","created_at":"2026-05-18T02:24:55Z"},{"alias_kind":"arxiv_version","alias_value":"0906.4725v3","created_at":"2026-05-18T02:24:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.4725","created_at":"2026-05-18T02:24:55Z"},{"alias_kind":"pith_short_12","alias_value":"PT5DVMPHFCFT","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"PT5DVMPHFCFTLHIG","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"PT5DVMPH","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:470d535a9086ac4f376ec32ab2ed5c16bc903b39074e4800caccefe50e5a4fde","target":"graph","created_at":"2026-05-18T02:24:55Z","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":"This paper has two tightly intertwined aims: (i) To introduce an intuitive and universal graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies derivations in the area of quantum computation and information. (ii) To axiomatise complementarity of quantum observables within a general framework for physical theories in terms of dagger symmetric monoidal categories. We also axiomatize phase shifts within this framework.\n  Using the well-studied canonical correspondence between graphical calculi and symmetric monoidal categories, our results provide a purely graphical","authors_text":"Bob Coecke, Ross Duncan","cross_cats":["cs.LO","math.CT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-06-25T15:58:11Z","title":"Interacting Quantum Observables: Categorical Algebra and Diagrammatics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.4725","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":"sha256:9d93510b2d475197e197a9a199a7722c7b92c6ae0b20b99060716d6fd67de10e","target":"record","created_at":"2026-05-18T02:24:55Z","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":"550b436d1d48b88b92766962cc9287d71a488ee24df8f37a27613223da8a560d","cross_cats_sorted":["cs.LO","math.CT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-06-25T15:58:11Z","title_canon_sha256":"f1e0ec1a37dc2eeda0b2c17a32571da7dd9749a122887855b351b03f50f4c404"},"schema_version":"1.0","source":{"id":"0906.4725","kind":"arxiv","version":3}},"canonical_sha256":"7cfa3ab1e7288b359d0630416dc03d6c6c5d77d192b8a77205b47e5d023e3820","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cfa3ab1e7288b359d0630416dc03d6c6c5d77d192b8a77205b47e5d023e3820","first_computed_at":"2026-05-18T02:24:55.309407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:55.309407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zu03/q5B6+upFTuqKan4ARysPkG06+BKlLZX0AwKkhjjRFdMYHQcYG/ekJqalH2HOSDwEnhJ0i5/l0RPvSwmBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:55.310087Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.4725","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d93510b2d475197e197a9a199a7722c7b92c6ae0b20b99060716d6fd67de10e","sha256:470d535a9086ac4f376ec32ab2ed5c16bc903b39074e4800caccefe50e5a4fde"],"state_sha256":"bdabe29980436af989e677f15971d5ab6f34037adefe413b072b64c9937978c2"}