{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:IEDHIYVZYYMW5PF7WLGFPVZ34J","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":"9d7ff3894fa4ddf9e165e87615153fa028fcf271923e9c62851d3920afa8bf1b","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2008-07-18T12:37:44Z","title_canon_sha256":"10f2f750634a5e30452ef3d88e943812488f5392a345a556d30b28a390f58339"},"schema_version":"1.0","source":{"id":"0807.2927","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.2927","created_at":"2026-05-18T03:45:10Z"},{"alias_kind":"arxiv_version","alias_value":"0807.2927v4","created_at":"2026-05-18T03:45:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.2927","created_at":"2026-05-18T03:45:10Z"},{"alias_kind":"pith_short_12","alias_value":"IEDHIYVZYYMW","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"IEDHIYVZYYMW5PF7","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"IEDHIYVZ","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:1154395c10f57702ce646b20bf2d7910e298411d6aca9824a26a67ba2ecc8adc","target":"graph","created_at":"2026-05-18T03:45:10Z","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":"The complex numbers are an important part of quantum theory, but are difficult to motivate from a theoretical perspective. We describe a simple formal framework for theories of physics, and show that if a theory of physics presented in this manner satisfies certain completeness properties, then it necessarily includes the complex numbers as a mathematical ingredient. Central to our approach are the techniques of category theory, and we introduce a new category-theoretical tool, called the dagger-limit, which governs the way in which systems can be combined to form larger systems. These dagger-","authors_text":"Jamie Vicary","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2008-07-18T12:37:44Z","title":"Completeness of dagger-categories and the complex numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.2927","kind":"arxiv","version":4},"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":"sha256:3368f8952fe9cda70417cf8d4ce4180232f3cd7e9559d8a069c6ffe107ab7f6e","target":"record","created_at":"2026-05-18T03:45:10Z","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":"9d7ff3894fa4ddf9e165e87615153fa028fcf271923e9c62851d3920afa8bf1b","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2008-07-18T12:37:44Z","title_canon_sha256":"10f2f750634a5e30452ef3d88e943812488f5392a345a556d30b28a390f58339"},"schema_version":"1.0","source":{"id":"0807.2927","kind":"arxiv","version":4}},"canonical_sha256":"41067462b9c6196ebcbfb2cc57d73be26bb221a16d0748cf1b60888efa28c513","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41067462b9c6196ebcbfb2cc57d73be26bb221a16d0748cf1b60888efa28c513","first_computed_at":"2026-05-18T03:45:10.977019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:10.977019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"We6pNjdCTwL92OCNsiuUCuPq7slU/XfLga6W7z0qlDbHxCCJluCd+8PRRxRG+Xypc9muPEpd+Me/18Xmb1avAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:10.977719Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.2927","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3368f8952fe9cda70417cf8d4ce4180232f3cd7e9559d8a069c6ffe107ab7f6e","sha256:1154395c10f57702ce646b20bf2d7910e298411d6aca9824a26a67ba2ecc8adc"],"state_sha256":"b040fcf2788dc19b16daa6e673539d23dfcd9bcbeeff30a583cb8977bead26be"}