{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:R2SYQYXKGFFLK5NIOWTH3LD3A2","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":"04ee4d5187f599445d9a2170b39ec044cee4f26f31d4b1ea1e8b874730d5741b","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-01-05T20:54:24Z","title_canon_sha256":"54516440add8b9cc9d95556be892046e00e8d7bc86a4b9e831bf559f2947edc2"},"schema_version":"1.0","source":{"id":"1101.1077","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1077","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1077v2","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1077","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"R2SYQYXKGFFL","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"R2SYQYXKGFFLK5NI","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"R2SYQYXK","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:1aad44e0250c80b3b9211e8561b412ffe6a8428c2856a0889dac3aaa5dc20953","target":"graph","created_at":"2026-05-18T03:50:59Z","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":"Within the context of an involutive monoidal category the notion of a comparison relation is identified. Instances are equality on sets, inequality on posets, orthogonality on orthomodular lattices, non-empty intersection on powersets, and inner product on vector or Hilbert spaces. Associated with a collection of such (symmetric) comparison relations a dagger category is defined with \"tame\" relations as morphisms. Examples include familiar categories in the foundations of quantum mechanics, such as sets with partial injections, or with locally bifinite relations, or with formal distributions b","authors_text":"Bart Jacobs","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-01-05T20:54:24Z","title":"Dagger Categories of Tame Relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1077","kind":"arxiv","version":2},"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:e1bf7fa6e45dd47d829628d8f6e731a7652df05fb23b7c7be9cb60555278f150","target":"record","created_at":"2026-05-18T03:50:59Z","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":"04ee4d5187f599445d9a2170b39ec044cee4f26f31d4b1ea1e8b874730d5741b","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-01-05T20:54:24Z","title_canon_sha256":"54516440add8b9cc9d95556be892046e00e8d7bc86a4b9e831bf559f2947edc2"},"schema_version":"1.0","source":{"id":"1101.1077","kind":"arxiv","version":2}},"canonical_sha256":"8ea58862ea314ab575a875a67dac7b06bbd20988591a60f9ca67753b9986e0ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ea58862ea314ab575a875a67dac7b06bbd20988591a60f9ca67753b9986e0ca","first_computed_at":"2026-05-18T03:50:59.316068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:59.316068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hr1xbFkluShlojeYrr67E477cmDkSHt/my3hYzoaecxoS9XXfvf/w+8uEnvdUjsAFLo8d0Py48ZbmSikdX8vAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:59.316830Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1077","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1bf7fa6e45dd47d829628d8f6e731a7652df05fb23b7c7be9cb60555278f150","sha256:1aad44e0250c80b3b9211e8561b412ffe6a8428c2856a0889dac3aaa5dc20953"],"state_sha256":"62e1dc13ab457c89d2146b4b656eb367f70ab5c87debe7780d541d6a7f75c524"}