{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:L6LMEN5FW6S2JLC2CB4YPH3E25","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":"3b7d91e90fc8db3ce94cdc7534eaf82304a2ec9062add83b6617163861c91b91","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-06-09T14:29:24Z","title_canon_sha256":"08a41ae78d72c9face03061895cf9bcff3e59c388deb4fbb0c71b1cc75405c50"},"schema_version":"1.0","source":{"id":"1506.02931","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02931","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02931v2","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02931","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"pith_short_12","alias_value":"L6LMEN5FW6S2","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L6LMEN5FW6S2JLC2","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L6LMEN5F","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:8ba5b45d5d943c4654ad1e4c51cab337a07b0791f1476917750dc7ca6f55ccb9","target":"graph","created_at":"2026-05-18T01:27:46Z","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":"There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical systems on an equal footing. The former has been axiomatized using environment structures. We extend this axiomatization to the latter by introducing decoherence structures.","authors_text":"Chris Heunen (University of Oxford), Oscar Cunningham (University of Oxford)","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-06-09T14:29:24Z","title":"Axiomatizing complete positivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02931","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":"sha256:067070445e1492f4fee504d97001aeed07735aeb769734c170ad2b579d403037","target":"record","created_at":"2026-05-18T01:27:46Z","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":"3b7d91e90fc8db3ce94cdc7534eaf82304a2ec9062add83b6617163861c91b91","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-06-09T14:29:24Z","title_canon_sha256":"08a41ae78d72c9face03061895cf9bcff3e59c388deb4fbb0c71b1cc75405c50"},"schema_version":"1.0","source":{"id":"1506.02931","kind":"arxiv","version":2}},"canonical_sha256":"5f96c237a5b7a5a4ac5a1079879f64d779f3114e2519d4d34c4eb0f402faa61c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f96c237a5b7a5a4ac5a1079879f64d779f3114e2519d4d34c4eb0f402faa61c","first_computed_at":"2026-05-18T01:27:46.004645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:46.004645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EeN8L6pZGWULJAZdpSufItfg0geT2/YntUkDwfdRpQd1Pe0v3P89gC0OAZhP9HxiSrL9E3hmif+PwTvWH1EnBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:46.005270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02931","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:067070445e1492f4fee504d97001aeed07735aeb769734c170ad2b579d403037","sha256:8ba5b45d5d943c4654ad1e4c51cab337a07b0791f1476917750dc7ca6f55ccb9"],"state_sha256":"b44f392573506612defe2cc95c70bc4af952f0ece3d921c315e3c9c1499480ba"}