{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LG4DSESWQ4HIL65NQZJRCQHMB4","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":"d3fcef26664db7e5e1fc126de05934b06263195d447ef04065e167b8f6e96251","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-18T13:37:37Z","title_canon_sha256":"df6744e6e1c8e53b00a10d3e49b00f393b5343b22b4ed396d9f51e97dde6976a"},"schema_version":"1.0","source":{"id":"1604.05387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05387","created_at":"2026-05-18T01:14:12Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05387v1","created_at":"2026-05-18T01:14:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05387","created_at":"2026-05-18T01:14:12Z"},{"alias_kind":"pith_short_12","alias_value":"LG4DSESWQ4HI","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LG4DSESWQ4HIL65N","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LG4DSESW","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:8876bde93fc828f6495a1bec4ca6b3cd4f88716ebfaeac44b8917b405934aa78","target":"graph","created_at":"2026-05-18T01:14:12Z","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":"We study the noncommutative operator graph ${\\mathcal L}_{\\theta }$ depending on complex parameter $\\theta $ recently introduced by M.E. Shirokov to construct channels with positive quantum zero-error capacity having vanishing n-shot capacity. We define the noncommutative group $G$ and the algebra ${\\mathcal A}_{\\theta }$ which is a quotient of ${\\mathbb C}G$ with respect to the special algebraic relation depending on $\\theta $ such that the matrix representation $\\phi $ of ${\\mathcal A}_{\\theta }$ results in the algebra ${\\mathcal M}_{\\theta }$ generated by ${\\mathcal L}_{\\theta }$. In the ca","authors_text":"G.G. Amosov, I.Yu. Zhdanovskiy","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-18T13:37:37Z","title":"On the noncommutative deformation of the operator graph corresponding to the Klein group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05387","kind":"arxiv","version":1},"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":"sha256:67b244a8e840012c7d7a9db52c34d0b7ffd6c0201cd1a5ccb259b6de5bb1d75d","target":"record","created_at":"2026-05-18T01:14:12Z","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":"d3fcef26664db7e5e1fc126de05934b06263195d447ef04065e167b8f6e96251","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-18T13:37:37Z","title_canon_sha256":"df6744e6e1c8e53b00a10d3e49b00f393b5343b22b4ed396d9f51e97dde6976a"},"schema_version":"1.0","source":{"id":"1604.05387","kind":"arxiv","version":1}},"canonical_sha256":"59b8391256870e85fbad86531140ec0f1ce095bdc70a219ae74fb510eba4e31f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59b8391256870e85fbad86531140ec0f1ce095bdc70a219ae74fb510eba4e31f","first_computed_at":"2026-05-18T01:14:12.319344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:12.319344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U4rH1YRp1k8TMFxLUiEO4WmhHBZaHBzCNyl6Kk2QlAj8FPNuDJcwssZK59mtKRkO7nB99jdiSaUR/wzPhnQxCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:12.320026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.05387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67b244a8e840012c7d7a9db52c34d0b7ffd6c0201cd1a5ccb259b6de5bb1d75d","sha256:8876bde93fc828f6495a1bec4ca6b3cd4f88716ebfaeac44b8917b405934aa78"],"state_sha256":"de2a42f06cc1c0a36f4a3689d4030f4388f95ef24528d7ac596b853345ec93f1"}