{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:IN5DU3OHIEQD4EWLIG222JIL5Q","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":"bbfd2f34991e95841dfcf1746c4a8b4e3c8f5b4945ad75a4f6be4bc9987aa46f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-07-24T03:01:00Z","title_canon_sha256":"aae09b7c504352972150f7c4e67d0dd369a05c9613989466529ac30b483b79f9"},"schema_version":"1.0","source":{"id":"0907.4207","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.4207","created_at":"2026-07-04T17:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"0907.4207v1","created_at":"2026-07-04T17:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4207","created_at":"2026-07-04T17:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"IN5DU3OHIEQD","created_at":"2026-07-04T17:17:12Z"},{"alias_kind":"pith_short_16","alias_value":"IN5DU3OHIEQD4EWL","created_at":"2026-07-04T17:17:12Z"},{"alias_kind":"pith_short_8","alias_value":"IN5DU3OH","created_at":"2026-07-04T17:17:12Z"}],"graph_snapshots":[{"event_id":"sha256:0af3df455ae96a0559ac3a82ac8d93b8d9a50e4ca895316aa08cf1b249943050","target":"graph","created_at":"2026-07-04T17:17:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0907.4207/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the approximate correctability of general algebras of observables, which represent hybrid quantum-classical information. This includes approximate quantum error correcting codes and subsystems codes. We show that the main result of arXiv:quant-ph/0605009 yields a natural generalization of the Knill-Laflamme conditions in the form of a dimension independent estimate of the optimal reconstruction error for a given encoding, measured using the trace-norm distance to a noiseless channel.","authors_text":"C\\'edric B\\'eny","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-07-24T03:01:00Z","title":"Conditions for the approximate correction of algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4207","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:cfefd23d15e9886f327029a1596d3ede31bef1fbdcc93ca5f3797523bcbc53b2","target":"record","created_at":"2026-07-04T17:17:12Z","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":"bbfd2f34991e95841dfcf1746c4a8b4e3c8f5b4945ad75a4f6be4bc9987aa46f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-07-24T03:01:00Z","title_canon_sha256":"aae09b7c504352972150f7c4e67d0dd369a05c9613989466529ac30b483b79f9"},"schema_version":"1.0","source":{"id":"0907.4207","kind":"arxiv","version":1}},"canonical_sha256":"437a3a6dc741203e12cb41b5ad250bec024df8a5ee789d983372f4edafb6efcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"437a3a6dc741203e12cb41b5ad250bec024df8a5ee789d983372f4edafb6efcf","first_computed_at":"2026-07-04T17:17:12.160328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:17:12.160328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KnrtERHdXbnU7dEjWQMOfP8oLRGV16l19oxDbEnRBMwAyiXS9ED+9h6EwY6QKoFHmq6Kvik4MuDK0HsdKn5jAg==","signature_status":"signed_v1","signed_at":"2026-07-04T17:17:12.160835Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.4207","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfefd23d15e9886f327029a1596d3ede31bef1fbdcc93ca5f3797523bcbc53b2","sha256:0af3df455ae96a0559ac3a82ac8d93b8d9a50e4ca895316aa08cf1b249943050"],"state_sha256":"d36efc90b834246c9e22010b1469add0a11e6056b4c67c69c31183542d85f7ea"}