{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YD3UDZXT4KOJ3MUYDVLU2XYLJH","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":"87bbe3588aa663a9888b1439cefb7b9cf7ec8c3831c440922a5069703cb86bd6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-07-16T15:20:07Z","title_canon_sha256":"e494b658bf0f4b47153f4178fef17bdcfb737177543e95e4235eabdeb906c008"},"schema_version":"1.0","source":{"id":"2507.12326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.12326","created_at":"2026-07-05T11:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"2507.12326v1","created_at":"2026-07-05T11:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12326","created_at":"2026-07-05T11:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"YD3UDZXT4KOJ","created_at":"2026-07-05T11:38:18Z"},{"alias_kind":"pith_short_16","alias_value":"YD3UDZXT4KOJ3MUY","created_at":"2026-07-05T11:38:18Z"},{"alias_kind":"pith_short_8","alias_value":"YD3UDZXT","created_at":"2026-07-05T11:38:18Z"}],"graph_snapshots":[{"event_id":"sha256:f712c96541ae1767caf45cb99373b84f9efeb40c10f4d733ad3fb8a28148a709","target":"graph","created_at":"2026-07-05T11:38:18Z","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/2507.12326/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We revisit the extendability-based semi-definite programming hierarchy introduced by Berta et al. [Mathematical Programming, 1 - 49 (2021)], which provides converging outer bounds on the optimal fidelity of approximate quantum error correction (AQEC). As our first contribution, we introduce a measurement-based rounding scheme that extracts inner sequences of certifiably good encoder-decoder pairs from this outer hierarchy. To address the computational complexity of evaluating fixed levels of the hierarchy, we investigate the use of symmetry-based dimension reduction. In particular, we combine ","authors_text":"Gereon Ko{\\ss}mann, Julius A. Zeiss, Mario Berta, Omar Fawzi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-07-16T15:20:07Z","title":"On approximate quantum error correction for symmetric noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12326","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:e6af2d94dba915e7448d15eda624e31dc5bd50d63072d523bab3520b67f6066e","target":"record","created_at":"2026-07-05T11:38:18Z","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":"87bbe3588aa663a9888b1439cefb7b9cf7ec8c3831c440922a5069703cb86bd6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-07-16T15:20:07Z","title_canon_sha256":"e494b658bf0f4b47153f4178fef17bdcfb737177543e95e4235eabdeb906c008"},"schema_version":"1.0","source":{"id":"2507.12326","kind":"arxiv","version":1}},"canonical_sha256":"c0f741e6f3e29c9db2981d574d5f0b49e9a27dceb4208fa80dfae03fa6a96a06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0f741e6f3e29c9db2981d574d5f0b49e9a27dceb4208fa80dfae03fa6a96a06","first_computed_at":"2026-07-05T11:38:18.393965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:18.393965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NcK8GRNX2dUnB69ytZ9/t2ImW2UTMjaGMOU6Cy9fokKkq4laLF2ZvCBcDLRzqV6CUjeyGKtrQ6E7terfKemoBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:18.394560Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.12326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6af2d94dba915e7448d15eda624e31dc5bd50d63072d523bab3520b67f6066e","sha256:f712c96541ae1767caf45cb99373b84f9efeb40c10f4d733ad3fb8a28148a709"],"state_sha256":"43379e988d838b5d4a50805bb1684e01efd68291d4074152f5c36ff7b7558f32"}