{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QGQ64UU6ALNUWS7U43OLSBOFN5","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":"d20e3982e337fc438e08db09ea3b66585cde85b56926b054f054b6b9fd914770","cross_cats_sorted":["math.GT","math.IT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-17T15:46:39Z","title_canon_sha256":"b9397a588f2bcf9efe5e81ef03d8b58cb288339807a8ac75d7ce8d54126f5477"},"schema_version":"1.0","source":{"id":"1307.4677","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4677","created_at":"2026-05-18T00:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4677v1","created_at":"2026-05-18T00:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4677","created_at":"2026-05-18T00:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"QGQ64UU6ALNU","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QGQ64UU6ALNUWS7U","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QGQ64UU6","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:c5614a49a9bcf74860322f8f02d70f4c144fa0521b84d553641fbefd68e4f780","target":"graph","created_at":"2026-05-18T00:31:52Z","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 use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters [[3^(2l+1)/sqrt(8{\\pi}l);1;2^l]]; unlink codes with asymptotical parameters [[sqrt(2/2{\\pi}l)6^l;2^l;2^l]] and (2,l)-torus link codes with asymptotical parameters [[n;1;d_n]] where d_n>\\sqrt(n)/1.62.","authors_text":"Benjamin Audoux","cross_cats":["math.GT","math.IT","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-17T15:46:39Z","title":"An application of Khovanov homology to quantum codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4677","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":"sha256:2dce49b1e8562c596e3e20e747ed8c73437d75bf6bc5c068bc8306a5077ba109","target":"record","created_at":"2026-05-18T00:31:52Z","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":"d20e3982e337fc438e08db09ea3b66585cde85b56926b054f054b6b9fd914770","cross_cats_sorted":["math.GT","math.IT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-17T15:46:39Z","title_canon_sha256":"b9397a588f2bcf9efe5e81ef03d8b58cb288339807a8ac75d7ce8d54126f5477"},"schema_version":"1.0","source":{"id":"1307.4677","kind":"arxiv","version":1}},"canonical_sha256":"81a1ee529e02db4b4bf4e6dcb905c56f60e6accfcb77c7163d3e6269be6d7145","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81a1ee529e02db4b4bf4e6dcb905c56f60e6accfcb77c7163d3e6269be6d7145","first_computed_at":"2026-05-18T00:31:52.588810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:52.588810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PoIcsSGkt7DWjrYb9wQen3mp+AAxz/diXwBdVIYHoQauEXW+hVMvWtfkradsMD2iFmjavap+cUoS9p86Gkk8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:52.589445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4677","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2dce49b1e8562c596e3e20e747ed8c73437d75bf6bc5c068bc8306a5077ba109","sha256:c5614a49a9bcf74860322f8f02d70f4c144fa0521b84d553641fbefd68e4f780"],"state_sha256":"35df462078944db3337b01dec8a5dec59304b9c8e092f65c40a454a6b573d837"}