{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QFS3TN54XUZH2CAXJOOBAUOSSU","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":"c4f37ff1e5d4f117452c490d28bd10e403d5934fe1b2d2f30c45829f55212f3b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-08-16T08:21:20Z","title_canon_sha256":"1ed4a5dcdfcbedea6f1b314294f208894b6a5a1d1252a3377a099b6028c8faf2"},"schema_version":"1.0","source":{"id":"1308.3578","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3578","created_at":"2026-05-18T03:15:44Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3578v1","created_at":"2026-05-18T03:15:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3578","created_at":"2026-05-18T03:15:44Z"},{"alias_kind":"pith_short_12","alias_value":"QFS3TN54XUZH","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QFS3TN54XUZH2CAX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QFS3TN54","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:d3c9e1ce6b4610fef4c3fd1d84eec7300f823406681606a9f88079b85127237c","target":"graph","created_at":"2026-05-18T03:15:44Z","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":"It is well known that quantum codes can be constructed through classical symplectic self-orthogonal codes. In this paper, we give a kind of Gilbert-Varshamov bound for symplectic self-orthogonal codes first and then obtain the Gilbert-Varshamov bound for quantum codes. The idea of obtaining the Gilbert-Varshamov bound for symplectic self-orthogonal codes follows from counting arguments.","authors_text":"Chaoping Xing, Lingfei Jin","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-08-16T08:21:20Z","title":"Quantum Gilbert-Varshamov Bound Through Symplectic Self-Orthogonal Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3578","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":"sha256:391333edbce1b8ad7c89dc6c1936510fb6d12c6467688d753aaf3b0fb018d40f","target":"record","created_at":"2026-05-18T03:15:44Z","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":"c4f37ff1e5d4f117452c490d28bd10e403d5934fe1b2d2f30c45829f55212f3b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-08-16T08:21:20Z","title_canon_sha256":"1ed4a5dcdfcbedea6f1b314294f208894b6a5a1d1252a3377a099b6028c8faf2"},"schema_version":"1.0","source":{"id":"1308.3578","kind":"arxiv","version":1}},"canonical_sha256":"8165b9b7bcbd327d08174b9c1051d2953a856a2601039d922bfbf510307725f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8165b9b7bcbd327d08174b9c1051d2953a856a2601039d922bfbf510307725f2","first_computed_at":"2026-05-18T03:15:44.511718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:44.511718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ac+Q894+Sn4uip2g+olbcHYrWVS12X/recNb68eUbq5OV4yuxzSDpSGAZUxEoToUzgDkMLsnoapylssLbJILDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:44.512376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3578","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:391333edbce1b8ad7c89dc6c1936510fb6d12c6467688d753aaf3b0fb018d40f","sha256:d3c9e1ce6b4610fef4c3fd1d84eec7300f823406681606a9f88079b85127237c"],"state_sha256":"ae05635a3591ec5a2ff5c2383679856b242a68ad892206eec937eebc0b7c1a6e"}