{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XDKIF325HMVD3PUOURKNPTNUIB","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":"c1d0d9a507fa6f6eb8108f49dc865ec87d2a5e13c2d8685560f3922eeb955286","cross_cats_sorted":["math.IT","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-08-19T03:47:09Z","title_canon_sha256":"331b81ef53de841af8beb42e1770fb331787e99f93e45d0fd13845b79fbf1268"},"schema_version":"1.0","source":{"id":"2408.09685","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.09685","created_at":"2026-07-05T08:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"2408.09685v1","created_at":"2026-07-05T08:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.09685","created_at":"2026-07-05T08:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"XDKIF325HMVD","created_at":"2026-07-05T08:56:35Z"},{"alias_kind":"pith_short_16","alias_value":"XDKIF325HMVD3PUO","created_at":"2026-07-05T08:56:35Z"},{"alias_kind":"pith_short_8","alias_value":"XDKIF325","created_at":"2026-07-05T08:56:35Z"}],"graph_snapshots":[{"event_id":"sha256:83ab4992c4d7e21334e3c6397b6af20cb972b04d95949d3416bd916c2089dcb7","target":"graph","created_at":"2026-07-05T08:56:35Z","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/2408.09685/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Triorthogonal matrices were introduced in Quantum Information Theory in connection with distillation of magic states (Bravyi and Haah (2012)). We give an algorithm to construct binary triorthogonal matrices from binary self-dual codes. Further, we generalize to this setting the classical coding techniques of shortening and extending. We also give some simple propagation rules.","authors_text":"Haodong Lu, Jon-Lark Kim, Minjia Shi, Patrick Sole","cross_cats":["math.IT","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-08-19T03:47:09Z","title":"Triorthogonal Codes and Self-dual Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.09685","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":"sha256:4b40a644e037116fec902375cf08948c3d8d1a41e46d812c9b6f272a1e627d57","target":"record","created_at":"2026-07-05T08:56:35Z","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":"c1d0d9a507fa6f6eb8108f49dc865ec87d2a5e13c2d8685560f3922eeb955286","cross_cats_sorted":["math.IT","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-08-19T03:47:09Z","title_canon_sha256":"331b81ef53de841af8beb42e1770fb331787e99f93e45d0fd13845b79fbf1268"},"schema_version":"1.0","source":{"id":"2408.09685","kind":"arxiv","version":1}},"canonical_sha256":"b8d482ef5d3b2a3dbe8ea454d7cdb4404497cef8a8e7b18bb367ada9f890992a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8d482ef5d3b2a3dbe8ea454d7cdb4404497cef8a8e7b18bb367ada9f890992a","first_computed_at":"2026-07-05T08:56:35.524022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:56:35.524022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AMHV/WHCz48YpAk6sqCcEKYRk1rkID8pmnPmzX7F8M8iWgP/NWTDQlg9b7ZBH1SaV3sWf237Q1ll5zu2VEbWCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:56:35.524502Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.09685","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b40a644e037116fec902375cf08948c3d8d1a41e46d812c9b6f272a1e627d57","sha256:83ab4992c4d7e21334e3c6397b6af20cb972b04d95949d3416bd916c2089dcb7"],"state_sha256":"f959621676a8488f9a29df185f1b285b50668e7f123adffb80621946d9b4d5b0"}