{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:PZLJSXDQNNAHIVZ3KWRGWMKE3S","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":"5048ac9bb4b1a6145409cd115623a9b1835c1742d261f0ecba545a0766532c7a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-01-22T22:08:56Z","title_canon_sha256":"855fec2ab2923f8a440e4d35c187dbe6c96cb84a02adc1b2232cc663831ecfa7"},"schema_version":"1.0","source":{"id":"2101.09349","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.09349","created_at":"2026-07-05T08:47:03Z"},{"alias_kind":"arxiv_version","alias_value":"2101.09349v4","created_at":"2026-07-05T08:47:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.09349","created_at":"2026-07-05T08:47:03Z"},{"alias_kind":"pith_short_12","alias_value":"PZLJSXDQNNAH","created_at":"2026-07-05T08:47:03Z"},{"alias_kind":"pith_short_16","alias_value":"PZLJSXDQNNAHIVZ3","created_at":"2026-07-05T08:47:03Z"},{"alias_kind":"pith_short_8","alias_value":"PZLJSXDQ","created_at":"2026-07-05T08:47:03Z"}],"graph_snapshots":[{"event_id":"sha256:f8e70d8860fcc19dd64c82eb1ba4ce83a67c91f16776d2edb01bda8ce5ce8b02","target":"graph","created_at":"2026-07-05T08:47:03Z","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/2101.09349/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Twist defects in surface codes can be used to encode more logical qubits, improve the code rate, and implement logical gates. In this work we provide a rigorous formalism for constructing surface codes with twists generalizing the well-defined homological formalism introduced by Kitaev for describing CSS surface codes. In particular, we associate a surface code to any graph $G$ embedded on any 2D-manifold, in such a way that (1) qubits are associated to the vertices of the graph, (2) stabilizers are associated to faces, (3) twist defects are associated to odd-degree vertices. In this way, we a","authors_text":"Rahul Sarkar, Theodore J. Yoder","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-01-22T22:08:56Z","title":"A graph-based formalism for surface codes and twists"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.09349","kind":"arxiv","version":4},"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:d51c44163a9fcfba3fb5d7be459ed801a6505225880d6b1a17e232cbe7d40b93","target":"record","created_at":"2026-07-05T08:47:03Z","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":"5048ac9bb4b1a6145409cd115623a9b1835c1742d261f0ecba545a0766532c7a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-01-22T22:08:56Z","title_canon_sha256":"855fec2ab2923f8a440e4d35c187dbe6c96cb84a02adc1b2232cc663831ecfa7"},"schema_version":"1.0","source":{"id":"2101.09349","kind":"arxiv","version":4}},"canonical_sha256":"7e56995c706b4074573b55a26b3144dc8d9e3e6c1ce314d478c8ce99bd953e73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e56995c706b4074573b55a26b3144dc8d9e3e6c1ce314d478c8ce99bd953e73","first_computed_at":"2026-07-05T08:47:03.167255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:47:03.167255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FRifVO5Le6fD+Scb88OVjqh8Qjbd6mD/+zLoxdQRmCU5EZ8SEcwX1fljyS43W+ZKZyndV+V4+TTUoCY7FtzOBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:47:03.167765Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.09349","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d51c44163a9fcfba3fb5d7be459ed801a6505225880d6b1a17e232cbe7d40b93","sha256:f8e70d8860fcc19dd64c82eb1ba4ce83a67c91f16776d2edb01bda8ce5ce8b02"],"state_sha256":"2593e9f8082b5bdefbe667bd60459251ca2413f21b1c5e8331fc403fba892fa2"}