{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:K4PHUAI2XZOO3T4EVGDCLWUB55","short_pith_number":"pith:K4PHUAI2","schema_version":"1.0","canonical_sha256":"571e7a011abe5cedcf84a98625da81ef491b604901379fc5d2fdce0a4558a86d","source":{"kind":"arxiv","id":"1804.00866","version":1},"attestation_state":"computed","paper":{"title":"On the Local Equivalence of 2D Color Codes and Surface Codes with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Arjun Nitin Bhagoji, Arun B. Aloshious, Pradeep Kiran Sarvepalli","submitted_at":"2018-04-03T08:22:34Z","abstract_excerpt":"In recent years, there have been many studies on local stabilizer codes. Under the assumption of translation and scale invariance Yoshida classified such codes. His result implies that translation invariant 2D color codes are equivalent to copies of toric codes. Independently, Bombin, Duclos-Cianci, and Poulin showed that a local translation invariant 2D topological stabilizer code is locally equivalent to a finite number of copies of Kitaev's toric code. In this paper we focus on 2D topological color codes and relax the assumption of translation invariance. Using a linear algebraic framework "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.00866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-04-03T08:22:34Z","cross_cats_sorted":[],"title_canon_sha256":"9d03d74f422133afdb1f88ed71c75b9c2278cba97c77cde9c2a1a58d03505583","abstract_canon_sha256":"045829bbb035c264069a455ada58f93c121dff952c4673eeca59f88d81f89200"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:31.924062Z","signature_b64":"qA3pgGwSQ4gm/ioZEjZRVP+giM+b9h5p2mOa/fsJRMDJr1MwdlUuXGEv175myujdG6zt2jhZzM4wlYKB0lsBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"571e7a011abe5cedcf84a98625da81ef491b604901379fc5d2fdce0a4558a86d","last_reissued_at":"2026-05-18T00:19:31.923521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:31.923521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Local Equivalence of 2D Color Codes and Surface Codes with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Arjun Nitin Bhagoji, Arun B. Aloshious, Pradeep Kiran Sarvepalli","submitted_at":"2018-04-03T08:22:34Z","abstract_excerpt":"In recent years, there have been many studies on local stabilizer codes. Under the assumption of translation and scale invariance Yoshida classified such codes. His result implies that translation invariant 2D color codes are equivalent to copies of toric codes. Independently, Bombin, Duclos-Cianci, and Poulin showed that a local translation invariant 2D topological stabilizer code is locally equivalent to a finite number of copies of Kitaev's toric code. In this paper we focus on 2D topological color codes and relax the assumption of translation invariance. Using a linear algebraic framework "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00866","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.00866","created_at":"2026-05-18T00:19:31.923617+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.00866v1","created_at":"2026-05-18T00:19:31.923617+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00866","created_at":"2026-05-18T00:19:31.923617+00:00"},{"alias_kind":"pith_short_12","alias_value":"K4PHUAI2XZOO","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"K4PHUAI2XZOO3T4E","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"K4PHUAI2","created_at":"2026-05-18T12:32:33.847187+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K4PHUAI2XZOO3T4EVGDCLWUB55","json":"https://pith.science/pith/K4PHUAI2XZOO3T4EVGDCLWUB55.json","graph_json":"https://pith.science/api/pith-number/K4PHUAI2XZOO3T4EVGDCLWUB55/graph.json","events_json":"https://pith.science/api/pith-number/K4PHUAI2XZOO3T4EVGDCLWUB55/events.json","paper":"https://pith.science/paper/K4PHUAI2"},"agent_actions":{"view_html":"https://pith.science/pith/K4PHUAI2XZOO3T4EVGDCLWUB55","download_json":"https://pith.science/pith/K4PHUAI2XZOO3T4EVGDCLWUB55.json","view_paper":"https://pith.science/paper/K4PHUAI2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.00866&json=true","fetch_graph":"https://pith.science/api/pith-number/K4PHUAI2XZOO3T4EVGDCLWUB55/graph.json","fetch_events":"https://pith.science/api/pith-number/K4PHUAI2XZOO3T4EVGDCLWUB55/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K4PHUAI2XZOO3T4EVGDCLWUB55/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K4PHUAI2XZOO3T4EVGDCLWUB55/action/storage_attestation","attest_author":"https://pith.science/pith/K4PHUAI2XZOO3T4EVGDCLWUB55/action/author_attestation","sign_citation":"https://pith.science/pith/K4PHUAI2XZOO3T4EVGDCLWUB55/action/citation_signature","submit_replication":"https://pith.science/pith/K4PHUAI2XZOO3T4EVGDCLWUB55/action/replication_record"}},"created_at":"2026-05-18T00:19:31.923617+00:00","updated_at":"2026-05-18T00:19:31.923617+00:00"}