{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:JEFP7W75JUU7REWQ72WMOPX52R","short_pith_number":"pith:JEFP7W75","canonical_record":{"source":{"id":"2404.08552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-04-12T15:51:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"14c086e2a5ffbc184f516de2e80318e8f19464dcdbdd0a08cc820de379c69b74","abstract_canon_sha256":"42699e34426936458e30291c58589637a3cefe6482b8b83f8e1f83e4f378f638"},"schema_version":"1.0"},"canonical_sha256":"490affdbfd4d29f892d0feacc73efdd46d450d7818e2e72e1d9e79ef086b0d0e","source":{"kind":"arxiv","id":"2404.08552","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.08552","created_at":"2026-07-05T08:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"2404.08552v1","created_at":"2026-07-05T08:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.08552","created_at":"2026-07-05T08:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"JEFP7W75JUU7","created_at":"2026-07-05T08:07:23Z"},{"alias_kind":"pith_short_16","alias_value":"JEFP7W75JUU7REWQ","created_at":"2026-07-05T08:07:23Z"},{"alias_kind":"pith_short_8","alias_value":"JEFP7W75","created_at":"2026-07-05T08:07:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:JEFP7W75JUU7REWQ72WMOPX52R","target":"record","payload":{"canonical_record":{"source":{"id":"2404.08552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-04-12T15:51:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"14c086e2a5ffbc184f516de2e80318e8f19464dcdbdd0a08cc820de379c69b74","abstract_canon_sha256":"42699e34426936458e30291c58589637a3cefe6482b8b83f8e1f83e4f378f638"},"schema_version":"1.0"},"canonical_sha256":"490affdbfd4d29f892d0feacc73efdd46d450d7818e2e72e1d9e79ef086b0d0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:07:23.449115Z","signature_b64":"zdaxNsLlTjRedDFBsVpquIMZnq9hwCsfyp6v2Ib2QkJ2zaYal8z2r6EK8avA62SVb2qm86EnaynOGUMKLfBYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"490affdbfd4d29f892d0feacc73efdd46d450d7818e2e72e1d9e79ef086b0d0e","last_reissued_at":"2026-07-05T08:07:23.448764Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:07:23.448764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.08552","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ARJ7+W8oowfqz4YHppBFznSGFg6zci9N0lzmV+8LIw4WbFWwhPeAmQbWJC5kxfyCHKyc5EjuG2hmLVh7+IhoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T04:52:50.503754Z"},"content_sha256":"0deb86583932686f326dc4391522990a671f934abcc65685056b73972f7f1405","schema_version":"1.0","event_id":"sha256:0deb86583932686f326dc4391522990a671f934abcc65685056b73972f7f1405"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:JEFP7W75JUU7REWQ72WMOPX52R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abelian Group Quantum Error Correction in Kitaev's Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"C\\'esar Galindo, Diego Romero, Shawn X. Cui","submitted_at":"2024-04-12T15:51:41Z","abstract_excerpt":"In this paper, we present a detailed mathematical description of the error correction process for Kitaev's model for finite Abelian groups. The number of errors Kitaev's model can correct depends on the lattice and its topology. Although there is a theoretical maximum number of errors that can be corrected, we prove that correcting this number of errors, in general, is an NP-complete problem. Consequently, we introduce a polynomial-time correction algorithm that corrects a number of errors below the theoretical maximum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.08552","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.08552/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6CFpS5e3jKpkCPuXehc0C1kxrhBaG+J53gO1So4kS3MEBiJsvKV8LS0iwt9+A5vc558xqA+fURpPUos+TYEaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T04:52:50.504134Z"},"content_sha256":"0636d1f05db171c9bb0a66d338c917dd193b58351b1f1d13823274287a88421c","schema_version":"1.0","event_id":"sha256:0636d1f05db171c9bb0a66d338c917dd193b58351b1f1d13823274287a88421c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JEFP7W75JUU7REWQ72WMOPX52R/bundle.json","state_url":"https://pith.science/pith/JEFP7W75JUU7REWQ72WMOPX52R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JEFP7W75JUU7REWQ72WMOPX52R/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-07T04:52:50Z","links":{"resolver":"https://pith.science/pith/JEFP7W75JUU7REWQ72WMOPX52R","bundle":"https://pith.science/pith/JEFP7W75JUU7REWQ72WMOPX52R/bundle.json","state":"https://pith.science/pith/JEFP7W75JUU7REWQ72WMOPX52R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JEFP7W75JUU7REWQ72WMOPX52R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JEFP7W75JUU7REWQ72WMOPX52R","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":"42699e34426936458e30291c58589637a3cefe6482b8b83f8e1f83e4f378f638","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-04-12T15:51:41Z","title_canon_sha256":"14c086e2a5ffbc184f516de2e80318e8f19464dcdbdd0a08cc820de379c69b74"},"schema_version":"1.0","source":{"id":"2404.08552","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.08552","created_at":"2026-07-05T08:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"2404.08552v1","created_at":"2026-07-05T08:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.08552","created_at":"2026-07-05T08:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"JEFP7W75JUU7","created_at":"2026-07-05T08:07:23Z"},{"alias_kind":"pith_short_16","alias_value":"JEFP7W75JUU7REWQ","created_at":"2026-07-05T08:07:23Z"},{"alias_kind":"pith_short_8","alias_value":"JEFP7W75","created_at":"2026-07-05T08:07:23Z"}],"graph_snapshots":[{"event_id":"sha256:0636d1f05db171c9bb0a66d338c917dd193b58351b1f1d13823274287a88421c","target":"graph","created_at":"2026-07-05T08:07:23Z","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/2404.08552/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present a detailed mathematical description of the error correction process for Kitaev's model for finite Abelian groups. The number of errors Kitaev's model can correct depends on the lattice and its topology. Although there is a theoretical maximum number of errors that can be corrected, we prove that correcting this number of errors, in general, is an NP-complete problem. Consequently, we introduce a polynomial-time correction algorithm that corrects a number of errors below the theoretical maximum.","authors_text":"C\\'esar Galindo, Diego Romero, Shawn X. Cui","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-04-12T15:51:41Z","title":"Abelian Group Quantum Error Correction in Kitaev's Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.08552","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":"sha256:0deb86583932686f326dc4391522990a671f934abcc65685056b73972f7f1405","target":"record","created_at":"2026-07-05T08:07:23Z","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":"42699e34426936458e30291c58589637a3cefe6482b8b83f8e1f83e4f378f638","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-04-12T15:51:41Z","title_canon_sha256":"14c086e2a5ffbc184f516de2e80318e8f19464dcdbdd0a08cc820de379c69b74"},"schema_version":"1.0","source":{"id":"2404.08552","kind":"arxiv","version":1}},"canonical_sha256":"490affdbfd4d29f892d0feacc73efdd46d450d7818e2e72e1d9e79ef086b0d0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"490affdbfd4d29f892d0feacc73efdd46d450d7818e2e72e1d9e79ef086b0d0e","first_computed_at":"2026-07-05T08:07:23.448764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:07:23.448764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zdaxNsLlTjRedDFBsVpquIMZnq9hwCsfyp6v2Ib2QkJ2zaYal8z2r6EK8avA62SVb2qm86EnaynOGUMKLfBYAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:07:23.449115Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.08552","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0deb86583932686f326dc4391522990a671f934abcc65685056b73972f7f1405","sha256:0636d1f05db171c9bb0a66d338c917dd193b58351b1f1d13823274287a88421c"],"state_sha256":"58f0cb4ff68c77643f9e05f377395926c985e374a353f961d973869dcaf197f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ayRdteHF9HJ6cnjoTiJ2OaXc1UFyOQL5wCUIj2WQId0749wgFsvUMGTGesZKMbyve8AfHLnfx6ebUNhXdASCDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T04:52:50.506675Z","bundle_sha256":"02a7b4fb5c525d768354679e205c2182af8b8eb41066736714199b9f559f838f"}}