{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:F2A5RNXMGVUFX7BJJXWXQMKHIF","short_pith_number":"pith:F2A5RNXM","canonical_record":{"source":{"id":"2306.16400","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-06-28T17:50:33Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"80426afe6bf188ba6b356b547f92f9b879254ab1900bffc31c3ea086e682876b","abstract_canon_sha256":"3c752866527f685a5dde840cc0685824be63978b206d055694ac47e12fb20af2"},"schema_version":"1.0"},"canonical_sha256":"2e81d8b6ec35685bfc294ded78314741751b137925e515ed2a2b168f6b60d6cd","source":{"kind":"arxiv","id":"2306.16400","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.16400","created_at":"2026-07-05T06:25:55Z"},{"alias_kind":"arxiv_version","alias_value":"2306.16400v1","created_at":"2026-07-05T06:25:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.16400","created_at":"2026-07-05T06:25:55Z"},{"alias_kind":"pith_short_12","alias_value":"F2A5RNXMGVUF","created_at":"2026-07-05T06:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"F2A5RNXMGVUFX7BJ","created_at":"2026-07-05T06:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"F2A5RNXM","created_at":"2026-07-05T06:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:F2A5RNXMGVUFX7BJJXWXQMKHIF","target":"record","payload":{"canonical_record":{"source":{"id":"2306.16400","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-06-28T17:50:33Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"80426afe6bf188ba6b356b547f92f9b879254ab1900bffc31c3ea086e682876b","abstract_canon_sha256":"3c752866527f685a5dde840cc0685824be63978b206d055694ac47e12fb20af2"},"schema_version":"1.0"},"canonical_sha256":"2e81d8b6ec35685bfc294ded78314741751b137925e515ed2a2b168f6b60d6cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:25:55.715494Z","signature_b64":"BQMjmcJDbuyM+93C6ZeXcgdvnlLYLxvDi13gAPuJim8cqy1/YRJBxjhTO9sierXLCoBaxkhzVF7zJ0vcwtXiAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e81d8b6ec35685bfc294ded78314741751b137925e515ed2a2b168f6b60d6cd","last_reissued_at":"2026-07-05T06:25:55.715024Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:25:55.715024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.16400","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":"2026-07-05T06:25:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DNUlQ76vYBcRMERo6bFiZhcUntvtiyQwMvmk8ALYnDTqTbnhcU6IlZ0r35oz5fbdaktFT8Q9DgUc6iP0as9mBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T04:16:25.951705Z"},"content_sha256":"293a0b39f0baab8822caa40809481282b59307b06eb86e8aaa27479f8d400621","schema_version":"1.0","event_id":"sha256:293a0b39f0baab8822caa40809481282b59307b06eb86e8aaa27479f8d400621"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:F2A5RNXMGVUFX7BJJXWXQMKHIF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum two-block group algebra codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Hsiang-Ku Lin, Leonid P. Pryadko","submitted_at":"2023-06-28T17:50:33Z","abstract_excerpt":"We consider quantum two-block group algebra (2BGA) codes, a previously unstudied family of smallest lifted-product (LP) codes. These codes are related to generalized-bicycle (GB) codes, except a cyclic group is replaced with an arbitrary finite group, generally non-abelian. As special cases, 2BGA codes include a subset of square-matrix LP codes over abelian groups, including quasi-cyclic codes, and all square-matrix hypergraph-product codes constructed from a pair of classical group codes. We establish criteria for permutation equivalence of 2BGA codes and give bounds for their parameters, bot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.16400","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/2306.16400/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":"2026-07-05T06:25:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y2UVh/R+CySA/yEMwbZLEtm0OyeXbzyEHbhAhhnxB7Jn/nzxVD67RbAV4Kb3iXSfZlKaWAG52oe9Z3xUPJExAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T04:16:25.952272Z"},"content_sha256":"a6f9deed01375ee3955f7143b9603b328c76321b7beb0774c99c4af400a8ee98","schema_version":"1.0","event_id":"sha256:a6f9deed01375ee3955f7143b9603b328c76321b7beb0774c99c4af400a8ee98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F2A5RNXMGVUFX7BJJXWXQMKHIF/bundle.json","state_url":"https://pith.science/pith/F2A5RNXMGVUFX7BJJXWXQMKHIF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F2A5RNXMGVUFX7BJJXWXQMKHIF/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":"2026-08-15T04:16:25Z","links":{"resolver":"https://pith.science/pith/F2A5RNXMGVUFX7BJJXWXQMKHIF","bundle":"https://pith.science/pith/F2A5RNXMGVUFX7BJJXWXQMKHIF/bundle.json","state":"https://pith.science/pith/F2A5RNXMGVUFX7BJJXWXQMKHIF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F2A5RNXMGVUFX7BJJXWXQMKHIF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:F2A5RNXMGVUFX7BJJXWXQMKHIF","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":"3c752866527f685a5dde840cc0685824be63978b206d055694ac47e12fb20af2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-06-28T17:50:33Z","title_canon_sha256":"80426afe6bf188ba6b356b547f92f9b879254ab1900bffc31c3ea086e682876b"},"schema_version":"1.0","source":{"id":"2306.16400","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.16400","created_at":"2026-07-05T06:25:55Z"},{"alias_kind":"arxiv_version","alias_value":"2306.16400v1","created_at":"2026-07-05T06:25:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.16400","created_at":"2026-07-05T06:25:55Z"},{"alias_kind":"pith_short_12","alias_value":"F2A5RNXMGVUF","created_at":"2026-07-05T06:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"F2A5RNXMGVUFX7BJ","created_at":"2026-07-05T06:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"F2A5RNXM","created_at":"2026-07-05T06:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:a6f9deed01375ee3955f7143b9603b328c76321b7beb0774c99c4af400a8ee98","target":"graph","created_at":"2026-07-05T06:25:55Z","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/2306.16400/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider quantum two-block group algebra (2BGA) codes, a previously unstudied family of smallest lifted-product (LP) codes. These codes are related to generalized-bicycle (GB) codes, except a cyclic group is replaced with an arbitrary finite group, generally non-abelian. As special cases, 2BGA codes include a subset of square-matrix LP codes over abelian groups, including quasi-cyclic codes, and all square-matrix hypergraph-product codes constructed from a pair of classical group codes. We establish criteria for permutation equivalence of 2BGA codes and give bounds for their parameters, bot","authors_text":"Hsiang-Ku Lin, Leonid P. Pryadko","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-06-28T17:50:33Z","title":"Quantum two-block group algebra codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.16400","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":"sha256:293a0b39f0baab8822caa40809481282b59307b06eb86e8aaa27479f8d400621","target":"record","created_at":"2026-07-05T06:25:55Z","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":"3c752866527f685a5dde840cc0685824be63978b206d055694ac47e12fb20af2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-06-28T17:50:33Z","title_canon_sha256":"80426afe6bf188ba6b356b547f92f9b879254ab1900bffc31c3ea086e682876b"},"schema_version":"1.0","source":{"id":"2306.16400","kind":"arxiv","version":1}},"canonical_sha256":"2e81d8b6ec35685bfc294ded78314741751b137925e515ed2a2b168f6b60d6cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e81d8b6ec35685bfc294ded78314741751b137925e515ed2a2b168f6b60d6cd","first_computed_at":"2026-07-05T06:25:55.715024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:25:55.715024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BQMjmcJDbuyM+93C6ZeXcgdvnlLYLxvDi13gAPuJim8cqy1/YRJBxjhTO9sierXLCoBaxkhzVF7zJ0vcwtXiAw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:25:55.715494Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.16400","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:293a0b39f0baab8822caa40809481282b59307b06eb86e8aaa27479f8d400621","sha256:a6f9deed01375ee3955f7143b9603b328c76321b7beb0774c99c4af400a8ee98"],"state_sha256":"2e3afded9d2d1a17f321c2e5db359e438db9920b74147ffe8c80ef2539051275"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gMim2opZgAlxLTzAiYJjqloSqllRxBxIEbDNWofyAaIy23mSQiiZW7EbzkT05XQmYlENqJyE0i3YoJypKiA7CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T04:16:25.956106Z","bundle_sha256":"53d55d3b4605d6a709ac59c383fa2e7e09381600e42caef8d23d1011ab27205d"}}