{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3I3BZU6O2KTRQK4EAIMCGOOIFE","short_pith_number":"pith:3I3BZU6O","canonical_record":{"source":{"id":"2608.00165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2026-07-31T18:00:01Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"6602a4fbf361097284d94857fedb6bde164f8ace0e24746652e237d4c9fcb0d4","abstract_canon_sha256":"3cc3125a124c7dbe27c1e571b8564e7f8d02e5a1d1fe74236688c120741f086d"},"schema_version":"1.0"},"canonical_sha256":"da361cd3ced2a7182b8402182339c8292495065f5e7825521d6af8d1333bb9f0","source":{"kind":"arxiv","id":"2608.00165","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00165","created_at":"2026-08-04T00:33:06Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00165v1","created_at":"2026-08-04T00:33:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00165","created_at":"2026-08-04T00:33:06Z"},{"alias_kind":"pith_short_12","alias_value":"3I3BZU6O2KTR","created_at":"2026-08-04T00:33:06Z"},{"alias_kind":"pith_short_16","alias_value":"3I3BZU6O2KTRQK4E","created_at":"2026-08-04T00:33:06Z"},{"alias_kind":"pith_short_8","alias_value":"3I3BZU6O","created_at":"2026-08-04T00:33:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3I3BZU6O2KTRQK4EAIMCGOOIFE","target":"record","payload":{"canonical_record":{"source":{"id":"2608.00165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2026-07-31T18:00:01Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"6602a4fbf361097284d94857fedb6bde164f8ace0e24746652e237d4c9fcb0d4","abstract_canon_sha256":"3cc3125a124c7dbe27c1e571b8564e7f8d02e5a1d1fe74236688c120741f086d"},"schema_version":"1.0"},"canonical_sha256":"da361cd3ced2a7182b8402182339c8292495065f5e7825521d6af8d1333bb9f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T00:33:06.410720Z","signature_b64":"WQLAB2R/Zi4tCHRjPpPkmfYcDX2fujijY+Cb67cM84XYYihrOL03kMpCoFeKME6R6ekPcNKgYkcCF207QyP4Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da361cd3ced2a7182b8402182339c8292495065f5e7825521d6af8d1333bb9f0","last_reissued_at":"2026-08-04T00:33:06.409334Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T00:33:06.409334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.00165","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":"2026-08-04T00:33:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pOuMdNVJRNf4ngsITy5AB/JYl3gSymOrWmpr1LwYy49IsHU76dTRXrJnzTfIBrDMQnaGtTeKG5qbd6QSJH3dAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T18:18:52.375742Z"},"content_sha256":"e3c391a96aa87f6e401ee4e58ad852aa8343931dacad0505986d4ee8576fa335","schema_version":"1.0","event_id":"sha256:e3c391a96aa87f6e401ee4e58ad852aa8343931dacad0505986d4ee8576fa335"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3I3BZU6O2KTRQK4EAIMCGOOIFE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arbitrary-Distance Quantum Error Correction with Gauss's Law for $\\mathbb Z_2$ Lattice Gauge Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"hep-lat","authors_text":"Christian W. Bauer, Lento Nagano, Masazumi Honda, Neel S. Modi, Nobuyuki Yoshioka","submitted_at":"2026-07-31T18:00:01Z","abstract_excerpt":"It has previously been shown by Rajput, Roggero, and Wiebe that $\\mathbb Z_2$ Gauss's law constraints can be used to build efficient quantum error-correcting codes (QECCs) that are robust against arbitrary single-qubit errors. In this work, we generalize the construction to be robust against arbitrary $t$-qubit errors, where $t$ is any positive integer. This includes a derivation of the optimal Gauss's law code within the considered family by minimizing the number of physical qubits required for a given code distance. Finally, we compare our codes against other efficient QECCs on metrics such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00165","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/2608.00165/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":"2026-08-04T00:33:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"POJBWeUXlVuHUdhU88Jh9z7vXUXHHC9kTyrgbvp0XcKnaWldeZafSPgFLBbS0Wf3VslOh/f/IVLdJKW67YcmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T18:18:52.376463Z"},"content_sha256":"321ce47bbf179473c3a6a895054aee23d97b940ec401ec803d4c197ad5e43462","schema_version":"1.0","event_id":"sha256:321ce47bbf179473c3a6a895054aee23d97b940ec401ec803d4c197ad5e43462"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3I3BZU6O2KTRQK4EAIMCGOOIFE/bundle.json","state_url":"https://pith.science/pith/3I3BZU6O2KTRQK4EAIMCGOOIFE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3I3BZU6O2KTRQK4EAIMCGOOIFE/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":"2026-08-04T18:18:52Z","links":{"resolver":"https://pith.science/pith/3I3BZU6O2KTRQK4EAIMCGOOIFE","bundle":"https://pith.science/pith/3I3BZU6O2KTRQK4EAIMCGOOIFE/bundle.json","state":"https://pith.science/pith/3I3BZU6O2KTRQK4EAIMCGOOIFE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3I3BZU6O2KTRQK4EAIMCGOOIFE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3I3BZU6O2KTRQK4EAIMCGOOIFE","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":"3cc3125a124c7dbe27c1e571b8564e7f8d02e5a1d1fe74236688c120741f086d","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2026-07-31T18:00:01Z","title_canon_sha256":"6602a4fbf361097284d94857fedb6bde164f8ace0e24746652e237d4c9fcb0d4"},"schema_version":"1.0","source":{"id":"2608.00165","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00165","created_at":"2026-08-04T00:33:06Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00165v1","created_at":"2026-08-04T00:33:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00165","created_at":"2026-08-04T00:33:06Z"},{"alias_kind":"pith_short_12","alias_value":"3I3BZU6O2KTR","created_at":"2026-08-04T00:33:06Z"},{"alias_kind":"pith_short_16","alias_value":"3I3BZU6O2KTRQK4E","created_at":"2026-08-04T00:33:06Z"},{"alias_kind":"pith_short_8","alias_value":"3I3BZU6O","created_at":"2026-08-04T00:33:06Z"}],"graph_snapshots":[{"event_id":"sha256:321ce47bbf179473c3a6a895054aee23d97b940ec401ec803d4c197ad5e43462","target":"graph","created_at":"2026-08-04T00:33:06Z","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/2608.00165/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It has previously been shown by Rajput, Roggero, and Wiebe that $\\mathbb Z_2$ Gauss's law constraints can be used to build efficient quantum error-correcting codes (QECCs) that are robust against arbitrary single-qubit errors. In this work, we generalize the construction to be robust against arbitrary $t$-qubit errors, where $t$ is any positive integer. This includes a derivation of the optimal Gauss's law code within the considered family by minimizing the number of physical qubits required for a given code distance. Finally, we compare our codes against other efficient QECCs on metrics such ","authors_text":"Christian W. Bauer, Lento Nagano, Masazumi Honda, Neel S. Modi, Nobuyuki Yoshioka","cross_cats":["hep-th","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2026-07-31T18:00:01Z","title":"Arbitrary-Distance Quantum Error Correction with Gauss's Law for $\\mathbb Z_2$ Lattice Gauge Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00165","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:e3c391a96aa87f6e401ee4e58ad852aa8343931dacad0505986d4ee8576fa335","target":"record","created_at":"2026-08-04T00:33:06Z","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":"3cc3125a124c7dbe27c1e571b8564e7f8d02e5a1d1fe74236688c120741f086d","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2026-07-31T18:00:01Z","title_canon_sha256":"6602a4fbf361097284d94857fedb6bde164f8ace0e24746652e237d4c9fcb0d4"},"schema_version":"1.0","source":{"id":"2608.00165","kind":"arxiv","version":1}},"canonical_sha256":"da361cd3ced2a7182b8402182339c8292495065f5e7825521d6af8d1333bb9f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da361cd3ced2a7182b8402182339c8292495065f5e7825521d6af8d1333bb9f0","first_computed_at":"2026-08-04T00:33:06.409334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T00:33:06.409334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WQLAB2R/Zi4tCHRjPpPkmfYcDX2fujijY+Cb67cM84XYYihrOL03kMpCoFeKME6R6ekPcNKgYkcCF207QyP4Aw==","signature_status":"signed_v1","signed_at":"2026-08-04T00:33:06.410720Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.00165","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3c391a96aa87f6e401ee4e58ad852aa8343931dacad0505986d4ee8576fa335","sha256:321ce47bbf179473c3a6a895054aee23d97b940ec401ec803d4c197ad5e43462"],"state_sha256":"aee341f807f7d47439b844463ded27bbff8b46041eccd33de45b2f56f6ef1230"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uzBnezcp/O08ium0wb/EoSh1FjGpRWSuUKgLZvdDwWSSMrNqqdbyB5s7hCk9mSZAQ7Latsthf38X0FpAEgfNCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T18:18:52.383442Z","bundle_sha256":"3e42ab79e41010b06cb9380ac8feeff9fe7f39fd464b14dbb4837d12affe752b"}}