{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GXBGCOBWW6YE6N54WAWXRMDRZS","short_pith_number":"pith:GXBGCOBW","canonical_record":{"source":{"id":"2608.00601","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-08-01T11:36:03Z","cross_cats_sorted":["math.IT","quant-ph"],"title_canon_sha256":"9aa46486edacdac9f96e64a32752d614fbc50276f507902d31fa80c4e5156e1a","abstract_canon_sha256":"f42bbada8b12e06c0acf5cb7ada83cc5d45156af14faf0f7b254f2032197f327"},"schema_version":"1.0"},"canonical_sha256":"35c2613836b7b04f37bcb02d78b071ccbf40deb9f813e876a939f804b6b44e99","source":{"kind":"arxiv","id":"2608.00601","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00601","created_at":"2026-08-04T00:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00601v1","created_at":"2026-08-04T00:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00601","created_at":"2026-08-04T00:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"GXBGCOBWW6YE","created_at":"2026-08-04T00:38:00Z"},{"alias_kind":"pith_short_16","alias_value":"GXBGCOBWW6YE6N54","created_at":"2026-08-04T00:38:00Z"},{"alias_kind":"pith_short_8","alias_value":"GXBGCOBW","created_at":"2026-08-04T00:38:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GXBGCOBWW6YE6N54WAWXRMDRZS","target":"record","payload":{"canonical_record":{"source":{"id":"2608.00601","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-08-01T11:36:03Z","cross_cats_sorted":["math.IT","quant-ph"],"title_canon_sha256":"9aa46486edacdac9f96e64a32752d614fbc50276f507902d31fa80c4e5156e1a","abstract_canon_sha256":"f42bbada8b12e06c0acf5cb7ada83cc5d45156af14faf0f7b254f2032197f327"},"schema_version":"1.0"},"canonical_sha256":"35c2613836b7b04f37bcb02d78b071ccbf40deb9f813e876a939f804b6b44e99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T00:38:00.875727Z","signature_b64":"YhI2tpsiLeCXtex2COtq5qnFD/vvIV9e1O6sxYFkEv2lmBX8d6UKwRBs6DJzi527PQlTmoav6JCQVpP8vC2KBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35c2613836b7b04f37bcb02d78b071ccbf40deb9f813e876a939f804b6b44e99","last_reissued_at":"2026-08-04T00:38:00.874315Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T00:38:00.874315Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.00601","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":"2026-08-04T00:38:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Km3snz7JHxyEbA7mFA4HMiL2p3tlsPvk5dcD4OYbKzfesU/UfMepv/x3H/71PvMFb4nzTSy3b+GYubywqARkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T08:19:00.071557Z"},"content_sha256":"112e9eb94dbc1cfb7bbf8c04303d9ccaca70b976d96462a92fd7367bec069a51","schema_version":"1.0","event_id":"sha256:112e9eb94dbc1cfb7bbf8c04303d9ccaca70b976d96462a92fd7367bec069a51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GXBGCOBWW6YE6N54WAWXRMDRZS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symplectic Barnes-Wall GKP Codes: Deterministic $O(N \\log^2 N)$ Decoding and Logarithmic Rate Scaling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT","quant-ph"],"primary_cat":"cs.IT","authors_text":"Shanxiang Lyu","submitted_at":"2026-08-01T11:36:03Z","abstract_excerpt":"We construct an explicit symplectic realization of the Barnes-Wall lattice that yields a family of multimode Gottesman-Kitaev-Preskill (GKP) codes with encoding rate $R = \\frac{1}{2}\\log_2 N$ and a deterministic $O(N\\log^2 N)$ bounded-distance decoder. The recursive generator $G_{m+1} = \\bigl(\\begin{smallmatrix} G_m & 0 \\\\ G_m & R_m G_m \\end{smallmatrix}\\bigr)$ with $R_m = I + \\Omega$ simultaneously guarantees symplectic integrality for valid quantum stabilizers and preserves the exact Barnes-Wall decoding structure through a chain of isometric isomorphisms. The code distance is constant at $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00601","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/2608.00601/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":"2026-08-04T00:38:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j4PoCwzI2jCMsYHHf92BlIoCBDEgnMKEMfpwhW0f85colFsoRICRdyfwdRO3EKW2Fs24uJf6QacSIwaaEw+mBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T08:19:00.072163Z"},"content_sha256":"27b9e6ccb0adc8be7424d7a416d27ac5ff2045b43ddc95a7b7cc2a9d268dbe4c","schema_version":"1.0","event_id":"sha256:27b9e6ccb0adc8be7424d7a416d27ac5ff2045b43ddc95a7b7cc2a9d268dbe4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GXBGCOBWW6YE6N54WAWXRMDRZS/bundle.json","state_url":"https://pith.science/pith/GXBGCOBWW6YE6N54WAWXRMDRZS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GXBGCOBWW6YE6N54WAWXRMDRZS/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":"2026-08-23T08:19:00Z","links":{"resolver":"https://pith.science/pith/GXBGCOBWW6YE6N54WAWXRMDRZS","bundle":"https://pith.science/pith/GXBGCOBWW6YE6N54WAWXRMDRZS/bundle.json","state":"https://pith.science/pith/GXBGCOBWW6YE6N54WAWXRMDRZS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GXBGCOBWW6YE6N54WAWXRMDRZS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GXBGCOBWW6YE6N54WAWXRMDRZS","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":"f42bbada8b12e06c0acf5cb7ada83cc5d45156af14faf0f7b254f2032197f327","cross_cats_sorted":["math.IT","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-08-01T11:36:03Z","title_canon_sha256":"9aa46486edacdac9f96e64a32752d614fbc50276f507902d31fa80c4e5156e1a"},"schema_version":"1.0","source":{"id":"2608.00601","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00601","created_at":"2026-08-04T00:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00601v1","created_at":"2026-08-04T00:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00601","created_at":"2026-08-04T00:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"GXBGCOBWW6YE","created_at":"2026-08-04T00:38:00Z"},{"alias_kind":"pith_short_16","alias_value":"GXBGCOBWW6YE6N54","created_at":"2026-08-04T00:38:00Z"},{"alias_kind":"pith_short_8","alias_value":"GXBGCOBW","created_at":"2026-08-04T00:38:00Z"}],"graph_snapshots":[{"event_id":"sha256:27b9e6ccb0adc8be7424d7a416d27ac5ff2045b43ddc95a7b7cc2a9d268dbe4c","target":"graph","created_at":"2026-08-04T00:38:00Z","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/2608.00601/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct an explicit symplectic realization of the Barnes-Wall lattice that yields a family of multimode Gottesman-Kitaev-Preskill (GKP) codes with encoding rate $R = \\frac{1}{2}\\log_2 N$ and a deterministic $O(N\\log^2 N)$ bounded-distance decoder. The recursive generator $G_{m+1} = \\bigl(\\begin{smallmatrix} G_m & 0 \\\\ G_m & R_m G_m \\end{smallmatrix}\\bigr)$ with $R_m = I + \\Omega$ simultaneously guarantees symplectic integrality for valid quantum stabilizers and preserves the exact Barnes-Wall decoding structure through a chain of isometric isomorphisms. The code distance is constant at $\\","authors_text":"Shanxiang Lyu","cross_cats":["math.IT","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-08-01T11:36:03Z","title":"Symplectic Barnes-Wall GKP Codes: Deterministic $O(N \\log^2 N)$ Decoding and Logarithmic Rate Scaling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00601","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":"sha256:112e9eb94dbc1cfb7bbf8c04303d9ccaca70b976d96462a92fd7367bec069a51","target":"record","created_at":"2026-08-04T00:38:00Z","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":"f42bbada8b12e06c0acf5cb7ada83cc5d45156af14faf0f7b254f2032197f327","cross_cats_sorted":["math.IT","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-08-01T11:36:03Z","title_canon_sha256":"9aa46486edacdac9f96e64a32752d614fbc50276f507902d31fa80c4e5156e1a"},"schema_version":"1.0","source":{"id":"2608.00601","kind":"arxiv","version":1}},"canonical_sha256":"35c2613836b7b04f37bcb02d78b071ccbf40deb9f813e876a939f804b6b44e99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35c2613836b7b04f37bcb02d78b071ccbf40deb9f813e876a939f804b6b44e99","first_computed_at":"2026-08-04T00:38:00.874315Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T00:38:00.874315Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YhI2tpsiLeCXtex2COtq5qnFD/vvIV9e1O6sxYFkEv2lmBX8d6UKwRBs6DJzi527PQlTmoav6JCQVpP8vC2KBQ==","signature_status":"signed_v1","signed_at":"2026-08-04T00:38:00.875727Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.00601","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:112e9eb94dbc1cfb7bbf8c04303d9ccaca70b976d96462a92fd7367bec069a51","sha256:27b9e6ccb0adc8be7424d7a416d27ac5ff2045b43ddc95a7b7cc2a9d268dbe4c"],"state_sha256":"f22fa3c80a6bfddca08771edab029d262e471239027ec6095520e022fb65774d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9pCCMsb+1EB1YR37s+SiDVIBsqmQ8wa8+hCop5Z+vzsz74cpzEMt+/sEqGdPOj9X7v8dLrnFBucGFpE0D85ECg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T08:19:00.077691Z","bundle_sha256":"dee7bdb6340cb02c24b9a8ddcb67ba3fcd982e88b184cc47f624c883d8e14143"}}