{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:GTYP3A7BDG324ZKPP3SOEJYXZC","short_pith_number":"pith:GTYP3A7B","canonical_record":{"source":{"id":"2505.10403","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-05-15T15:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"18153b1fdd2a30488ef079d2c9b8cf378aa29085b83ff4cc0ab8875c6a0b58c4","abstract_canon_sha256":"1c58509fe4abd184df35cf05d5ecd8943bd482f6870ee1d074809fa191b6bb23"},"schema_version":"1.0"},"canonical_sha256":"34f0fd83e119b7ae654f7ee4e22717c8ac66eb9a82c4db5a1ee783783241f32c","source":{"kind":"arxiv","id":"2505.10403","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.10403","created_at":"2026-07-05T11:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.10403v2","created_at":"2026-07-05T11:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.10403","created_at":"2026-07-05T11:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"GTYP3A7BDG32","created_at":"2026-07-05T11:26:51Z"},{"alias_kind":"pith_short_16","alias_value":"GTYP3A7BDG324ZKP","created_at":"2026-07-05T11:26:51Z"},{"alias_kind":"pith_short_8","alias_value":"GTYP3A7B","created_at":"2026-07-05T11:26:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:GTYP3A7BDG324ZKPP3SOEJYXZC","target":"record","payload":{"canonical_record":{"source":{"id":"2505.10403","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-05-15T15:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"18153b1fdd2a30488ef079d2c9b8cf378aa29085b83ff4cc0ab8875c6a0b58c4","abstract_canon_sha256":"1c58509fe4abd184df35cf05d5ecd8943bd482f6870ee1d074809fa191b6bb23"},"schema_version":"1.0"},"canonical_sha256":"34f0fd83e119b7ae654f7ee4e22717c8ac66eb9a82c4db5a1ee783783241f32c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:26:51.288184Z","signature_b64":"Hjv1mHDWBYA5uxIvK4Jo6lD0tdkMYUf2Xw8viXGJ5oRI8nN855hZ4V9lm4RKL+Q+zAIFIjPf8+N+/HbmWN58Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34f0fd83e119b7ae654f7ee4e22717c8ac66eb9a82c4db5a1ee783783241f32c","last_reissued_at":"2026-07-05T11:26:51.287704Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:26:51.287704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.10403","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:26:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4JiMW1gTqPxvz5XkdaU5kiKu0y5WsBFn5Ly4Tq6RbtJwbaoJANb2DBLxDn1X5+1BjWFFhWk54IMijeqyXzQ/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T16:54:49.744418Z"},"content_sha256":"138ada0f7305715589c90e85e21b4d32a19c21bda5a828cded176ffd7776a337","schema_version":"1.0","event_id":"sha256:138ada0f7305715589c90e85e21b4d32a19c21bda5a828cded176ffd7776a337"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:GTYP3A7BDG324ZKPP3SOEJYXZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometrically Enhanced Topological Quantum Codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"David Aasen, Jeongwan Haah, Matthew B. Hastings, Zhenghan Wang","submitted_at":"2025-05-15T15:27:52Z","abstract_excerpt":"We consider geometric methods of ``rotating\" the toric code in higher dimensions to reduce the qubit count. These geometric methods can be used to prepare higher dimensional toric code states using single shot techniques, and in turn these may be used to prepare entangled logical states such as Bell pairs or GHZ states. This bears some relation to measurement-based quantum computing in a twisted spacetime. We also propose a generalization to more general stabilizer codes, and we present computer analysis of optimal rotations in low dimensions. We present methods to do logical Clifford operatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.10403","kind":"arxiv","version":2},"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/2505.10403/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":"2026-07-05T11:26:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mC6ulymYDKX1SOAQ1MI+SkDRx0MRR3qgS5h6Ox+xkEDvD7prBbJdbgMIABsMNaqGdwotUxmbSRt5Kdi1BhA0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T16:54:49.745432Z"},"content_sha256":"e3a2ee995eed64b60cd929c660dc7aa6f2bb55057b81561bd70ad07e9312a19e","schema_version":"1.0","event_id":"sha256:e3a2ee995eed64b60cd929c660dc7aa6f2bb55057b81561bd70ad07e9312a19e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GTYP3A7BDG324ZKPP3SOEJYXZC/bundle.json","state_url":"https://pith.science/pith/GTYP3A7BDG324ZKPP3SOEJYXZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GTYP3A7BDG324ZKPP3SOEJYXZC/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":"2026-08-07T16:54:49Z","links":{"resolver":"https://pith.science/pith/GTYP3A7BDG324ZKPP3SOEJYXZC","bundle":"https://pith.science/pith/GTYP3A7BDG324ZKPP3SOEJYXZC/bundle.json","state":"https://pith.science/pith/GTYP3A7BDG324ZKPP3SOEJYXZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GTYP3A7BDG324ZKPP3SOEJYXZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GTYP3A7BDG324ZKPP3SOEJYXZC","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":"1c58509fe4abd184df35cf05d5ecd8943bd482f6870ee1d074809fa191b6bb23","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-05-15T15:27:52Z","title_canon_sha256":"18153b1fdd2a30488ef079d2c9b8cf378aa29085b83ff4cc0ab8875c6a0b58c4"},"schema_version":"1.0","source":{"id":"2505.10403","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.10403","created_at":"2026-07-05T11:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.10403v2","created_at":"2026-07-05T11:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.10403","created_at":"2026-07-05T11:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"GTYP3A7BDG32","created_at":"2026-07-05T11:26:51Z"},{"alias_kind":"pith_short_16","alias_value":"GTYP3A7BDG324ZKP","created_at":"2026-07-05T11:26:51Z"},{"alias_kind":"pith_short_8","alias_value":"GTYP3A7B","created_at":"2026-07-05T11:26:51Z"}],"graph_snapshots":[{"event_id":"sha256:e3a2ee995eed64b60cd929c660dc7aa6f2bb55057b81561bd70ad07e9312a19e","target":"graph","created_at":"2026-07-05T11:26:51Z","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/2505.10403/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider geometric methods of ``rotating\" the toric code in higher dimensions to reduce the qubit count. These geometric methods can be used to prepare higher dimensional toric code states using single shot techniques, and in turn these may be used to prepare entangled logical states such as Bell pairs or GHZ states. This bears some relation to measurement-based quantum computing in a twisted spacetime. We also propose a generalization to more general stabilizer codes, and we present computer analysis of optimal rotations in low dimensions. We present methods to do logical Clifford operatio","authors_text":"David Aasen, Jeongwan Haah, Matthew B. Hastings, Zhenghan Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-05-15T15:27:52Z","title":"Geometrically Enhanced Topological Quantum Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.10403","kind":"arxiv","version":2},"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":"sha256:138ada0f7305715589c90e85e21b4d32a19c21bda5a828cded176ffd7776a337","target":"record","created_at":"2026-07-05T11:26:51Z","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":"1c58509fe4abd184df35cf05d5ecd8943bd482f6870ee1d074809fa191b6bb23","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-05-15T15:27:52Z","title_canon_sha256":"18153b1fdd2a30488ef079d2c9b8cf378aa29085b83ff4cc0ab8875c6a0b58c4"},"schema_version":"1.0","source":{"id":"2505.10403","kind":"arxiv","version":2}},"canonical_sha256":"34f0fd83e119b7ae654f7ee4e22717c8ac66eb9a82c4db5a1ee783783241f32c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34f0fd83e119b7ae654f7ee4e22717c8ac66eb9a82c4db5a1ee783783241f32c","first_computed_at":"2026-07-05T11:26:51.287704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:26:51.287704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hjv1mHDWBYA5uxIvK4Jo6lD0tdkMYUf2Xw8viXGJ5oRI8nN855hZ4V9lm4RKL+Q+zAIFIjPf8+N+/HbmWN58Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:26:51.288184Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.10403","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:138ada0f7305715589c90e85e21b4d32a19c21bda5a828cded176ffd7776a337","sha256:e3a2ee995eed64b60cd929c660dc7aa6f2bb55057b81561bd70ad07e9312a19e"],"state_sha256":"013cfbde92b0af20e648e13bb301c551e4cfddab706a28c2fd1eb819f94235e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eknr4yy+phYfwBpy2qEJxj6x38ViDUk4ILfJtFjzjmdYKoxJgnG/D/Kkn9LpGbdTXMHEi3HhN5m1mhyP2Px1Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T16:54:49.751833Z","bundle_sha256":"753a6cbfdd446fbfa72541583a5f944f6ad8b4f6db0e6f209f2fcdb158c95a2e"}}