{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Q2AV6TTRIA7MKETCFWXFYP4YOB","short_pith_number":"pith:Q2AV6TTR","canonical_record":{"source":{"id":"1106.5210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-06-26T11:29:54Z","cross_cats_sorted":[],"title_canon_sha256":"a91acd6ba7dc52fee64f563f10f454f4583700366b832d8dafcda7e6f19531e2","abstract_canon_sha256":"d8423529d468d2b15f6c4ce4d159706d6e014b35ce127e501de435d48396483b"},"schema_version":"1.0"},"canonical_sha256":"86815f4e71403ec512622dae5c3f987050eb08647fc9634b356e05ed1a4e67fe","source":{"kind":"arxiv","id":"1106.5210","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5210","created_at":"2026-05-18T03:23:47Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5210v1","created_at":"2026-05-18T03:23:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5210","created_at":"2026-05-18T03:23:47Z"},{"alias_kind":"pith_short_12","alias_value":"Q2AV6TTRIA7M","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q2AV6TTRIA7MKETC","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q2AV6TTR","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Q2AV6TTRIA7MKETCFWXFYP4YOB","target":"record","payload":{"canonical_record":{"source":{"id":"1106.5210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-06-26T11:29:54Z","cross_cats_sorted":[],"title_canon_sha256":"a91acd6ba7dc52fee64f563f10f454f4583700366b832d8dafcda7e6f19531e2","abstract_canon_sha256":"d8423529d468d2b15f6c4ce4d159706d6e014b35ce127e501de435d48396483b"},"schema_version":"1.0"},"canonical_sha256":"86815f4e71403ec512622dae5c3f987050eb08647fc9634b356e05ed1a4e67fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:23:47.008495Z","signature_b64":"exaWSsmJb+OR4Y5ht34Tk2qRqTZnMKRIdMCRm8aXWEp4KthaekP8wepNBXAZ8ZqQXMNQxLNGz9d7GEgChJbTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86815f4e71403ec512622dae5c3f987050eb08647fc9634b356e05ed1a4e67fe","last_reissued_at":"2026-05-18T03:23:47.007901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:23:47.007901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.5210","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":"2026-05-18T03:23:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"80NNj0X5PdjUCg1CGIZzh45Xb5oNe7ChSA9TQV1BD/Cvv6Skqg0IeiirkcTBc1ttTJvPIEzJ+KvCkNGcZLHjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:30:40.093123Z"},"content_sha256":"925433ef7abbb3c391b78eb4ca85294966840a2894afdd377daae0483bb55344","schema_version":"1.0","event_id":"sha256:925433ef7abbb3c391b78eb4ca85294966840a2894afdd377daae0483bb55344"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Q2AV6TTRIA7MKETCFWXFYP4YOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Chi-Kwong Li, Hiroyuki Tomita, Mikio Nakahara, Nung-sing Sze, Yiu-Tung Poon","submitted_at":"2011-06-26T11:29:54Z","abstract_excerpt":"When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free subspace are known to correct such collective errors. We construct simple quantum circuits, which implement these collective error correction codes, for a small number $n$ of physical qubits. A single logical qubit is encoded with $n=3$ and $n=4$, while two logical qubits are encoded with $n=5$. The recursive relations among the subspaces employed in noiseless subs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5210","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":""},"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":"2026-05-18T03:23:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ds2I69JCUN4DRHft7RDO3xViOT/Vkmvb5d20pWpiItInVdN6i0j042JLqgHUtKEpbGJpsRcO7Z2hqM8DmyokAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:30:40.093776Z"},"content_sha256":"37afd1de08a20cf5bcd0f15fc48c080c402fe2eab859c753c3377afe75cd279b","schema_version":"1.0","event_id":"sha256:37afd1de08a20cf5bcd0f15fc48c080c402fe2eab859c753c3377afe75cd279b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q2AV6TTRIA7MKETCFWXFYP4YOB/bundle.json","state_url":"https://pith.science/pith/Q2AV6TTRIA7MKETCFWXFYP4YOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q2AV6TTRIA7MKETCFWXFYP4YOB/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":"2026-05-28T07:30:40Z","links":{"resolver":"https://pith.science/pith/Q2AV6TTRIA7MKETCFWXFYP4YOB","bundle":"https://pith.science/pith/Q2AV6TTRIA7MKETCFWXFYP4YOB/bundle.json","state":"https://pith.science/pith/Q2AV6TTRIA7MKETCFWXFYP4YOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q2AV6TTRIA7MKETCFWXFYP4YOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Q2AV6TTRIA7MKETCFWXFYP4YOB","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":"d8423529d468d2b15f6c4ce4d159706d6e014b35ce127e501de435d48396483b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-06-26T11:29:54Z","title_canon_sha256":"a91acd6ba7dc52fee64f563f10f454f4583700366b832d8dafcda7e6f19531e2"},"schema_version":"1.0","source":{"id":"1106.5210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5210","created_at":"2026-05-18T03:23:47Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5210v1","created_at":"2026-05-18T03:23:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5210","created_at":"2026-05-18T03:23:47Z"},{"alias_kind":"pith_short_12","alias_value":"Q2AV6TTRIA7M","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q2AV6TTRIA7MKETC","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q2AV6TTR","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:37afd1de08a20cf5bcd0f15fc48c080c402fe2eab859c753c3377afe75cd279b","target":"graph","created_at":"2026-05-18T03:23:47Z","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"},"paper":{"abstract_excerpt":"When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free subspace are known to correct such collective errors. We construct simple quantum circuits, which implement these collective error correction codes, for a small number $n$ of physical qubits. A single logical qubit is encoded with $n=3$ and $n=4$, while two logical qubits are encoded with $n=5$. The recursive relations among the subspaces employed in noiseless subs","authors_text":"Chi-Kwong Li, Hiroyuki Tomita, Mikio Nakahara, Nung-sing Sze, Yiu-Tung Poon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-06-26T11:29:54Z","title":"Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5210","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":"sha256:925433ef7abbb3c391b78eb4ca85294966840a2894afdd377daae0483bb55344","target":"record","created_at":"2026-05-18T03:23:47Z","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":"d8423529d468d2b15f6c4ce4d159706d6e014b35ce127e501de435d48396483b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-06-26T11:29:54Z","title_canon_sha256":"a91acd6ba7dc52fee64f563f10f454f4583700366b832d8dafcda7e6f19531e2"},"schema_version":"1.0","source":{"id":"1106.5210","kind":"arxiv","version":1}},"canonical_sha256":"86815f4e71403ec512622dae5c3f987050eb08647fc9634b356e05ed1a4e67fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86815f4e71403ec512622dae5c3f987050eb08647fc9634b356e05ed1a4e67fe","first_computed_at":"2026-05-18T03:23:47.007901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:23:47.007901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"exaWSsmJb+OR4Y5ht34Tk2qRqTZnMKRIdMCRm8aXWEp4KthaekP8wepNBXAZ8ZqQXMNQxLNGz9d7GEgChJbTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:23:47.008495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:925433ef7abbb3c391b78eb4ca85294966840a2894afdd377daae0483bb55344","sha256:37afd1de08a20cf5bcd0f15fc48c080c402fe2eab859c753c3377afe75cd279b"],"state_sha256":"4a2bd8ea9ea6853d4266fa13ae4fa095f38f07ba2225079a975320214b1081c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7DeU3CmqB8sqvayHQb+K8yqxmAUhSaiheoiEAhY1dMmobx+QKVmMNLefYw4BEceksI7WonRk8Uto3wxWrzffBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:30:40.097835Z","bundle_sha256":"d99c0fc61bf07be6670d72a90ed226abde1350f3da7b9c3caa9e205afe51612e"}}