{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LUA6G3X6S4SGMBKZ7COXX3TKPC","short_pith_number":"pith:LUA6G3X6","canonical_record":{"source":{"id":"1509.07796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-09-25T17:27:23Z","cross_cats_sorted":[],"title_canon_sha256":"73fa18a5a2abc3bb50c3d1ee08961d568101e7ded78be961758c6f16d46a1929","abstract_canon_sha256":"29b840ea38145255b835b8836b7f7935582c832f75baf77956239e17acf88ba4"},"schema_version":"1.0"},"canonical_sha256":"5d01e36efe9724660559f89d7bee6a78812680412dc17593960c7b27b82e57f9","source":{"kind":"arxiv","id":"1509.07796","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07796","created_at":"2026-05-18T01:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07796v1","created_at":"2026-05-18T01:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07796","created_at":"2026-05-18T01:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"LUA6G3X6S4SG","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LUA6G3X6S4SGMBKZ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LUA6G3X6","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LUA6G3X6S4SGMBKZ7COXX3TKPC","target":"record","payload":{"canonical_record":{"source":{"id":"1509.07796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-09-25T17:27:23Z","cross_cats_sorted":[],"title_canon_sha256":"73fa18a5a2abc3bb50c3d1ee08961d568101e7ded78be961758c6f16d46a1929","abstract_canon_sha256":"29b840ea38145255b835b8836b7f7935582c832f75baf77956239e17acf88ba4"},"schema_version":"1.0"},"canonical_sha256":"5d01e36efe9724660559f89d7bee6a78812680412dc17593960c7b27b82e57f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:20.251768Z","signature_b64":"co59SuWsedZmxlcfls9Mt04pLE9fxEZksVtsgoUvicD0ZC+zMMuTZh/P8Lli4wDXN0yF5jVRBt5W0Fh+NxB3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d01e36efe9724660559f89d7bee6a78812680412dc17593960c7b27b82e57f9","last_reissued_at":"2026-05-18T01:03:20.251188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:20.251188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.07796","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":"2026-05-18T01:03:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9riXVJQpU4PmfisspLiQ5EwMkhpxGBq7Pg9aJkXKLxpNMkZbYRqD/a0w+uu9qXJyrLdwVr02OtBCvf/1aXpFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:21:28.416671Z"},"content_sha256":"293773ebd4be054fc552366fe414f97d2be00af4f50f4429f083be183a4adbb6","schema_version":"1.0","event_id":"sha256:293773ebd4be054fc552366fe414f97d2be00af4f50f4429f083be183a4adbb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LUA6G3X6S4SGMBKZ7COXX3TKPC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hierarchical surface code for network quantum computing with modules of arbitrary size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Simon C. Benjamin, Ying Li","submitted_at":"2015-09-25T17:27:23Z","abstract_excerpt":"The network paradigm for quantum computing involves interconnecting many modules to form a scalable machine. Typically it is assumed that the links between modules are prone to noise while operations within modules have significantly higher fidelity. To optimise fault tolerance in such architectures we introduce a hierarchical generalisation of the surface code: a small `patch' of the code exists within each module, and constitutes a single effective qubit of the logic-level surface code. Errors primarily occur in a two-dimensional subspace, i.e. patch perimeters extruded over time, and the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07796","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":"2026-05-18T01:03:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CcOZqc0c63F+jzmj517Q/5eqXqMVncKUwcSUo/ahmagvlZ3v5XnrdovcVEEBrRvK8tahN4tAXJGYShB2HVkpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:21:28.417015Z"},"content_sha256":"974860a4fc9d1fb4333541ed88fd29ba8171fda1e0acf5f53e9e316856674679","schema_version":"1.0","event_id":"sha256:974860a4fc9d1fb4333541ed88fd29ba8171fda1e0acf5f53e9e316856674679"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LUA6G3X6S4SGMBKZ7COXX3TKPC/bundle.json","state_url":"https://pith.science/pith/LUA6G3X6S4SGMBKZ7COXX3TKPC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LUA6G3X6S4SGMBKZ7COXX3TKPC/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":"2026-06-08T22:21:28Z","links":{"resolver":"https://pith.science/pith/LUA6G3X6S4SGMBKZ7COXX3TKPC","bundle":"https://pith.science/pith/LUA6G3X6S4SGMBKZ7COXX3TKPC/bundle.json","state":"https://pith.science/pith/LUA6G3X6S4SGMBKZ7COXX3TKPC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LUA6G3X6S4SGMBKZ7COXX3TKPC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LUA6G3X6S4SGMBKZ7COXX3TKPC","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":"29b840ea38145255b835b8836b7f7935582c832f75baf77956239e17acf88ba4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-09-25T17:27:23Z","title_canon_sha256":"73fa18a5a2abc3bb50c3d1ee08961d568101e7ded78be961758c6f16d46a1929"},"schema_version":"1.0","source":{"id":"1509.07796","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07796","created_at":"2026-05-18T01:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07796v1","created_at":"2026-05-18T01:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07796","created_at":"2026-05-18T01:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"LUA6G3X6S4SG","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LUA6G3X6S4SGMBKZ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LUA6G3X6","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:974860a4fc9d1fb4333541ed88fd29ba8171fda1e0acf5f53e9e316856674679","target":"graph","created_at":"2026-05-18T01:03:20Z","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":"The network paradigm for quantum computing involves interconnecting many modules to form a scalable machine. Typically it is assumed that the links between modules are prone to noise while operations within modules have significantly higher fidelity. To optimise fault tolerance in such architectures we introduce a hierarchical generalisation of the surface code: a small `patch' of the code exists within each module, and constitutes a single effective qubit of the logic-level surface code. Errors primarily occur in a two-dimensional subspace, i.e. patch perimeters extruded over time, and the re","authors_text":"Simon C. Benjamin, Ying Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-09-25T17:27:23Z","title":"Hierarchical surface code for network quantum computing with modules of arbitrary size"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07796","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":"sha256:293773ebd4be054fc552366fe414f97d2be00af4f50f4429f083be183a4adbb6","target":"record","created_at":"2026-05-18T01:03:20Z","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":"29b840ea38145255b835b8836b7f7935582c832f75baf77956239e17acf88ba4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-09-25T17:27:23Z","title_canon_sha256":"73fa18a5a2abc3bb50c3d1ee08961d568101e7ded78be961758c6f16d46a1929"},"schema_version":"1.0","source":{"id":"1509.07796","kind":"arxiv","version":1}},"canonical_sha256":"5d01e36efe9724660559f89d7bee6a78812680412dc17593960c7b27b82e57f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d01e36efe9724660559f89d7bee6a78812680412dc17593960c7b27b82e57f9","first_computed_at":"2026-05-18T01:03:20.251188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:20.251188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"co59SuWsedZmxlcfls9Mt04pLE9fxEZksVtsgoUvicD0ZC+zMMuTZh/P8Lli4wDXN0yF5jVRBt5W0Fh+NxB3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:20.251768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07796","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:293773ebd4be054fc552366fe414f97d2be00af4f50f4429f083be183a4adbb6","sha256:974860a4fc9d1fb4333541ed88fd29ba8171fda1e0acf5f53e9e316856674679"],"state_sha256":"3898d9363591c1e429b227208a24d360a38f4faea216ae2f5f8d10b8b8244803"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/SpExeFKR+f1RSU7WyEuiaRa00I8EIfKUyMfFXOTiQkjcKY4VVcUrOmXjz94+wM7PLZM3V9YhtYPMXcZC1lBCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:21:28.418873Z","bundle_sha256":"faf48d1f4bef2a44b142f3b1fc325e21d5d0f4904ddc57e8097d849783801705"}}