{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:LQZPWP726WSOE33LD23GQAWPNY","short_pith_number":"pith:LQZPWP72","canonical_record":{"source":{"id":"quant-ph/9908066","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1999-08-19T22:43:44Z","cross_cats_sorted":[],"title_canon_sha256":"64120cb761eb3c4b6406ed0e1c87b4f7adb69aef0eb89002d408103bbdae4904","abstract_canon_sha256":"3a238777b18ce5fdb5861b691e2c534bb2102e74a037046dd73c13e30ef31f63"},"schema_version":"1.0"},"canonical_sha256":"5c32fb3ffaf5a4e26f6b1eb66802cf6e2a77a017610c14a33529fb88badff964","source":{"kind":"arxiv","id":"quant-ph/9908066","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9908066","created_at":"2026-07-04T14:47:27Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9908066v1","created_at":"2026-07-04T14:47:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9908066","created_at":"2026-07-04T14:47:27Z"},{"alias_kind":"pith_short_12","alias_value":"LQZPWP726WSO","created_at":"2026-07-04T14:47:27Z"},{"alias_kind":"pith_short_16","alias_value":"LQZPWP726WSOE33L","created_at":"2026-07-04T14:47:27Z"},{"alias_kind":"pith_short_8","alias_value":"LQZPWP72","created_at":"2026-07-04T14:47:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:LQZPWP726WSOE33LD23GQAWPNY","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/9908066","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1999-08-19T22:43:44Z","cross_cats_sorted":[],"title_canon_sha256":"64120cb761eb3c4b6406ed0e1c87b4f7adb69aef0eb89002d408103bbdae4904","abstract_canon_sha256":"3a238777b18ce5fdb5861b691e2c534bb2102e74a037046dd73c13e30ef31f63"},"schema_version":"1.0"},"canonical_sha256":"5c32fb3ffaf5a4e26f6b1eb66802cf6e2a77a017610c14a33529fb88badff964","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:47:27.887427Z","signature_b64":"fzKPgGvZkyX6ESFUHoadth4TtfpKXdRvsElwdf3rFxafeFqjgj/q3KpBYVYAaGCm2IoofZKLQ3wBxvFarG7aAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c32fb3ffaf5a4e26f6b1eb66802cf6e2a77a017610c14a33529fb88badff964","last_reissued_at":"2026-07-04T14:47:27.887044Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:47:27.887044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/9908066","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":"2026-07-04T14:47:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S619NAl6qWeUyydkXMK9fQpqz6zLfzFDp2flBQQ2ylbmkdVO2rIkCXSINusLtkk4xF3kel9EEINQgiyGGKxLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T23:11:43.405558Z"},"content_sha256":"332bb432b28d51f940eaa7f4135923044f436b76adff7f13b3d77ba05cc7dd5f","schema_version":"1.0","event_id":"sha256:332bb432b28d51f940eaa7f4135923044f436b76adff7f13b3d77ba05cc7dd5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:LQZPWP726WSOE33LD23GQAWPNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theory of Quantum Error Correction for General Noise","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Emanuel Knill, Lorenza Viola, Raymond Laflamme","submitted_at":"1999-08-19T22:43:44Z","abstract_excerpt":"Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of errors'' e makes sense for any system in the presence of arbitrary environmental interactions. In fact, the notion is directly related to the lowest order in time with which uncorrectable errors are introduced, and this in turn is derived from a grading of the algebra generated by the interaction operators. As a result, e-error-correcting codes are effective "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9908066","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/quant-ph/9908066/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":"2026-07-04T14:47:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g78+YskyJy5sGnpE/oKAaDCBwSwj/GN8JLU3kNS0jNZ5RAqQ+9mQHUeFE6Fgsyvlg22NU7tDbBvfQz7RnUvzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T23:11:43.406384Z"},"content_sha256":"cdba083f71d2aa39adf3105f3e9f780ecb446fb1f32e547a555df6e88ba6035f","schema_version":"1.0","event_id":"sha256:cdba083f71d2aa39adf3105f3e9f780ecb446fb1f32e547a555df6e88ba6035f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LQZPWP726WSOE33LD23GQAWPNY/bundle.json","state_url":"https://pith.science/pith/LQZPWP726WSOE33LD23GQAWPNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LQZPWP726WSOE33LD23GQAWPNY/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":"2026-08-13T23:11:43Z","links":{"resolver":"https://pith.science/pith/LQZPWP726WSOE33LD23GQAWPNY","bundle":"https://pith.science/pith/LQZPWP726WSOE33LD23GQAWPNY/bundle.json","state":"https://pith.science/pith/LQZPWP726WSOE33LD23GQAWPNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LQZPWP726WSOE33LD23GQAWPNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:LQZPWP726WSOE33LD23GQAWPNY","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":"3a238777b18ce5fdb5861b691e2c534bb2102e74a037046dd73c13e30ef31f63","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1999-08-19T22:43:44Z","title_canon_sha256":"64120cb761eb3c4b6406ed0e1c87b4f7adb69aef0eb89002d408103bbdae4904"},"schema_version":"1.0","source":{"id":"quant-ph/9908066","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9908066","created_at":"2026-07-04T14:47:27Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9908066v1","created_at":"2026-07-04T14:47:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9908066","created_at":"2026-07-04T14:47:27Z"},{"alias_kind":"pith_short_12","alias_value":"LQZPWP726WSO","created_at":"2026-07-04T14:47:27Z"},{"alias_kind":"pith_short_16","alias_value":"LQZPWP726WSOE33L","created_at":"2026-07-04T14:47:27Z"},{"alias_kind":"pith_short_8","alias_value":"LQZPWP72","created_at":"2026-07-04T14:47:27Z"}],"graph_snapshots":[{"event_id":"sha256:cdba083f71d2aa39adf3105f3e9f780ecb446fb1f32e547a555df6e88ba6035f","target":"graph","created_at":"2026-07-04T14:47:27Z","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/quant-ph/9908066/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of errors'' e makes sense for any system in the presence of arbitrary environmental interactions. In fact, the notion is directly related to the lowest order in time with which uncorrectable errors are introduced, and this in turn is derived from a grading of the algebra generated by the interaction operators. As a result, e-error-correcting codes are effective ","authors_text":"Emanuel Knill, Lorenza Viola, Raymond Laflamme","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"1999-08-19T22:43:44Z","title":"Theory of Quantum Error Correction for General Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9908066","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":"sha256:332bb432b28d51f940eaa7f4135923044f436b76adff7f13b3d77ba05cc7dd5f","target":"record","created_at":"2026-07-04T14:47:27Z","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":"3a238777b18ce5fdb5861b691e2c534bb2102e74a037046dd73c13e30ef31f63","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1999-08-19T22:43:44Z","title_canon_sha256":"64120cb761eb3c4b6406ed0e1c87b4f7adb69aef0eb89002d408103bbdae4904"},"schema_version":"1.0","source":{"id":"quant-ph/9908066","kind":"arxiv","version":1}},"canonical_sha256":"5c32fb3ffaf5a4e26f6b1eb66802cf6e2a77a017610c14a33529fb88badff964","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c32fb3ffaf5a4e26f6b1eb66802cf6e2a77a017610c14a33529fb88badff964","first_computed_at":"2026-07-04T14:47:27.887044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:47:27.887044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fzKPgGvZkyX6ESFUHoadth4TtfpKXdRvsElwdf3rFxafeFqjgj/q3KpBYVYAaGCm2IoofZKLQ3wBxvFarG7aAg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:47:27.887427Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9908066","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:332bb432b28d51f940eaa7f4135923044f436b76adff7f13b3d77ba05cc7dd5f","sha256:cdba083f71d2aa39adf3105f3e9f780ecb446fb1f32e547a555df6e88ba6035f"],"state_sha256":"4075b3c9cb319fdde989c213a8ec3933865e833ecdeee8c396c3576102edbcae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Dfwkn/LgoA2BuN1Jt9daDcgMYCNif/mfnuanR+MBaloJAnW0QqUlZ/qYY3frc37eCzjdGEnCkDn/BPvzWrkCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T23:11:43.413558Z","bundle_sha256":"0acfa06181f7bc56dd79fc2cfd2ae2051599bb4fbe9d2ca2007798c57e4eda74"}}