{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZEE6EC3IA6QMKJEQ6BA45R5XLM","short_pith_number":"pith:ZEE6EC3I","canonical_record":{"source":{"id":"1107.1627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-07-08T13:21:28Z","cross_cats_sorted":["cs.DC","math.IT"],"title_canon_sha256":"00ee115be1ae2ddeb2d26c03e5590a10b770a8a5bca93db845639680267e1212","abstract_canon_sha256":"ddec3586d04c1445d4056ca71b8fe94b3a8970259922ca75603c971a715b96fb"},"schema_version":"1.0"},"canonical_sha256":"c909e20b6807a0c52490f041cec7b75b2b0f6f601c2bffa25ecbfed9d8ad401f","source":{"kind":"arxiv","id":"1107.1627","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1627","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1627v1","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1627","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"pith_short_12","alias_value":"ZEE6EC3IA6QM","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZEE6EC3IA6QMKJEQ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZEE6EC3I","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZEE6EC3IA6QMKJEQ6BA45R5XLM","target":"record","payload":{"canonical_record":{"source":{"id":"1107.1627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-07-08T13:21:28Z","cross_cats_sorted":["cs.DC","math.IT"],"title_canon_sha256":"00ee115be1ae2ddeb2d26c03e5590a10b770a8a5bca93db845639680267e1212","abstract_canon_sha256":"ddec3586d04c1445d4056ca71b8fe94b3a8970259922ca75603c971a715b96fb"},"schema_version":"1.0"},"canonical_sha256":"c909e20b6807a0c52490f041cec7b75b2b0f6f601c2bffa25ecbfed9d8ad401f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:35.323356Z","signature_b64":"4u7twdl0pQP1TWo93ijQRF06txMlbkOhYBJ4w/HUIBdJwugpCBupQZpP0/o+LVsB3mqODqHBz16FedU/nWSfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c909e20b6807a0c52490f041cec7b75b2b0f6f601c2bffa25ecbfed9d8ad401f","last_reissued_at":"2026-05-18T04:18:35.322922Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:35.322922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.1627","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":"2026-05-18T04:18:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6DQF+qFtmW/cSnnNg/PKtfmdVLIRHUEGSlRAY2Nw4DuT0vwXHuK/YR+5BFPIjPQyYPCM81+sruHOWTxuTYt+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:48:21.411773Z"},"content_sha256":"0cedb84007c181d441c8b6ecf83ba4ec8ddafe640d3ce5ad1b14f1cce5201e28","schema_version":"1.0","event_id":"sha256:0cedb84007c181d441c8b6ecf83ba4ec8ddafe640d3ce5ad1b14f1cce5201e28"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZEE6EC3IA6QMKJEQ6BA45R5XLM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Codes for Optimal Rebuilding Access","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","math.IT"],"primary_cat":"cs.IT","authors_text":"Itzhak Tamo, Jehoshua Bruck, Zhiying Wang","submitted_at":"2011-07-08T13:21:28Z","abstract_excerpt":"MDS (maximum distance separable) array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with r redundancy nodes can correct any r erasures by accessing (reading) all the remaining information in both the systematic nodes and the parity (redundancy) nodes. However, in practice, a single erasure is the most likely failure event; hence, a natural question is how much information do we need to access in order to rebuild a single storage node? We define the rebuilding ratio as the fraction of remaining information accessed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1627","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":"2026-05-18T04:18:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6EyPJk2kZj8EQ3aCucrDP3AD75friri88TXX33HbmHUTCswsBqNENpLhDrsxQYd3V1nV1nAph9hLSC/bkk12Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:48:21.412119Z"},"content_sha256":"eec544edd3812ea0b5c6537dac220640db934b9481eb42626a2777a4938252bc","schema_version":"1.0","event_id":"sha256:eec544edd3812ea0b5c6537dac220640db934b9481eb42626a2777a4938252bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZEE6EC3IA6QMKJEQ6BA45R5XLM/bundle.json","state_url":"https://pith.science/pith/ZEE6EC3IA6QMKJEQ6BA45R5XLM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZEE6EC3IA6QMKJEQ6BA45R5XLM/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":"2026-06-22T11:48:21Z","links":{"resolver":"https://pith.science/pith/ZEE6EC3IA6QMKJEQ6BA45R5XLM","bundle":"https://pith.science/pith/ZEE6EC3IA6QMKJEQ6BA45R5XLM/bundle.json","state":"https://pith.science/pith/ZEE6EC3IA6QMKJEQ6BA45R5XLM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZEE6EC3IA6QMKJEQ6BA45R5XLM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZEE6EC3IA6QMKJEQ6BA45R5XLM","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":"ddec3586d04c1445d4056ca71b8fe94b3a8970259922ca75603c971a715b96fb","cross_cats_sorted":["cs.DC","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-07-08T13:21:28Z","title_canon_sha256":"00ee115be1ae2ddeb2d26c03e5590a10b770a8a5bca93db845639680267e1212"},"schema_version":"1.0","source":{"id":"1107.1627","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1627","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1627v1","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1627","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"pith_short_12","alias_value":"ZEE6EC3IA6QM","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZEE6EC3IA6QMKJEQ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZEE6EC3I","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:eec544edd3812ea0b5c6537dac220640db934b9481eb42626a2777a4938252bc","target":"graph","created_at":"2026-05-18T04:18:35Z","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":"MDS (maximum distance separable) array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with r redundancy nodes can correct any r erasures by accessing (reading) all the remaining information in both the systematic nodes and the parity (redundancy) nodes. However, in practice, a single erasure is the most likely failure event; hence, a natural question is how much information do we need to access in order to rebuild a single storage node? We define the rebuilding ratio as the fraction of remaining information accessed","authors_text":"Itzhak Tamo, Jehoshua Bruck, Zhiying Wang","cross_cats":["cs.DC","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-07-08T13:21:28Z","title":"On Codes for Optimal Rebuilding Access"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1627","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":"sha256:0cedb84007c181d441c8b6ecf83ba4ec8ddafe640d3ce5ad1b14f1cce5201e28","target":"record","created_at":"2026-05-18T04:18:35Z","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":"ddec3586d04c1445d4056ca71b8fe94b3a8970259922ca75603c971a715b96fb","cross_cats_sorted":["cs.DC","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-07-08T13:21:28Z","title_canon_sha256":"00ee115be1ae2ddeb2d26c03e5590a10b770a8a5bca93db845639680267e1212"},"schema_version":"1.0","source":{"id":"1107.1627","kind":"arxiv","version":1}},"canonical_sha256":"c909e20b6807a0c52490f041cec7b75b2b0f6f601c2bffa25ecbfed9d8ad401f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c909e20b6807a0c52490f041cec7b75b2b0f6f601c2bffa25ecbfed9d8ad401f","first_computed_at":"2026-05-18T04:18:35.322922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:35.322922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4u7twdl0pQP1TWo93ijQRF06txMlbkOhYBJ4w/HUIBdJwugpCBupQZpP0/o+LVsB3mqODqHBz16FedU/nWSfCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:35.323356Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1627","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cedb84007c181d441c8b6ecf83ba4ec8ddafe640d3ce5ad1b14f1cce5201e28","sha256:eec544edd3812ea0b5c6537dac220640db934b9481eb42626a2777a4938252bc"],"state_sha256":"3f25bedb9317750fa0c2a44fa72de656005d2192f63df31bd9b647d8f09e316e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2fJz1pSZReofasQbSUD/xQdWXr6ScRh7aXuTpSZXB2UioNEQpSY6Ey3ul3t4gdOhpcQOTssM5GbnMLENOSwgDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:48:21.414201Z","bundle_sha256":"0eaf81512e656f90fa595b7024c5955c0b7feb9a5fa371d8306968bc76a7f0cc"}}