{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IEHFGCU42H53EOGWFJQJFPODPH","short_pith_number":"pith:IEHFGCU4","canonical_record":{"source":{"id":"1303.3668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-15T03:45:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9c4b5bb6fc4f6f683c8e1cbf9583970721aeeb2d1cdb6039a8ad5734f82dc601","abstract_canon_sha256":"838449356f77ce7216572b655a7f71cf79c15cf530e1c94bc8e03a388d55e258"},"schema_version":"1.0"},"canonical_sha256":"410e530a9cd1fbb238d62a6092bdc379e859e1e1c53adc9b16fe9ba3acda9fb6","source":{"kind":"arxiv","id":"1303.3668","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3668","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3668v1","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3668","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"IEHFGCU42H53","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IEHFGCU42H53EOGW","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IEHFGCU4","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IEHFGCU42H53EOGWFJQJFPODPH","target":"record","payload":{"canonical_record":{"source":{"id":"1303.3668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-15T03:45:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9c4b5bb6fc4f6f683c8e1cbf9583970721aeeb2d1cdb6039a8ad5734f82dc601","abstract_canon_sha256":"838449356f77ce7216572b655a7f71cf79c15cf530e1c94bc8e03a388d55e258"},"schema_version":"1.0"},"canonical_sha256":"410e530a9cd1fbb238d62a6092bdc379e859e1e1c53adc9b16fe9ba3acda9fb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:42.557653Z","signature_b64":"Qldhk91sTLbzit051+IRLWvRU3fMcLR7ahIzdSUcW1So22V9w/yAx6UlkBI/h/JvreNqXfRHb3hD5IZB8oYTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"410e530a9cd1fbb238d62a6092bdc379e859e1e1c53adc9b16fe9ba3acda9fb6","last_reissued_at":"2026-05-18T00:58:42.557112Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:42.557112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.3668","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":"2026-05-18T00:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iqcz8DvlHOOZh0bvve/RtE6elzxuV3sgYL8kA7hip/AbMGIxRVHA/jL3rNN4VQx0yQaGioeE8qZdGyIzdWU8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:37:26.545290Z"},"content_sha256":"f7682b3ef50ce19451c073ed2af02479298fc536692ebf4fe4a6dc386064ed6b","schema_version":"1.0","event_id":"sha256:f7682b3ef50ce19451c073ed2af02479298fc536692ebf4fe4a6dc386064ed6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IEHFGCU42H53EOGWFJQJFPODPH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Access vs. Bandwidth in Codes for Storage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Itzhak Tamo, Jehoshua Bruck, Zhiying Wang","submitted_at":"2013-03-15T03:45:07Z","abstract_excerpt":"Maximum distance separable (MDS) codes are widely used in storage systems to protect against disk (node) failures. A node is said to have capacity $l$ over some field $\\mathbb{F}$, if it can store that amount of symbols of the field. An $(n,k,l)$ MDS code uses $n$ nodes of capacity $l$ to store $k$ information nodes. The MDS property guarantees the resiliency to any $n-k$ node failures. An \\emph{optimal bandwidth} (resp. \\emph{optimal access}) MDS code communicates (resp. accesses) the minimum amount of data during the repair process of a single failed node. It was shown that this amount equal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3668","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":"2026-05-18T00:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aVJVN49WpTOKsd4CnE6P1WkVoFFwE2GpQ3g7lbx9E5lTPcLkdQtNU1Tb69xS1l+0RglkB6Z7IdNoNGKHjH/wBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:37:26.545654Z"},"content_sha256":"bd9231c54245830cda1778efb3aa6477148f42fbc5d64c525fcf72f1b84e9e90","schema_version":"1.0","event_id":"sha256:bd9231c54245830cda1778efb3aa6477148f42fbc5d64c525fcf72f1b84e9e90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IEHFGCU42H53EOGWFJQJFPODPH/bundle.json","state_url":"https://pith.science/pith/IEHFGCU42H53EOGWFJQJFPODPH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IEHFGCU42H53EOGWFJQJFPODPH/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":"2026-06-22T10:37:26Z","links":{"resolver":"https://pith.science/pith/IEHFGCU42H53EOGWFJQJFPODPH","bundle":"https://pith.science/pith/IEHFGCU42H53EOGWFJQJFPODPH/bundle.json","state":"https://pith.science/pith/IEHFGCU42H53EOGWFJQJFPODPH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IEHFGCU42H53EOGWFJQJFPODPH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IEHFGCU42H53EOGWFJQJFPODPH","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":"838449356f77ce7216572b655a7f71cf79c15cf530e1c94bc8e03a388d55e258","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-15T03:45:07Z","title_canon_sha256":"9c4b5bb6fc4f6f683c8e1cbf9583970721aeeb2d1cdb6039a8ad5734f82dc601"},"schema_version":"1.0","source":{"id":"1303.3668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3668","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3668v1","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3668","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"IEHFGCU42H53","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IEHFGCU42H53EOGW","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IEHFGCU4","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:bd9231c54245830cda1778efb3aa6477148f42fbc5d64c525fcf72f1b84e9e90","target":"graph","created_at":"2026-05-18T00:58:42Z","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":"Maximum distance separable (MDS) codes are widely used in storage systems to protect against disk (node) failures. A node is said to have capacity $l$ over some field $\\mathbb{F}$, if it can store that amount of symbols of the field. An $(n,k,l)$ MDS code uses $n$ nodes of capacity $l$ to store $k$ information nodes. The MDS property guarantees the resiliency to any $n-k$ node failures. An \\emph{optimal bandwidth} (resp. \\emph{optimal access}) MDS code communicates (resp. accesses) the minimum amount of data during the repair process of a single failed node. It was shown that this amount equal","authors_text":"Itzhak Tamo, Jehoshua Bruck, Zhiying Wang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-15T03:45:07Z","title":"Access vs. Bandwidth in Codes for Storage"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3668","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:f7682b3ef50ce19451c073ed2af02479298fc536692ebf4fe4a6dc386064ed6b","target":"record","created_at":"2026-05-18T00:58:42Z","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":"838449356f77ce7216572b655a7f71cf79c15cf530e1c94bc8e03a388d55e258","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-15T03:45:07Z","title_canon_sha256":"9c4b5bb6fc4f6f683c8e1cbf9583970721aeeb2d1cdb6039a8ad5734f82dc601"},"schema_version":"1.0","source":{"id":"1303.3668","kind":"arxiv","version":1}},"canonical_sha256":"410e530a9cd1fbb238d62a6092bdc379e859e1e1c53adc9b16fe9ba3acda9fb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"410e530a9cd1fbb238d62a6092bdc379e859e1e1c53adc9b16fe9ba3acda9fb6","first_computed_at":"2026-05-18T00:58:42.557112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:42.557112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qldhk91sTLbzit051+IRLWvRU3fMcLR7ahIzdSUcW1So22V9w/yAx6UlkBI/h/JvreNqXfRHb3hD5IZB8oYTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:42.557653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7682b3ef50ce19451c073ed2af02479298fc536692ebf4fe4a6dc386064ed6b","sha256:bd9231c54245830cda1778efb3aa6477148f42fbc5d64c525fcf72f1b84e9e90"],"state_sha256":"7d3d406603798c24963dbbdf8302e96138b62c84b0aff0f731130f0690189959"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N696yU26JnfKfLnyAN657iSF49E9ewrEIr6fHDAJLIlppUMMIUh4cv45GBZ/a84bFHVm7rxJIOBncahAv2j2DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:37:26.547638Z","bundle_sha256":"89bd88765a9e3dfecd5c89c48e7bb2493d49c04a6e16b7c5fd221d856da18d79"}}