{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FUCCULBJYY3QUBQNSQIZZ7MSC2","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":"a6e66642cbbd43999299fc1eec429080a76cb7143d59aca72f2721e113d342fc","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-18T00:46:39Z","title_canon_sha256":"901d5a69ab050edbafca1eb49dcf2b09c47a3a5cf5d27bfbbf30f8575a58f23b"},"schema_version":"1.0","source":{"id":"1708.05474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05474","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05474v1","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05474","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"pith_short_12","alias_value":"FUCCULBJYY3Q","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FUCCULBJYY3QUBQN","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FUCCULBJ","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:54a0d76849d7bb1ccba9448ee75d9a1d1589137022aaf3cbf531994aeef6f16e","target":"graph","created_at":"2026-05-18T00:37:49Z","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":"We study the trade-off between storage overhead and inter-cluster repair bandwidth in clustered storage systems, while recovering from multiple node failures within a cluster. A cluster is a collection of $m$ nodes, and there are $n$ clusters. For data collection, we download the entire content from any $k$ clusters. For repair of $t \\geq 2$ nodes within a cluster, we take help from $\\ell$ local nodes, as well as $d$ helper clusters. We characterize the optimal trade-off under functional repair, and also under exact repair for the minimum storage and minimum inter-cluster bandwidth (MBR) opera","authors_text":"Muriel M\\'edard, N. Prakash, Vitaly Abdrashitov","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-18T00:46:39Z","title":"The Storage vs Repair Bandwidth Trade-off for Multiple Failures in Clustered Storage Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05474","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":"sha256:59e932201ab96fa8ff9f3f499d20a6d595843d0c1dde91894adda4010fb852a2","target":"record","created_at":"2026-05-18T00:37:49Z","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":"a6e66642cbbd43999299fc1eec429080a76cb7143d59aca72f2721e113d342fc","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-18T00:46:39Z","title_canon_sha256":"901d5a69ab050edbafca1eb49dcf2b09c47a3a5cf5d27bfbbf30f8575a58f23b"},"schema_version":"1.0","source":{"id":"1708.05474","kind":"arxiv","version":1}},"canonical_sha256":"2d042a2c29c6370a060d94119cfd9216a6f1c4e1263d5fce8ad7a3b96439d780","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d042a2c29c6370a060d94119cfd9216a6f1c4e1263d5fce8ad7a3b96439d780","first_computed_at":"2026-05-18T00:37:49.963732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:49.963732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2CytsaIgsCs3+4z9upkAIbrwlu/usheTVINpprl9xqRz0pBktFvWcNOfn7Vbz4NKm9QJJsQr9gD1nm23PsFIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:49.964396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.05474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59e932201ab96fa8ff9f3f499d20a6d595843d0c1dde91894adda4010fb852a2","sha256:54a0d76849d7bb1ccba9448ee75d9a1d1589137022aaf3cbf531994aeef6f16e"],"state_sha256":"ffa8d87cf7b222a5f89d4c1b94a052cd2a6b4e8d4284cf610d7ca22a4df24e6b"}