{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SN5SQFEG7C24IAHDJUKN4ZRVF3","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":"d0f2eeb0716ad186be37c5030e5c70d29e304f62764c20b35a1f834510bc5db5","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-09-13T02:15:34Z","title_canon_sha256":"a0edd3ea88019114db7b8217b1b61e90867bf02b24b12339944d9a705641d7a6"},"schema_version":"1.0","source":{"id":"1409.3900","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3900","created_at":"2026-05-18T01:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3900v2","created_at":"2026-05-18T01:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3900","created_at":"2026-05-18T01:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"SN5SQFEG7C24","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SN5SQFEG7C24IAHD","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SN5SQFEG","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:8f7afd906c5b47556938f965716e0d8ffe8cffd15017b3c13de74031b1a26a76","target":"graph","created_at":"2026-05-18T01:21:49Z","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":"Erasure-correcting codes, that support local repair of codeword symbols, have attracted substantial attention recently for their application in distributed storage systems. This paper investigates a generalization of the usual locally repairable codes. In particular, this paper studies a class of codes with the following property: any small set of codeword symbols can be reconstructed (repaired) from a small number of other symbols. This is referred to as cooperative local repair. The main contribution of this paper is bounds on the trade-off of the minimum distance and the dimension of such c","authors_text":"Ankit Singh Rawat, Arya Mazumdar, Sriram Vishwanath","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-09-13T02:15:34Z","title":"Cooperative Local Repair in Distributed Storage"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3900","kind":"arxiv","version":2},"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":"sha256:752a3e1437ed4c12cd9cf86596cda05f183007907430e9be43e1c5f88d4621ee","target":"record","created_at":"2026-05-18T01:21:49Z","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":"d0f2eeb0716ad186be37c5030e5c70d29e304f62764c20b35a1f834510bc5db5","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-09-13T02:15:34Z","title_canon_sha256":"a0edd3ea88019114db7b8217b1b61e90867bf02b24b12339944d9a705641d7a6"},"schema_version":"1.0","source":{"id":"1409.3900","kind":"arxiv","version":2}},"canonical_sha256":"937b281486f8b5c400e34d14de66352eed9d026172697e8784c293f7b601f070","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"937b281486f8b5c400e34d14de66352eed9d026172697e8784c293f7b601f070","first_computed_at":"2026-05-18T01:21:49.360369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:49.360369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qEfP3vBgJt1OPzybnB1uKZj+8ckdRGtbkpGD/jqybvWtIInsedN5Pyiev5zus/4bAAcJvo+LlAeBVUS8pN1RDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:49.360900Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3900","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:752a3e1437ed4c12cd9cf86596cda05f183007907430e9be43e1c5f88d4621ee","sha256:8f7afd906c5b47556938f965716e0d8ffe8cffd15017b3c13de74031b1a26a76"],"state_sha256":"a1290d782345a2c53fe75e6dcbacee123ea8b385d7c13a5690f3dd41ffe02ef0"}