{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RTUVMHWXPTJVEQCUAAUON4ZYE4","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":"0b7bc666672cc1af59809ea0e11c30d28228a39da24fe3812b4b27f7a5f40724","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-05-31T07:04:12Z","title_canon_sha256":"b9c168803f59da618ed440b6b7c96f8ffbcaa7075e5f1fa041a715505d6c6dbf"},"schema_version":"1.0","source":{"id":"1805.12345","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.12345","created_at":"2026-05-18T00:04:23Z"},{"alias_kind":"arxiv_version","alias_value":"1805.12345v2","created_at":"2026-05-18T00:04:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.12345","created_at":"2026-05-18T00:04:23Z"},{"alias_kind":"pith_short_12","alias_value":"RTUVMHWXPTJV","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RTUVMHWXPTJVEQCU","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RTUVMHWX","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:cae2ef18050d32bc8972aeeaede3e4531d99ce6f5ac81c807529a8b8f273f489","target":"graph","created_at":"2026-05-18T00:04:23Z","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":"Locally repairable codes with locality $r$ ($r$-LRCs for short) were introduced by Gopalan et al. \\cite{1} to recover a failed node of the code from at most other $r$ available nodes. And then $(r,\\delta)$ locally repairable codes ($(r,\\delta)$-LRCs for short) were produced by Prakash et al. \\cite{2} for tolerating multiple failed nodes. An $r$-LRC can be viewed as an $(r,2)$-LRC. An $(r,\\delta)$-LRC is called optimal if it achieves the Singleton-type bound. It has been a great challenge to construct $q$-ary optimal $(r,\\delta)$-LRCs with length much larger than $q$. Surprisingly, Luo et al. \\","authors_text":"Fang-Wei Fu, Weijun Fang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-05-31T07:04:12Z","title":"Optimal cyclic $(r,\\delta)$ locally repairable codes with unbounded length"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12345","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":"sha256:701bd401861facdba53dc0698e8492b5dec6a8f8abe3675ae906936898a09199","target":"record","created_at":"2026-05-18T00:04:23Z","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":"0b7bc666672cc1af59809ea0e11c30d28228a39da24fe3812b4b27f7a5f40724","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-05-31T07:04:12Z","title_canon_sha256":"b9c168803f59da618ed440b6b7c96f8ffbcaa7075e5f1fa041a715505d6c6dbf"},"schema_version":"1.0","source":{"id":"1805.12345","kind":"arxiv","version":2}},"canonical_sha256":"8ce9561ed77cd35240540028e6f33827020ce7cb5309cf32197012f33d453e7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ce9561ed77cd35240540028e6f33827020ce7cb5309cf32197012f33d453e7f","first_computed_at":"2026-05-18T00:04:23.041112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:23.041112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0QS1NZMiAqzo1tCV8sisXvqv1K7I3eMCnAvmIuy2QdAAL0wVx9VjvszBWzFLLoI9oZAzgu4a+XywiF7ePcoVCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:23.041824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.12345","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:701bd401861facdba53dc0698e8492b5dec6a8f8abe3675ae906936898a09199","sha256:cae2ef18050d32bc8972aeeaede3e4531d99ce6f5ac81c807529a8b8f273f489"],"state_sha256":"c7597ca47cdccd1e400af5a9dc47f8e723671978721597e960bafee224ee5941"}