{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CDPF5GR2ZOTS3TBCXDW2COVFLU","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":"f84fc57b59202ba4221c20692a09734575d328c0ac25a58374987e6948be57b4","cross_cats_sorted":["cs.CC","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-03T10:13:09Z","title_canon_sha256":"bd3815440db62311a13f4024f331adc4d5bc30dd90d8c0ccb10d9165e24c467c"},"schema_version":"1.0","source":{"id":"1807.01064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01064","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01064v1","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01064","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"CDPF5GR2ZOTS","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CDPF5GR2ZOTS3TBC","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CDPF5GR2","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:27af5ae86a87236c0c66f1d539b4ca90401a618c1336dd69e454d661e6b9de2a","target":"graph","created_at":"2026-05-18T00:11:45Z","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":"A locally repairable code (LRC) with locality $r$ allows for the recovery of any erased codeword symbol using only $r$ other codeword symbols. A Singleton-type bound dictates the best possible trade-off between the dimension and distance of LRCs --- an LRC attaining this trade-off is deemed \\emph{optimal}. Such optimal LRCs have been constructed over alphabets growing linearly in the block length. Unlike the classical Singleton bound, however, it was not known if such a linear growth in the alphabet size is necessary, or for that matter even if the alphabet needs to grow at all with the block ","authors_text":"Chaoping Xing, Chen Yuan, Venkatesan Guruswami","cross_cats":["cs.CC","math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-03T10:13:09Z","title":"How long can optimal locally repairable codes be?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01064","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":"sha256:90d76fb83ba6a049cd71848a6325d5c00a30b6112ced28f1a0db1e79420a6176","target":"record","created_at":"2026-05-18T00:11:45Z","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":"f84fc57b59202ba4221c20692a09734575d328c0ac25a58374987e6948be57b4","cross_cats_sorted":["cs.CC","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-03T10:13:09Z","title_canon_sha256":"bd3815440db62311a13f4024f331adc4d5bc30dd90d8c0ccb10d9165e24c467c"},"schema_version":"1.0","source":{"id":"1807.01064","kind":"arxiv","version":1}},"canonical_sha256":"10de5e9a3acba72dcc22b8eda13aa55d218b34a96cbf7d3360b409249b8165ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10de5e9a3acba72dcc22b8eda13aa55d218b34a96cbf7d3360b409249b8165ab","first_computed_at":"2026-05-18T00:11:45.497552Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:45.497552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lbPP/Z5mroVNdFIfcj3SSX/Mf7lk0WjMYuGl0uu46QhNAtbE3x7o2mR3xyMPrIANWqRaId50q34AaVCeZMjqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:45.498268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90d76fb83ba6a049cd71848a6325d5c00a30b6112ced28f1a0db1e79420a6176","sha256:27af5ae86a87236c0c66f1d539b4ca90401a618c1336dd69e454d661e6b9de2a"],"state_sha256":"f3666962dd5214c406877b001eb0bbbb24190034a55e7d0f983dc4893f9a8024"}