{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XRIUFDGLE7YMV2WCPI5X3FRVTN","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":"5526a47aeae0be2689c3c5680ee37f0589457995be8910152458b5ebc7f0926c","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-10-19T14:05:54Z","title_canon_sha256":"179a17fc39dda8c5f2e030afec06a4ab143fe7856061b8fbd769138675e84bb5"},"schema_version":"1.0","source":{"id":"1810.08510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08510","created_at":"2026-05-17T23:44:02Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08510v2","created_at":"2026-05-17T23:44:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08510","created_at":"2026-05-17T23:44:02Z"},{"alias_kind":"pith_short_12","alias_value":"XRIUFDGLE7YM","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XRIUFDGLE7YMV2WC","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XRIUFDGL","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:d3c574c158883023f8c6217ab2143d4adf965b6c510fa4d398d5e89f9a3a308c","target":"graph","created_at":"2026-05-17T23:44:02Z","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 (LRCs) have gained significant interest for the design of large distributed storage systems as they allow a small number of erased nodes to be recovered by accessing only a few others. Several works have thus been carried out to understand the optimal rate-distance tradeoff, but only recently the size of the alphabet has been taken into account. In this paper, a novel definition of locality is proposed to keep track of the precise number of nodes required for a local repair when the repair sets do not yield MDS codes. Then, a new alphabet-dependent bound is derived, wh","authors_text":"Camilla Hollanti, Matthias Grezet, Ragnar Freij-Hollanti, Thomas Westerb\\\"ack","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-10-19T14:05:54Z","title":"Alphabet-Dependent Bounds for Linear Locally Repairable Codes Based on Residual Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08510","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":"sha256:508eab0aa3791424da1ac66cb36650173a303fde23ace3eb9672371be1b337bc","target":"record","created_at":"2026-05-17T23:44:02Z","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":"5526a47aeae0be2689c3c5680ee37f0589457995be8910152458b5ebc7f0926c","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-10-19T14:05:54Z","title_canon_sha256":"179a17fc39dda8c5f2e030afec06a4ab143fe7856061b8fbd769138675e84bb5"},"schema_version":"1.0","source":{"id":"1810.08510","kind":"arxiv","version":2}},"canonical_sha256":"bc51428ccb27f0caeac27a3b7d96359b4269bf2c5967c91eb9f0502f7726656e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc51428ccb27f0caeac27a3b7d96359b4269bf2c5967c91eb9f0502f7726656e","first_computed_at":"2026-05-17T23:44:02.749541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:02.749541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fud4OLVB6wFiJQPZUgtiPLhsqMx45OoWck+TXyLBUkhafEBbGnxob0HxeoKObBi5SRtUvFV4l5yod797iNo2BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:02.750036Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:508eab0aa3791424da1ac66cb36650173a303fde23ace3eb9672371be1b337bc","sha256:d3c574c158883023f8c6217ab2143d4adf965b6c510fa4d398d5e89f9a3a308c"],"state_sha256":"1cfdbf51f31810711b5a129d7511eac1aa1dd8d3ae858b7bcc2b7bc89ea6d2ed"}