{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NCJ7OBLY2J4LEICD2NZUSJYDHG","short_pith_number":"pith:NCJ7OBLY","canonical_record":{"source":{"id":"1812.02502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-12-06T12:49:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"52479b580c42563045230dc31893a9d32031e4bfdb9205695c9aed05c9a43089","abstract_canon_sha256":"dabd547995b04a144c9512005d3d0072e0893db47d5046c8d128f7c8a265f411"},"schema_version":"1.0"},"canonical_sha256":"6893f70578d278b22043d3734927033987c4a798ca6ed6ab7d12e7df7a3c3515","source":{"kind":"arxiv","id":"1812.02502","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02502","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02502v1","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02502","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"NCJ7OBLY2J4L","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NCJ7OBLY2J4LEICD","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NCJ7OBLY","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NCJ7OBLY2J4LEICD2NZUSJYDHG","target":"record","payload":{"canonical_record":{"source":{"id":"1812.02502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-12-06T12:49:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"52479b580c42563045230dc31893a9d32031e4bfdb9205695c9aed05c9a43089","abstract_canon_sha256":"dabd547995b04a144c9512005d3d0072e0893db47d5046c8d128f7c8a265f411"},"schema_version":"1.0"},"canonical_sha256":"6893f70578d278b22043d3734927033987c4a798ca6ed6ab7d12e7df7a3c3515","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:55.535887Z","signature_b64":"dqKi6JZkPIRCFc8EyG4jm/Qx4UKTyT6W6YRBybBgZp63eqQZRhFrKtR9/Jxx2Zl6TfJPiHL9o7JaxgMb/2HvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6893f70578d278b22043d3734927033987c4a798ca6ed6ab7d12e7df7a3c3515","last_reissued_at":"2026-05-17T23:58:55.535407Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:55.535407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.02502","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tGrnu3J7FqfVINYh4m029b/LmaIBJKQzvtzxipAR6AbWQ26wv/9CCe4qrCSVdiRQHmBc7qQqw9Uv9P6rqtOTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:39:05.785915Z"},"content_sha256":"eb7208ba70aa91a0b799f86ac4e4e22b6f588b28c388dbf29f723475f49a1841","schema_version":"1.0","event_id":"sha256:eb7208ba70aa91a0b799f86ac4e4e22b6f588b28c388dbf29f723475f49a1841"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NCJ7OBLY2J4LEICD2NZUSJYDHG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Tight Rate Bound and Matching Construction for Locally Recoverable Codes with Sequential Recovery From Any Number of Multiple Erasures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ganesh R. Kini, P. Vijay Kumar, S. B. Balaji","submitted_at":"2018-12-06T12:49:49Z","abstract_excerpt":"By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local recovery of a set of $t$ erased symbols. There have been several approaches proposed for the handling of multiple erasures. The approach considered here, is one of sequential recovery meaning that the $t$ erased symbols are recovered in succession, each time contacting at most $r$ other symbols for assistance in recovery. Under the constraint that each eras"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02502","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5C6GS/72fR1R1GsY+O3ANue/G/BMRx6lus7PWi1xx1DOWrVInhEgiPfOMMgekHCQQPiDCAp+Qsep4KFmPnlZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:39:05.786294Z"},"content_sha256":"18d542d8d3ed532fc87b85a6dfafa5de7c6c5391ed39cf5c2079995c751b5434","schema_version":"1.0","event_id":"sha256:18d542d8d3ed532fc87b85a6dfafa5de7c6c5391ed39cf5c2079995c751b5434"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NCJ7OBLY2J4LEICD2NZUSJYDHG/bundle.json","state_url":"https://pith.science/pith/NCJ7OBLY2J4LEICD2NZUSJYDHG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NCJ7OBLY2J4LEICD2NZUSJYDHG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T06:39:05Z","links":{"resolver":"https://pith.science/pith/NCJ7OBLY2J4LEICD2NZUSJYDHG","bundle":"https://pith.science/pith/NCJ7OBLY2J4LEICD2NZUSJYDHG/bundle.json","state":"https://pith.science/pith/NCJ7OBLY2J4LEICD2NZUSJYDHG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NCJ7OBLY2J4LEICD2NZUSJYDHG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NCJ7OBLY2J4LEICD2NZUSJYDHG","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":"dabd547995b04a144c9512005d3d0072e0893db47d5046c8d128f7c8a265f411","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-12-06T12:49:49Z","title_canon_sha256":"52479b580c42563045230dc31893a9d32031e4bfdb9205695c9aed05c9a43089"},"schema_version":"1.0","source":{"id":"1812.02502","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02502","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02502v1","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02502","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"NCJ7OBLY2J4L","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NCJ7OBLY2J4LEICD","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NCJ7OBLY","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:18d542d8d3ed532fc87b85a6dfafa5de7c6c5391ed39cf5c2079995c751b5434","target":"graph","created_at":"2026-05-17T23:58:55Z","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":"By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local recovery of a set of $t$ erased symbols. There have been several approaches proposed for the handling of multiple erasures. The approach considered here, is one of sequential recovery meaning that the $t$ erased symbols are recovered in succession, each time contacting at most $r$ other symbols for assistance in recovery. Under the constraint that each eras","authors_text":"Ganesh R. Kini, P. Vijay Kumar, S. B. Balaji","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-12-06T12:49:49Z","title":"A Tight Rate Bound and Matching Construction for Locally Recoverable Codes with Sequential Recovery From Any Number of Multiple Erasures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02502","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:eb7208ba70aa91a0b799f86ac4e4e22b6f588b28c388dbf29f723475f49a1841","target":"record","created_at":"2026-05-17T23:58:55Z","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":"dabd547995b04a144c9512005d3d0072e0893db47d5046c8d128f7c8a265f411","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-12-06T12:49:49Z","title_canon_sha256":"52479b580c42563045230dc31893a9d32031e4bfdb9205695c9aed05c9a43089"},"schema_version":"1.0","source":{"id":"1812.02502","kind":"arxiv","version":1}},"canonical_sha256":"6893f70578d278b22043d3734927033987c4a798ca6ed6ab7d12e7df7a3c3515","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6893f70578d278b22043d3734927033987c4a798ca6ed6ab7d12e7df7a3c3515","first_computed_at":"2026-05-17T23:58:55.535407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:55.535407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dqKi6JZkPIRCFc8EyG4jm/Qx4UKTyT6W6YRBybBgZp63eqQZRhFrKtR9/Jxx2Zl6TfJPiHL9o7JaxgMb/2HvCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:55.535887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02502","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb7208ba70aa91a0b799f86ac4e4e22b6f588b28c388dbf29f723475f49a1841","sha256:18d542d8d3ed532fc87b85a6dfafa5de7c6c5391ed39cf5c2079995c751b5434"],"state_sha256":"eaff43739d41bae05925a664e5ddcf4d8b3435d807de5399daa7303d22fb9473"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ddALGPHFAMu4PeGkzjauIh+JRpeDGk36l0pMHFMlAufhnFLWCVYBgSI1n40RPuV+sKMhbdFg9LxmtU4MaFE9BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:39:05.789122Z","bundle_sha256":"416a3737eab0ddd8ef42dfc4583e03db199d6284ae2c24b5555ce6e02ff78638"}}