{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UW45GL3XQODXRWJNY7DVRARK7D","short_pith_number":"pith:UW45GL3X","canonical_record":{"source":{"id":"1507.02796","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-10T07:50:09Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"195a4bc8be005d897fcd9ec130d977b35e9254cdc3d472355c4fe9cad6ade54f","abstract_canon_sha256":"81d2a8a715506b43e47aa86c5f134f2974591306b9cbabff849d362c37173357"},"schema_version":"1.0"},"canonical_sha256":"a5b9d32f77838778d92dc7c758822af8f28c9e6176c49dac410a72663632631b","source":{"kind":"arxiv","id":"1507.02796","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02796","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02796v3","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02796","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"UW45GL3XQODX","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UW45GL3XQODXRWJN","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UW45GL3X","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UW45GL3XQODXRWJNY7DVRARK7D","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02796","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-10T07:50:09Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"195a4bc8be005d897fcd9ec130d977b35e9254cdc3d472355c4fe9cad6ade54f","abstract_canon_sha256":"81d2a8a715506b43e47aa86c5f134f2974591306b9cbabff849d362c37173357"},"schema_version":"1.0"},"canonical_sha256":"a5b9d32f77838778d92dc7c758822af8f28c9e6176c49dac410a72663632631b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:08.967115Z","signature_b64":"LyECRW7m51S/oE1AUrEfuRu0c0Alig+4u7xnlDItgOLl+rugrEZbM6pc8pXQKqPnnkcUnxsTU8lzg10NGvHKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5b9d32f77838778d92dc7c758822af8f28c9e6176c49dac410a72663632631b","last_reissued_at":"2026-05-18T01:36:08.966490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:08.966490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02796","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rQWP5085CSNaXM4Uox1UOOfRHXpC6a+ByjDed2NeE5sq2laWlHt58Qxx+Vu5RT3Xc64ktNQwBzyFhmBjtr6VCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:33:21.179785Z"},"content_sha256":"b18b4c75e2d5ec1f4ddd4b2ea63e603c36c711ad183a3d6b8ba5e3ebc12803db","schema_version":"1.0","event_id":"sha256:b18b4c75e2d5ec1f4ddd4b2ea63e603c36c711ad183a3d6b8ba5e3ebc12803db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UW45GL3XQODXRWJNY7DVRARK7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Locally Repairable Codes with Functional Repair and Multiple Erasure Tolerance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chau Yuen, Wentu Song","submitted_at":"2015-07-10T07:50:09Z","abstract_excerpt":"We consider the problem of designing [n; k] linear codes for distributed storage systems (DSS) that satisfy the (r, t)-Local Repair Property, where any t'(<=t) simultaneously failed nodes can be locally repaired, each with locality r. The parameters n, k, r, t are positive integers such that r<k<n and t <= n-k. We consider the functional repair model and the sequential approach for repairing multiple failed nodes. By functional repair, we mean that the packet stored in each newcomer is not necessarily an exact copy of the lost data but a symbol that keep the (r, t)-local repair property. By th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02796","kind":"arxiv","version":3},"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":"2026-05-18T01:36:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f8fKE9eyxD6hbodSqP+qyUL7vX4BX00j0369sZ027q7uxRXlYTQgmQnYEo+NwWsr3hvmyclk/cKwq++6d0dODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:33:21.180132Z"},"content_sha256":"625aca756782f8372ab96f718caebf33939eb7f85b919cf5b2d249a6ae4b50d3","schema_version":"1.0","event_id":"sha256:625aca756782f8372ab96f718caebf33939eb7f85b919cf5b2d249a6ae4b50d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UW45GL3XQODXRWJNY7DVRARK7D/bundle.json","state_url":"https://pith.science/pith/UW45GL3XQODXRWJNY7DVRARK7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UW45GL3XQODXRWJNY7DVRARK7D/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":"2026-06-03T22:33:21Z","links":{"resolver":"https://pith.science/pith/UW45GL3XQODXRWJNY7DVRARK7D","bundle":"https://pith.science/pith/UW45GL3XQODXRWJNY7DVRARK7D/bundle.json","state":"https://pith.science/pith/UW45GL3XQODXRWJNY7DVRARK7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UW45GL3XQODXRWJNY7DVRARK7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UW45GL3XQODXRWJNY7DVRARK7D","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":"81d2a8a715506b43e47aa86c5f134f2974591306b9cbabff849d362c37173357","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-10T07:50:09Z","title_canon_sha256":"195a4bc8be005d897fcd9ec130d977b35e9254cdc3d472355c4fe9cad6ade54f"},"schema_version":"1.0","source":{"id":"1507.02796","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02796","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02796v3","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02796","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"UW45GL3XQODX","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UW45GL3XQODXRWJN","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UW45GL3X","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:625aca756782f8372ab96f718caebf33939eb7f85b919cf5b2d249a6ae4b50d3","target":"graph","created_at":"2026-05-18T01:36:08Z","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":"We consider the problem of designing [n; k] linear codes for distributed storage systems (DSS) that satisfy the (r, t)-Local Repair Property, where any t'(<=t) simultaneously failed nodes can be locally repaired, each with locality r. The parameters n, k, r, t are positive integers such that r<k<n and t <= n-k. We consider the functional repair model and the sequential approach for repairing multiple failed nodes. By functional repair, we mean that the packet stored in each newcomer is not necessarily an exact copy of the lost data but a symbol that keep the (r, t)-local repair property. By th","authors_text":"Chau Yuen, Wentu Song","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-10T07:50:09Z","title":"Locally Repairable Codes with Functional Repair and Multiple Erasure Tolerance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02796","kind":"arxiv","version":3},"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:b18b4c75e2d5ec1f4ddd4b2ea63e603c36c711ad183a3d6b8ba5e3ebc12803db","target":"record","created_at":"2026-05-18T01:36:08Z","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":"81d2a8a715506b43e47aa86c5f134f2974591306b9cbabff849d362c37173357","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-10T07:50:09Z","title_canon_sha256":"195a4bc8be005d897fcd9ec130d977b35e9254cdc3d472355c4fe9cad6ade54f"},"schema_version":"1.0","source":{"id":"1507.02796","kind":"arxiv","version":3}},"canonical_sha256":"a5b9d32f77838778d92dc7c758822af8f28c9e6176c49dac410a72663632631b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5b9d32f77838778d92dc7c758822af8f28c9e6176c49dac410a72663632631b","first_computed_at":"2026-05-18T01:36:08.966490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:08.966490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LyECRW7m51S/oE1AUrEfuRu0c0Alig+4u7xnlDItgOLl+rugrEZbM6pc8pXQKqPnnkcUnxsTU8lzg10NGvHKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:08.967115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02796","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b18b4c75e2d5ec1f4ddd4b2ea63e603c36c711ad183a3d6b8ba5e3ebc12803db","sha256:625aca756782f8372ab96f718caebf33939eb7f85b919cf5b2d249a6ae4b50d3"],"state_sha256":"1f3eb6955ba3b4295e71ed54e5abc23212a15d43e635c0d34dae6a3af081300b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MBRO2P9gAA+ClhZxMQgGiIgms6W/iEm0m2n5CFB+ZycuUgBsAiSZPppTQ5ysaOCKycUb53x7X2buiT+l/R97BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T22:33:21.182086Z","bundle_sha256":"d5c46547bfdf836558ea3edb42f5a05564ef52d25aaf089be888ab933e0bb992"}}