{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:W4A4TYHF3XJMB6DQ5SHI2CN7MT","short_pith_number":"pith:W4A4TYHF","canonical_record":{"source":{"id":"1405.6157","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T13:04:14Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9cee96fc4127b7bd7cc8a6378d3ebb040013000c7c45f0b83a6ff1438c18b7e8","abstract_canon_sha256":"94f137e088e1536e4b83478edf66087ecc27fd70a35e85d0f4a054176f955d21"},"schema_version":"1.0"},"canonical_sha256":"b701c9e0e5ddd2c0f870ec8e8d09bf64e84c6c0c3b31449cf3fb4524e0684886","source":{"kind":"arxiv","id":"1405.6157","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6157","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6157v2","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6157","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"W4A4TYHF3XJM","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W4A4TYHF3XJMB6DQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W4A4TYHF","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:W4A4TYHF3XJMB6DQ5SHI2CN7MT","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6157","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T13:04:14Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9cee96fc4127b7bd7cc8a6378d3ebb040013000c7c45f0b83a6ff1438c18b7e8","abstract_canon_sha256":"94f137e088e1536e4b83478edf66087ecc27fd70a35e85d0f4a054176f955d21"},"schema_version":"1.0"},"canonical_sha256":"b701c9e0e5ddd2c0f870ec8e8d09bf64e84c6c0c3b31449cf3fb4524e0684886","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:48.179502Z","signature_b64":"INekVGtjR71mcJc7uVN4Qb/Ni4GmWOI4L46wPWPIr9LTU03nhowitBPUWZCA5qXR+EnWZWVHtMouJCpnVJyBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b701c9e0e5ddd2c0f870ec8e8d09bf64e84c6c0c3b31449cf3fb4524e0684886","last_reissued_at":"2026-05-18T02:39:48.179015Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:48.179015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6157","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CK1y+uOQ6McdE+wrM/Dlds/rPCJdn3ZrIy3lAKGdViocZkmQUzdzrUzehCy53Bakxv+5mXt+4utB2M/nLjY5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T22:00:46.095243Z"},"content_sha256":"ff8f4dbe4497a6cbece14bbc8f4cd1bb7df01227ad8e111bf9edf67227739e3c","schema_version":"1.0","event_id":"sha256:ff8f4dbe4497a6cbece14bbc8f4cd1bb7df01227ad8e111bf9edf67227739e3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:W4A4TYHF3XJMB6DQ5SHI2CN7MT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Repetition and Erasure Batch Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Natalia Silberstein","submitted_at":"2014-05-04T13:04:14Z","abstract_excerpt":"Batch codes are a family of codes that represent a distributed storage system (DSS) of $n$ nodes so that any batch of $t$ data symbols can be retrieved by reading at most one symbol from each node. Fractional repetition codes are a family of codes for DSS that enable efficient uncoded repairs of failed nodes. In this work these two families of codes are combined to obtain fractional repetition batch (FRB) codes which provide both uncoded repairs and parallel reads of subsets of stored symbols. In addition, new batch codes which can tolerate node failures are considered. This new family of batc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6157","kind":"arxiv","version":2},"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":"2026-05-18T02:39:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XEghzD/RXoRgC+YAqQOrmLRFqg65nOQNJmPoqh4qmUF6/Sl772cCsjc3zJDpRkWgoD6XzEo5AqiYaqtzordCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T22:00:46.095595Z"},"content_sha256":"2309c00b79ac8278b4ef69a9d0c740df40866ac0b0bfac0059ba8f880aa04dbc","schema_version":"1.0","event_id":"sha256:2309c00b79ac8278b4ef69a9d0c740df40866ac0b0bfac0059ba8f880aa04dbc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W4A4TYHF3XJMB6DQ5SHI2CN7MT/bundle.json","state_url":"https://pith.science/pith/W4A4TYHF3XJMB6DQ5SHI2CN7MT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W4A4TYHF3XJMB6DQ5SHI2CN7MT/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":"2026-06-26T22:00:46Z","links":{"resolver":"https://pith.science/pith/W4A4TYHF3XJMB6DQ5SHI2CN7MT","bundle":"https://pith.science/pith/W4A4TYHF3XJMB6DQ5SHI2CN7MT/bundle.json","state":"https://pith.science/pith/W4A4TYHF3XJMB6DQ5SHI2CN7MT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W4A4TYHF3XJMB6DQ5SHI2CN7MT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:W4A4TYHF3XJMB6DQ5SHI2CN7MT","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":"94f137e088e1536e4b83478edf66087ecc27fd70a35e85d0f4a054176f955d21","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T13:04:14Z","title_canon_sha256":"9cee96fc4127b7bd7cc8a6378d3ebb040013000c7c45f0b83a6ff1438c18b7e8"},"schema_version":"1.0","source":{"id":"1405.6157","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6157","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6157v2","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6157","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"W4A4TYHF3XJM","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W4A4TYHF3XJMB6DQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W4A4TYHF","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:2309c00b79ac8278b4ef69a9d0c740df40866ac0b0bfac0059ba8f880aa04dbc","target":"graph","created_at":"2026-05-18T02:39:48Z","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":"Batch codes are a family of codes that represent a distributed storage system (DSS) of $n$ nodes so that any batch of $t$ data symbols can be retrieved by reading at most one symbol from each node. Fractional repetition codes are a family of codes for DSS that enable efficient uncoded repairs of failed nodes. In this work these two families of codes are combined to obtain fractional repetition batch (FRB) codes which provide both uncoded repairs and parallel reads of subsets of stored symbols. In addition, new batch codes which can tolerate node failures are considered. This new family of batc","authors_text":"Natalia Silberstein","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T13:04:14Z","title":"Fractional Repetition and Erasure Batch Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6157","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:ff8f4dbe4497a6cbece14bbc8f4cd1bb7df01227ad8e111bf9edf67227739e3c","target":"record","created_at":"2026-05-18T02:39:48Z","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":"94f137e088e1536e4b83478edf66087ecc27fd70a35e85d0f4a054176f955d21","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T13:04:14Z","title_canon_sha256":"9cee96fc4127b7bd7cc8a6378d3ebb040013000c7c45f0b83a6ff1438c18b7e8"},"schema_version":"1.0","source":{"id":"1405.6157","kind":"arxiv","version":2}},"canonical_sha256":"b701c9e0e5ddd2c0f870ec8e8d09bf64e84c6c0c3b31449cf3fb4524e0684886","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b701c9e0e5ddd2c0f870ec8e8d09bf64e84c6c0c3b31449cf3fb4524e0684886","first_computed_at":"2026-05-18T02:39:48.179015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:48.179015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"INekVGtjR71mcJc7uVN4Qb/Ni4GmWOI4L46wPWPIr9LTU03nhowitBPUWZCA5qXR+EnWZWVHtMouJCpnVJyBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:48.179502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6157","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff8f4dbe4497a6cbece14bbc8f4cd1bb7df01227ad8e111bf9edf67227739e3c","sha256:2309c00b79ac8278b4ef69a9d0c740df40866ac0b0bfac0059ba8f880aa04dbc"],"state_sha256":"d547b7713784b32a73db98d4a7dc2f89878b8b880aa31cf2d52a1737e25de07f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TogShAjhrTUIhFRy/PzxpUTdds7zG76L5TwRtnHPZYNU8j9Ng88fkwxAawOx1lMx0DG612kRuKXUSaEkPl4eCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T22:00:46.097415Z","bundle_sha256":"82981bc4e6fc1cbe31f0f7335d3c8012cab83cc8064fb2a4fee78964d0e84d2d"}}