{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NPNYKFYUUKHGJSDXDGG2IRPES7","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":"abe2195d85bf70454f5d522a51561c1737da481dcfe7d518259d947f21026fe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-14T17:09:15Z","title_canon_sha256":"58f0c4595fe620a6b6205286d6202571dcc842a95b0044cbf700313c85de8d49"},"schema_version":"1.0","source":{"id":"1511.04580","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04580","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04580v2","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04580","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"NPNYKFYUUKHG","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NPNYKFYUUKHGJSDX","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NPNYKFYU","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:99eaa32419e569246abf198edae4952960feba2e9077c390c7f4200c3778b5b7","target":"graph","created_at":"2026-05-18T00:07:55Z","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":"Combinatorial batch codes were defined by Paterson, Stinson, and Wei as purely combinatorial versions of the batch codes introduced by Ishai, Kushilevitz, Ostrovsky, and Sahai. There are $n$ items and $m$ servers, each of which stores a subset of the items. A batch code is an arrangement for storing items on servers so that, for prescribed integers $k$ and $t$, any $k$ items can be retrieved by reading at most $t$ items from each server. Silberstein defined an erasure batch code (with redundancy $r$) as a batch code in which any $k$ items can be retrieved by reading at most $t$ items from each","authors_text":"Carl Mummert, Elizabeth Niese, JiYoon Jung, Michael W. Schroeder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-14T17:09:15Z","title":"On Erasure Combinatorial Batch Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04580","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":"sha256:7cb8b880c30bbaa75450620fae244312645a2151c3f071db121b75cc010c2641","target":"record","created_at":"2026-05-18T00:07:55Z","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":"abe2195d85bf70454f5d522a51561c1737da481dcfe7d518259d947f21026fe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-14T17:09:15Z","title_canon_sha256":"58f0c4595fe620a6b6205286d6202571dcc842a95b0044cbf700313c85de8d49"},"schema_version":"1.0","source":{"id":"1511.04580","kind":"arxiv","version":2}},"canonical_sha256":"6bdb851714a28e64c877198da445e497d11d5a8ef2e8f84a19b958708c3c82f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bdb851714a28e64c877198da445e497d11d5a8ef2e8f84a19b958708c3c82f0","first_computed_at":"2026-05-18T00:07:55.842491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:55.842491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lYUgRTLYx6b7fiTSI9SVZKQAObwD992aGPPujjj922K4XTekjbQ2/hgs837mfGadxcnOlw3trwF7lY/lopqrDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:55.843255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.04580","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cb8b880c30bbaa75450620fae244312645a2151c3f071db121b75cc010c2641","sha256:99eaa32419e569246abf198edae4952960feba2e9077c390c7f4200c3778b5b7"],"state_sha256":"5834878829f88f24b8199a9ebb1c8faaf4f6dc1cdf9b4ff215bbdb51b458720b"}