{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4NIH2HARTPJCXGOEBDYBKDYT4T","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":"af680cb89eacd876a9a23f9b5c6c187dcaf241030f7b23be80999f99ebda2069","cross_cats_sorted":["cs.CR","cs.IR","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-10T19:51:49Z","title_canon_sha256":"f08e0779bca9c963ccdb118aad185842e9662ab6d27eeeb64664eb410ccbe090"},"schema_version":"1.0","source":{"id":"1610.03048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03048","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03048v1","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03048","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"4NIH2HARTPJC","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4NIH2HARTPJCXGOE","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4NIH2HAR","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:d8015fd4326be07af5b4c7b71cf32e892fdd80237bf33b60a7363896ea7aa59a","target":"graph","created_at":"2026-05-18T01:02:50Z","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":"A private information retrieval scheme is a mechanism that allows a user to retrieve any one out of $K$ messages from $N$ non-communicating replicated databases, each of which stores all $K$ messages, without revealing anything about the identity of the desired message index to any individual database. If the size of each message is $L$ bits and the total download required by a PIR scheme from all $N$ databases is $D$ bits, then $D$ is called the download cost and the ratio $L/D$ is called an achievable rate. For fixed $K,N\\in\\mathbb{N}$, the capacity of PIR, denoted by $C$, is the supremum of","authors_text":"Hua Sun, Syed A. Jafar","cross_cats":["cs.CR","cs.IR","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-10T19:51:49Z","title":"Optimal Download Cost of Private Information Retrieval for Arbitrary Message Length"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03048","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:c96a9d5bcce87cb5861457bca0d2b793fc6eefc2fae28b59512400886e260519","target":"record","created_at":"2026-05-18T01:02:50Z","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":"af680cb89eacd876a9a23f9b5c6c187dcaf241030f7b23be80999f99ebda2069","cross_cats_sorted":["cs.CR","cs.IR","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-10T19:51:49Z","title_canon_sha256":"f08e0779bca9c963ccdb118aad185842e9662ab6d27eeeb64664eb410ccbe090"},"schema_version":"1.0","source":{"id":"1610.03048","kind":"arxiv","version":1}},"canonical_sha256":"e3507d1c119bd22b99c408f0150f13e4f306b123f2e4a00840c56d1de4e2362c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3507d1c119bd22b99c408f0150f13e4f306b123f2e4a00840c56d1de4e2362c","first_computed_at":"2026-05-18T01:02:50.126086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:50.126086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9G/SHJ4VTZtB9oCMVdQ1iaWmnIm0nQllweNGsMO+fVUUcYKLEjs2lpWZvlzUarQOtQZgAw0xc5Ny3to5Nxn2CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:50.126614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c96a9d5bcce87cb5861457bca0d2b793fc6eefc2fae28b59512400886e260519","sha256:d8015fd4326be07af5b4c7b71cf32e892fdd80237bf33b60a7363896ea7aa59a"],"state_sha256":"9215300eb9d3d261a5d374c8e3043d4c7198988d66e7a982ffdfa6bcc580dca3"}