{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QNBHY5TYJ6NGYHL6ZFXSYW7GJV","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":"55f270fd50db21778c67796bb680146ba6ab91d8b44ccaa20fd8ae983447f7e9","cross_cats_sorted":["cs.CR","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-09-10T00:49:08Z","title_canon_sha256":"3c7121657cb94291476ad97e32eabf343520f7935bb8fa7c1dae77084613b74b"},"schema_version":"1.0","source":{"id":"1709.03022","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03022","created_at":"2026-05-17T23:44:38Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03022v3","created_at":"2026-05-17T23:44:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03022","created_at":"2026-05-17T23:44:38Z"},{"alias_kind":"pith_short_12","alias_value":"QNBHY5TYJ6NG","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QNBHY5TYJ6NGYHL6","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QNBHY5TY","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:b015863ddade1fc3e6088e68322f19ec4035ebe1a3612077db9a36c2d4fca1c0","target":"graph","created_at":"2026-05-17T23:44:38Z","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 $T$-Private Information Retrieval with private side information (TPIR-PSI). In this problem, $N$ replicated databases store $K$ independent messages, and a user, equipped with a local cache that holds $M$ messages as side information, wishes to retrieve one of the other $K-M$ messages. The desired message index and the side information must remain jointly private even if any $T$ of the $N$ databases collude. We show that the capacity of TPIR-PSI is $\\left(1+\\frac{T}{N}+\\cdots+\\left(\\frac{T}{N}\\right)^{K-M-1}\\right)^{-1}$. As a special case obtained by setting $T=1$, ","authors_text":"Syed Jafar, Zhen Chen, Zhiying Wang","cross_cats":["cs.CR","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-09-10T00:49:08Z","title":"The Capacity of $T$-Private Information Retrieval with Private Side Information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03022","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":"sha256:9b50e6d2d5ecaa5948cdcd942bff47ad884428c715d38f77ad5d8a69b7a0b697","target":"record","created_at":"2026-05-17T23:44:38Z","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":"55f270fd50db21778c67796bb680146ba6ab91d8b44ccaa20fd8ae983447f7e9","cross_cats_sorted":["cs.CR","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-09-10T00:49:08Z","title_canon_sha256":"3c7121657cb94291476ad97e32eabf343520f7935bb8fa7c1dae77084613b74b"},"schema_version":"1.0","source":{"id":"1709.03022","kind":"arxiv","version":3}},"canonical_sha256":"83427c76784f9a6c1d7ec96f2c5be64d60c2fa4489e7fec45bf6631dc0e945d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83427c76784f9a6c1d7ec96f2c5be64d60c2fa4489e7fec45bf6631dc0e945d7","first_computed_at":"2026-05-17T23:44:38.407200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:38.407200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3xafRb6xhmmG4Vj89aad36BgFOJo6e0/En1h87JJikn9uv0Gt45UHB+15LFziuP7ewRgM8p98dx36s/5y0ooBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:38.407569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03022","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b50e6d2d5ecaa5948cdcd942bff47ad884428c715d38f77ad5d8a69b7a0b697","sha256:b015863ddade1fc3e6088e68322f19ec4035ebe1a3612077db9a36c2d4fca1c0"],"state_sha256":"84cb12ee976e88ab3bd5922dfe7aca20ff11567ece599bae11cc5f3e0d317501"}