{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ULQZLDAK2VMDG7ZZGPPG55UTY7","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":"b7c25e7a302b4c043498ae5a1bd06779c114f98ffc7d66b6986d4717066c4fe9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-07-11T23:28:55Z","title_canon_sha256":"8defccabcf593e5564a33297cd10832511ec86b22e8c55a44c79d8e4a84e732a"},"schema_version":"1.0","source":{"id":"1707.03495","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03495","created_at":"2026-05-18T00:25:18Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03495v3","created_at":"2026-05-18T00:25:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03495","created_at":"2026-05-18T00:25:18Z"},{"alias_kind":"pith_short_12","alias_value":"ULQZLDAK2VMD","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"ULQZLDAK2VMDG7ZZ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"ULQZLDAK","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:bcc328ce5f85cf94b21fe46956b9d029d3f927df498efe764dc8fbaa5f57960f","target":"graph","created_at":"2026-05-18T00:25:18Z","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":"It was recently shown by Fazeli et al. that the storage overhead of a traditional $t$-server private information retrieval (PIR) protocol can be significantly reduced using the concept of a $t$-server PIR code. In this work, we show that a family of $t$-server PIR codes (with increasing dimensions and blocklengths) can be constructed from an existing $t$-server PIR code through lengthening by a single information symbol and code extension by at most $\\bigl\\lceil t/2\\bigr\\rceil$ code symbols. Furthermore, by extending a code construction notion from Steiner systems by Fazeli et al., we obtain a","authors_text":"Eirik Rosnes, Hsuan-Yin Lin","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-07-11T23:28:55Z","title":"Lengthening and Extending Binary Private Information Retrieval Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03495","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":"sha256:6289210fdf6c14562eced0e3695e5b7fae9ef02c69eeccffe002660626b33818","target":"record","created_at":"2026-05-18T00:25:18Z","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":"b7c25e7a302b4c043498ae5a1bd06779c114f98ffc7d66b6986d4717066c4fe9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-07-11T23:28:55Z","title_canon_sha256":"8defccabcf593e5564a33297cd10832511ec86b22e8c55a44c79d8e4a84e732a"},"schema_version":"1.0","source":{"id":"1707.03495","kind":"arxiv","version":3}},"canonical_sha256":"a2e1958c0ad558337f3933de6ef693c7f6240d1ab00bfebe1f884e1511a4623e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2e1958c0ad558337f3933de6ef693c7f6240d1ab00bfebe1f884e1511a4623e","first_computed_at":"2026-05-18T00:25:18.036735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:18.036735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GY+uL+7aiJ0gLvx1b8GOOoaG+HzxIgzPCSLAD7PmuZUwDRp0SerhOC4CVgkdk8uhgPuQs04JOXPXJCO4PawUDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:18.037291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03495","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6289210fdf6c14562eced0e3695e5b7fae9ef02c69eeccffe002660626b33818","sha256:bcc328ce5f85cf94b21fe46956b9d029d3f927df498efe764dc8fbaa5f57960f"],"state_sha256":"e355a920874442b038fa22e9d3905fcd020f51a2fbc6aaa1a8cce96366a38bc6"}