{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JVDPPZAAWROANGDFSLOZ4WQUNB","short_pith_number":"pith:JVDPPZAA","canonical_record":{"source":{"id":"1702.05074","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-16T18:29:10Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"686c54a4e40932450927d73bbd0b2dfd721102874c177cdba0ab1e5478e90762","abstract_canon_sha256":"e87cec363f0849e1d7fbf30f63d576b331980e6ec6a31a260fb939d338ad557a"},"schema_version":"1.0"},"canonical_sha256":"4d46f7e400b45c06986592dd9e5a1468610f9011b6af96710ccb22164e47d75d","source":{"kind":"arxiv","id":"1702.05074","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05074","created_at":"2026-05-18T00:48:32Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05074v2","created_at":"2026-05-18T00:48:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05074","created_at":"2026-05-18T00:48:32Z"},{"alias_kind":"pith_short_12","alias_value":"JVDPPZAAWROA","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JVDPPZAAWROANGDF","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JVDPPZAA","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JVDPPZAAWROANGDFSLOZ4WQUNB","target":"record","payload":{"canonical_record":{"source":{"id":"1702.05074","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-16T18:29:10Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"686c54a4e40932450927d73bbd0b2dfd721102874c177cdba0ab1e5478e90762","abstract_canon_sha256":"e87cec363f0849e1d7fbf30f63d576b331980e6ec6a31a260fb939d338ad557a"},"schema_version":"1.0"},"canonical_sha256":"4d46f7e400b45c06986592dd9e5a1468610f9011b6af96710ccb22164e47d75d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:32.347474Z","signature_b64":"auNSQzvkqZTVcFNMY8oB889yomDjBkmt1vTkP3hE4osqsnHZeoL2+TUpj+dxdc5CueNiPgjZfbPyXXhwVjypAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d46f7e400b45c06986592dd9e5a1468610f9011b6af96710ccb22164e47d75d","last_reissued_at":"2026-05-18T00:48:32.346860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:32.346860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.05074","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":"2026-05-18T00:48:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rUuDN0hfqmwPQ+VTszVYPiE1lNWhVs8nRLwA0Cvn+iiadDRW3+V5ScR+pDAK60P6un84olDuWp1K6zyxJ5l+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:13:54.889738Z"},"content_sha256":"07b5475c8a7010def0737493131bef6f4327e3bfeeb38e4fc2c5a264043bb76c","schema_version":"1.0","event_id":"sha256:07b5475c8a7010def0737493131bef6f4327e3bfeeb38e4fc2c5a264043bb76c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JVDPPZAAWROANGDFSLOZ4WQUNB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Binary, Shortened Projective Reed Muller Codes for Coded Private Information Retrieval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Myna Vajha, P. Vijay Kumar, Vinayak Ramkumar","submitted_at":"2017-02-16T18:29:10Z","abstract_excerpt":"The notion of a Private Information Retrieval (PIR) code was recently introduced by Fazeli, Vardy and Yaakobi who showed that this class of codes permit PIR at reduced levels of storage overhead in comparison with replicated-server PIR. In the present paper, the construction of an $(n,k)$ $\\tau$-server binary, linear PIR code having parameters $n = \\sum\\limits_{i = 0}^{\\ell} {m \\choose i}$, $k = {m \\choose \\ell}$ and $\\tau = 2^{\\ell}$ is presented. These codes are obtained through homogeneous-polynomial evaluation and correspond to the binary, Projective Reed Muller (PRM) code. The constructio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05074","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":"2026-05-18T00:48:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"16VZrniz0U9RCWCkem3f3z6S69vcWuTZbKKg7qgJ8LkVuZ2WkoaH/B5IEDou8kIx8zKEXPHYvSbtPnXlZfsUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:13:54.890405Z"},"content_sha256":"1350cdc63e6cecbf030481936c06cfa35e03f3ca18a32d347b0f468764d556a4","schema_version":"1.0","event_id":"sha256:1350cdc63e6cecbf030481936c06cfa35e03f3ca18a32d347b0f468764d556a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVDPPZAAWROANGDFSLOZ4WQUNB/bundle.json","state_url":"https://pith.science/pith/JVDPPZAAWROANGDFSLOZ4WQUNB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVDPPZAAWROANGDFSLOZ4WQUNB/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":"2026-05-31T03:13:54Z","links":{"resolver":"https://pith.science/pith/JVDPPZAAWROANGDFSLOZ4WQUNB","bundle":"https://pith.science/pith/JVDPPZAAWROANGDFSLOZ4WQUNB/bundle.json","state":"https://pith.science/pith/JVDPPZAAWROANGDFSLOZ4WQUNB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVDPPZAAWROANGDFSLOZ4WQUNB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JVDPPZAAWROANGDFSLOZ4WQUNB","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":"e87cec363f0849e1d7fbf30f63d576b331980e6ec6a31a260fb939d338ad557a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-16T18:29:10Z","title_canon_sha256":"686c54a4e40932450927d73bbd0b2dfd721102874c177cdba0ab1e5478e90762"},"schema_version":"1.0","source":{"id":"1702.05074","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05074","created_at":"2026-05-18T00:48:32Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05074v2","created_at":"2026-05-18T00:48:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05074","created_at":"2026-05-18T00:48:32Z"},{"alias_kind":"pith_short_12","alias_value":"JVDPPZAAWROA","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JVDPPZAAWROANGDF","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JVDPPZAA","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:1350cdc63e6cecbf030481936c06cfa35e03f3ca18a32d347b0f468764d556a4","target":"graph","created_at":"2026-05-18T00:48:32Z","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":"The notion of a Private Information Retrieval (PIR) code was recently introduced by Fazeli, Vardy and Yaakobi who showed that this class of codes permit PIR at reduced levels of storage overhead in comparison with replicated-server PIR. In the present paper, the construction of an $(n,k)$ $\\tau$-server binary, linear PIR code having parameters $n = \\sum\\limits_{i = 0}^{\\ell} {m \\choose i}$, $k = {m \\choose \\ell}$ and $\\tau = 2^{\\ell}$ is presented. These codes are obtained through homogeneous-polynomial evaluation and correspond to the binary, Projective Reed Muller (PRM) code. The constructio","authors_text":"Myna Vajha, P. Vijay Kumar, Vinayak Ramkumar","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-16T18:29:10Z","title":"Binary, Shortened Projective Reed Muller Codes for Coded Private Information Retrieval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05074","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":"sha256:07b5475c8a7010def0737493131bef6f4327e3bfeeb38e4fc2c5a264043bb76c","target":"record","created_at":"2026-05-18T00:48:32Z","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":"e87cec363f0849e1d7fbf30f63d576b331980e6ec6a31a260fb939d338ad557a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-16T18:29:10Z","title_canon_sha256":"686c54a4e40932450927d73bbd0b2dfd721102874c177cdba0ab1e5478e90762"},"schema_version":"1.0","source":{"id":"1702.05074","kind":"arxiv","version":2}},"canonical_sha256":"4d46f7e400b45c06986592dd9e5a1468610f9011b6af96710ccb22164e47d75d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d46f7e400b45c06986592dd9e5a1468610f9011b6af96710ccb22164e47d75d","first_computed_at":"2026-05-18T00:48:32.346860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:32.346860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"auNSQzvkqZTVcFNMY8oB889yomDjBkmt1vTkP3hE4osqsnHZeoL2+TUpj+dxdc5CueNiPgjZfbPyXXhwVjypAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:32.347474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05074","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07b5475c8a7010def0737493131bef6f4327e3bfeeb38e4fc2c5a264043bb76c","sha256:1350cdc63e6cecbf030481936c06cfa35e03f3ca18a32d347b0f468764d556a4"],"state_sha256":"22b82e5102a79f72f9475679cdce6cddd20b208165d1ed333a416a02cc835f7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zJlTn4kMLxxK+0bePoVR5K8vRL7MZm8nIw7LJ6QK766ZhQoNHXimwGKx48hJ1t5xe0UXpGc9Q1zkvCPRFxySAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:13:54.893980Z","bundle_sha256":"c34348885106780a6b9958707f7c7dcf1a317dac6ced4cb4ecfa50d536df339c"}}