{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:O2O3LIA5E54ZZ4OBE4UWUAIJXE","short_pith_number":"pith:O2O3LIA5","canonical_record":{"source":{"id":"2207.06087","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.IT","submitted_at":"2022-07-13T09:54:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"bf1d8e87a0f7fd8918bfde663b560892c5930151f30efb1e4ce8e488ee160ac4","abstract_canon_sha256":"24a56d8cd6c92091c3eb99d3443640ddee75b65cce6717ac3cfe0530a9600691"},"schema_version":"1.0"},"canonical_sha256":"769db5a01d27799cf1c127296a0109b911b16f06bf7a5ca0ce08fb3a76628c6e","source":{"kind":"arxiv","id":"2207.06087","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.06087","created_at":"2026-07-05T04:43:03Z"},{"alias_kind":"arxiv_version","alias_value":"2207.06087v4","created_at":"2026-07-05T04:43:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.06087","created_at":"2026-07-05T04:43:03Z"},{"alias_kind":"pith_short_12","alias_value":"O2O3LIA5E54Z","created_at":"2026-07-05T04:43:03Z"},{"alias_kind":"pith_short_16","alias_value":"O2O3LIA5E54ZZ4OB","created_at":"2026-07-05T04:43:03Z"},{"alias_kind":"pith_short_8","alias_value":"O2O3LIA5","created_at":"2026-07-05T04:43:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:O2O3LIA5E54ZZ4OBE4UWUAIJXE","target":"record","payload":{"canonical_record":{"source":{"id":"2207.06087","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.IT","submitted_at":"2022-07-13T09:54:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"bf1d8e87a0f7fd8918bfde663b560892c5930151f30efb1e4ce8e488ee160ac4","abstract_canon_sha256":"24a56d8cd6c92091c3eb99d3443640ddee75b65cce6717ac3cfe0530a9600691"},"schema_version":"1.0"},"canonical_sha256":"769db5a01d27799cf1c127296a0109b911b16f06bf7a5ca0ce08fb3a76628c6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:43:03.264802Z","signature_b64":"YyLkhjTUDewVT9Flj5d2dZ+A/aZuUlmVlvxDKC69y6fn9NWvWRV8Jj9FIKPe0aG1uDvzDSjLBe6lU8b6F+zdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"769db5a01d27799cf1c127296a0109b911b16f06bf7a5ca0ce08fb3a76628c6e","last_reissued_at":"2026-07-05T04:43:03.264409Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:43:03.264409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.06087","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:43:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r2ZixgwmPKLNS23DqhLoP6j7/ti50QJugDA9odqFJkeK/hIi+O5/gY8TIY1R+IJkUf/eZP7bXMAuPF4MCoyeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:15:06.446855Z"},"content_sha256":"bfe7da16dafe42c8baf277eb2421c5a83b641b6a0460a6e2039569ede05fa57d","schema_version":"1.0","event_id":"sha256:bfe7da16dafe42c8baf277eb2421c5a83b641b6a0460a6e2039569ede05fa57d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:O2O3LIA5E54ZZ4OBE4UWUAIJXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Storage and Retrieval Codes in PIR Schemes with Colluding Servers","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hao Chen, Liqing Xu","submitted_at":"2022-07-13T09:54:17Z","abstract_excerpt":"Private information retrieval (PIR) schemes (with or without colluding servers) have been proposed for realistic coded distributed data storage systems. Star product PIR schemes with colluding servers for general coded distributed storage system were constructed over general finite fields by R. Freij-Hollanti, O. W. Gnilke, C. Hollanti and A. Karpuk in 2017. These star product PIR schemes with colluding servers are suitable for the storage of files over small fields and can be constructed for coded distributed storage system with large number of servers. In this paper for an efficient storage "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.06087","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.06087/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:43:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l3BrYjdt0jhwtw++orBfnA8b8ym3Eu2YkRWBBoxNjDJHKE1aH7tpxbuMB3ArU9PE5C8nnILVXEmjLqMkcE0UDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:15:06.447222Z"},"content_sha256":"486d22ef688061dd5e424de6f3cbd476339fc4d7122e9fa745bedcdc021ffcfc","schema_version":"1.0","event_id":"sha256:486d22ef688061dd5e424de6f3cbd476339fc4d7122e9fa745bedcdc021ffcfc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O2O3LIA5E54ZZ4OBE4UWUAIJXE/bundle.json","state_url":"https://pith.science/pith/O2O3LIA5E54ZZ4OBE4UWUAIJXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O2O3LIA5E54ZZ4OBE4UWUAIJXE/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":"2026-07-06T14:15:06Z","links":{"resolver":"https://pith.science/pith/O2O3LIA5E54ZZ4OBE4UWUAIJXE","bundle":"https://pith.science/pith/O2O3LIA5E54ZZ4OBE4UWUAIJXE/bundle.json","state":"https://pith.science/pith/O2O3LIA5E54ZZ4OBE4UWUAIJXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O2O3LIA5E54ZZ4OBE4UWUAIJXE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:O2O3LIA5E54ZZ4OBE4UWUAIJXE","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":"24a56d8cd6c92091c3eb99d3443640ddee75b65cce6717ac3cfe0530a9600691","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.IT","submitted_at":"2022-07-13T09:54:17Z","title_canon_sha256":"bf1d8e87a0f7fd8918bfde663b560892c5930151f30efb1e4ce8e488ee160ac4"},"schema_version":"1.0","source":{"id":"2207.06087","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.06087","created_at":"2026-07-05T04:43:03Z"},{"alias_kind":"arxiv_version","alias_value":"2207.06087v4","created_at":"2026-07-05T04:43:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.06087","created_at":"2026-07-05T04:43:03Z"},{"alias_kind":"pith_short_12","alias_value":"O2O3LIA5E54Z","created_at":"2026-07-05T04:43:03Z"},{"alias_kind":"pith_short_16","alias_value":"O2O3LIA5E54ZZ4OB","created_at":"2026-07-05T04:43:03Z"},{"alias_kind":"pith_short_8","alias_value":"O2O3LIA5","created_at":"2026-07-05T04:43:03Z"}],"graph_snapshots":[{"event_id":"sha256:486d22ef688061dd5e424de6f3cbd476339fc4d7122e9fa745bedcdc021ffcfc","target":"graph","created_at":"2026-07-05T04:43:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2207.06087/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Private information retrieval (PIR) schemes (with or without colluding servers) have been proposed for realistic coded distributed data storage systems. Star product PIR schemes with colluding servers for general coded distributed storage system were constructed over general finite fields by R. Freij-Hollanti, O. W. Gnilke, C. Hollanti and A. Karpuk in 2017. These star product PIR schemes with colluding servers are suitable for the storage of files over small fields and can be constructed for coded distributed storage system with large number of servers. In this paper for an efficient storage ","authors_text":"Hao Chen, Liqing Xu","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.IT","submitted_at":"2022-07-13T09:54:17Z","title":"Storage and Retrieval Codes in PIR Schemes with Colluding Servers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.06087","kind":"arxiv","version":4},"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:bfe7da16dafe42c8baf277eb2421c5a83b641b6a0460a6e2039569ede05fa57d","target":"record","created_at":"2026-07-05T04:43:03Z","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":"24a56d8cd6c92091c3eb99d3443640ddee75b65cce6717ac3cfe0530a9600691","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.IT","submitted_at":"2022-07-13T09:54:17Z","title_canon_sha256":"bf1d8e87a0f7fd8918bfde663b560892c5930151f30efb1e4ce8e488ee160ac4"},"schema_version":"1.0","source":{"id":"2207.06087","kind":"arxiv","version":4}},"canonical_sha256":"769db5a01d27799cf1c127296a0109b911b16f06bf7a5ca0ce08fb3a76628c6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"769db5a01d27799cf1c127296a0109b911b16f06bf7a5ca0ce08fb3a76628c6e","first_computed_at":"2026-07-05T04:43:03.264409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:43:03.264409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YyLkhjTUDewVT9Flj5d2dZ+A/aZuUlmVlvxDKC69y6fn9NWvWRV8Jj9FIKPe0aG1uDvzDSjLBe6lU8b6F+zdDA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:43:03.264802Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.06087","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfe7da16dafe42c8baf277eb2421c5a83b641b6a0460a6e2039569ede05fa57d","sha256:486d22ef688061dd5e424de6f3cbd476339fc4d7122e9fa745bedcdc021ffcfc"],"state_sha256":"62eed7f2e5729aea28f4085cd4c84bbfa9f62760a6f5e4a1eeee13ec50cbad9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mMAoHcsGDcfep92PixCQ98Od+ct+CVK3YVupZ9hXxzIuj53kY9utSHDz9qbPy+Ket9j1/Tz4S+U3XUP9M39DBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T14:15:06.449236Z","bundle_sha256":"86b900418c05cc54133e46c037b9c67a09321afb9a37c6a4154779c2ef7724a5"}}