{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:CFPHAFWKRWLTULTYH5I2WZQJ43","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":"1b67fbd5eaba88029b49e62bfbbb8cc2347bebb1a82e3ac2d0eabf46439e79a1","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2022-06-11T08:39:28Z","title_canon_sha256":"b753b5e17311302adc643e5b080189ffca62af030c768549eacdbc9e62a89923"},"schema_version":"1.0","source":{"id":"2206.05468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.05468","created_at":"2026-07-05T04:30:59Z"},{"alias_kind":"arxiv_version","alias_value":"2206.05468v1","created_at":"2026-07-05T04:30:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.05468","created_at":"2026-07-05T04:30:59Z"},{"alias_kind":"pith_short_12","alias_value":"CFPHAFWKRWLT","created_at":"2026-07-05T04:30:59Z"},{"alias_kind":"pith_short_16","alias_value":"CFPHAFWKRWLTULTY","created_at":"2026-07-05T04:30:59Z"},{"alias_kind":"pith_short_8","alias_value":"CFPHAFWK","created_at":"2026-07-05T04:30:59Z"}],"graph_snapshots":[{"event_id":"sha256:736a683345a01a353d0eb9d55eb28eb7baca76ee8e7bb51284ea6718e5275139","target":"graph","created_at":"2026-07-05T04:30:59Z","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/2206.05468/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate function computation problems under different secure conditions over a network with multiple source nodes and a single sink node which desires a function of all source messages without error. A wiretapper has access to some edges of the network. Based on different practical requirements, we consider two secure conditions named as secure and user secure respectively. The main parameter concerned here is the computing rate, which is the average times of the target function that can be computed securely or user securely without error for one use of the network. In th","authors_text":"Gennian Ge, Minqian Liu, Min Xu","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2022-06-11T08:39:28Z","title":"Network Function Computation With Different Secure Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.05468","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":"sha256:90c2272202d6e4a27415643aa4958cc9962eb4474a7d68e2ce3741cbb0ab88a0","target":"record","created_at":"2026-07-05T04:30:59Z","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":"1b67fbd5eaba88029b49e62bfbbb8cc2347bebb1a82e3ac2d0eabf46439e79a1","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2022-06-11T08:39:28Z","title_canon_sha256":"b753b5e17311302adc643e5b080189ffca62af030c768549eacdbc9e62a89923"},"schema_version":"1.0","source":{"id":"2206.05468","kind":"arxiv","version":1}},"canonical_sha256":"115e7016ca8d973a2e783f51ab6609e6fc9debdee27e055023b6dcb936ada966","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"115e7016ca8d973a2e783f51ab6609e6fc9debdee27e055023b6dcb936ada966","first_computed_at":"2026-07-05T04:30:59.713158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:30:59.713158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WyqM5580m+mJgl0rHe5lvp2eGM4qjAWeOLZcTweTTELoJ4m/ImJGBXuiVRBACmWGgbbBqahDJY83GYKmkr0FDg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:30:59.713710Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.05468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90c2272202d6e4a27415643aa4958cc9962eb4474a7d68e2ce3741cbb0ab88a0","sha256:736a683345a01a353d0eb9d55eb28eb7baca76ee8e7bb51284ea6718e5275139"],"state_sha256":"c8a0948bac7a761161ad75c6a124166a5da8cb5e9a8136f73c7dca3bf0050d7d"}