{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YNI7B5S2ZRAY6X2VLHT7A7QLCL","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":"80fe3c5f5d1ce0234c088a5385ca5896ac8bdf82bfb0209d91f1354c63c7cee4","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-04T20:15:42Z","title_canon_sha256":"dbcbb4b4b8f054a4499437dcaadce572daa4d687da5d0282679439b692dad1bd"},"schema_version":"1.0","source":{"id":"1312.1311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1311","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1311v1","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1311","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"YNI7B5S2ZRAY","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YNI7B5S2ZRAY6X2V","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YNI7B5S2","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:57f6de9486969ebc089f9daed3a8d2010b00bd370238a88f86527dda44653e0c","target":"graph","created_at":"2026-05-18T03:05:28Z","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 investigate the periodic structure of the exponential pseudorandom number generator obtained from the map $x\\mapsto g^x\\pmod p$ that acts on the set $\\{1, \\ldots, p-1\\}$.","authors_text":"Igor E. Shparlinski, Jonas Kaszian, Pieter Moree","cross_cats":["cs.CR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-04T20:15:42Z","title":"Periodic Structure of the Exponential Pseudorandom Number Generator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1311","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:bb7e942b6518f6ca787fc43dcf5ac5a63f7cbb0cf68fcb8b052d886ec230b9dc","target":"record","created_at":"2026-05-18T03:05:28Z","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":"80fe3c5f5d1ce0234c088a5385ca5896ac8bdf82bfb0209d91f1354c63c7cee4","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-04T20:15:42Z","title_canon_sha256":"dbcbb4b4b8f054a4499437dcaadce572daa4d687da5d0282679439b692dad1bd"},"schema_version":"1.0","source":{"id":"1312.1311","kind":"arxiv","version":1}},"canonical_sha256":"c351f0f65acc418f5f5559e7f07e0b12ca35432069898c0c9791147ee1e77116","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c351f0f65acc418f5f5559e7f07e0b12ca35432069898c0c9791147ee1e77116","first_computed_at":"2026-05-18T03:05:28.835014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:28.835014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w7Ikdl4qTHROyuFrbhASbB4kBzF0ZHrxTYxKU8xb0gc036r1JyezakwaXwcqVIbRxZnoJBn7Hunq8EWCrkr9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:28.836050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb7e942b6518f6ca787fc43dcf5ac5a63f7cbb0cf68fcb8b052d886ec230b9dc","sha256:57f6de9486969ebc089f9daed3a8d2010b00bd370238a88f86527dda44653e0c"],"state_sha256":"32c5819ebab47bd7c4db4d307a80914bf4661faf83b37f45423b422041dd8f29"}