{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HZGC5B24JTPHNNVYAACTBAM7OX","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":"c5975c6a2fd132ff38d5556ac160614ba506ed97b21ccf2b86dc6c54ed26fc55","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-08-13T03:48:42Z","title_canon_sha256":"0cd099708c56a7a5d6ad2fa3bdf25b484de4db4a1d3e0e0d6e604cc13618cff7"},"schema_version":"1.0","source":{"id":"1208.2488","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2488","created_at":"2026-05-18T03:48:57Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2488v1","created_at":"2026-05-18T03:48:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2488","created_at":"2026-05-18T03:48:57Z"},{"alias_kind":"pith_short_12","alias_value":"HZGC5B24JTPH","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HZGC5B24JTPHNNVY","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HZGC5B24","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:d0d4faa3159171f3e68f5f2c1d312b76a0559e91aeeb2ff125f0d9d166e5c683","target":"graph","created_at":"2026-05-18T03:48:57Z","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":"In 2009, Sol\\'{e} and Zinoviev (\\emph{Eur. J. Combin.}, vol. 30, no. 2, pp. 458-467, 2009) proposed an open problem of arithmetic interest to study the period of the inversive pseudorandom number generators (IPRNGs) and to give conditions bearing on $a, b$ to achieve maximal period, we focus on resolving this open problem. In this paper, the period distribution of the IPRNGs over the Galois ring $({\\rm Z}_{p^{e}},+,\\times)$ is considered, where $p>3$ is a prime and $e\\geq 2$ is an integer. The IPRNGs are transformed to 2-dimensional linear feedback shift registers (LFSRs) so that the analysis ","authors_text":"Bo Zhou, Qiankun Song","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-08-13T03:48:42Z","title":"Period Distribution of Inversive Pseudorandom Number Generators Over Galois Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2488","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:f351d50effaf5c34c8dc94cf7578767dda131c37a8b2f11bf51c04725ad6468b","target":"record","created_at":"2026-05-18T03:48:57Z","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":"c5975c6a2fd132ff38d5556ac160614ba506ed97b21ccf2b86dc6c54ed26fc55","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-08-13T03:48:42Z","title_canon_sha256":"0cd099708c56a7a5d6ad2fa3bdf25b484de4db4a1d3e0e0d6e604cc13618cff7"},"schema_version":"1.0","source":{"id":"1208.2488","kind":"arxiv","version":1}},"canonical_sha256":"3e4c2e875c4cde76b6b8000530819f75d3cf42fb6a98d7f9b874dafebb9c1f9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e4c2e875c4cde76b6b8000530819f75d3cf42fb6a98d7f9b874dafebb9c1f9d","first_computed_at":"2026-05-18T03:48:57.718855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:57.718855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6chAdwRIKRpc1eL79ZnnntV75SWa84iU5g3aE+TNjwbff/WVNFvoTqbnTB+gCYAVDMgl9FhpgSxJBX/hxgo8Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:57.719584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2488","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f351d50effaf5c34c8dc94cf7578767dda131c37a8b2f11bf51c04725ad6468b","sha256:d0d4faa3159171f3e68f5f2c1d312b76a0559e91aeeb2ff125f0d9d166e5c683"],"state_sha256":"58174b7929943ba8952dacf8330d8bd7af65890b7138daf822e8a89283f2d8b0"}