{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WR6WIYIZGTVWM2YPK5SQ2PENOL","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":"8b833c8b08fc02fc3c6be476e112c0d287fd63faa86f27e98024f3e0d4f0ad1a","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-20T19:02:36Z","title_canon_sha256":"77a9d60d5f52ee2b78ead9684f604bd093f12b8dc6c2405012384eacec5acda3"},"schema_version":"1.0","source":{"id":"1410.2182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2182","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2182v1","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2182","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"WR6WIYIZGTVW","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WR6WIYIZGTVWM2YP","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WR6WIYIZ","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:6ed7b73699f8c7edf6ef4caf2eb03966584d434cef02ca6fa62f8e854330e194","target":"graph","created_at":"2026-05-18T01:19:14Z","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 Euler quotient modulo an odd-prime power $p^r~(r>1)$ can be uniquely decomposed as a $p$-adic number of the form $$ \\frac{u^{(p-1)p^{r-1}} -1}{p^r}\\equiv a_0(u)+a_1(u)p+\\ldots+a_{r-1}(u)p^{r-1} \\pmod {p^r},~ \\gcd(u,p)=1, $$ where $0\\le a_j(u)<p$ for $0\\le j\\le r-1$ and we set all $a_j(u)=0$ if $\\gcd(u,p)>1$. We firstly study certain arithmetic properties of the level sequences $(a_j(u))_{u\\ge 0}$ over $\\mathbb{F}_p$ via introducing a new quotient. Then we determine the exact values of linear complexity of $(a_j(u))_{u\\ge 0}$ and values of $k$-error linear complexity for binary sequences de","authors_text":"Xiaoni Du, Zhihua Niu, Zhixiong Chen","cross_cats":["cs.CR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-20T19:02:36Z","title":"Linear complexity problems of level sequences of Euler quotients and their related binary sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2182","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:ba574ba9496258b1fe2da12c6c7bb82d67dfe41c085760e92172678cc44166a6","target":"record","created_at":"2026-05-18T01:19:14Z","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":"8b833c8b08fc02fc3c6be476e112c0d287fd63faa86f27e98024f3e0d4f0ad1a","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-20T19:02:36Z","title_canon_sha256":"77a9d60d5f52ee2b78ead9684f604bd093f12b8dc6c2405012384eacec5acda3"},"schema_version":"1.0","source":{"id":"1410.2182","kind":"arxiv","version":1}},"canonical_sha256":"b47d64611934eb666b0f57650d3c8d72eafdf9f39ce9cdcdebb4d28ed6ac49d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b47d64611934eb666b0f57650d3c8d72eafdf9f39ce9cdcdebb4d28ed6ac49d7","first_computed_at":"2026-05-18T01:19:14.287918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:14.287918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z/cRG2UZShdOuV4t3GY5c8yPnrs6a9bf2NR1wrXPMhyucW9E9C61FROzLzoft8J0kLv9migxJIue889R7NXSBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:14.288552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba574ba9496258b1fe2da12c6c7bb82d67dfe41c085760e92172678cc44166a6","sha256:6ed7b73699f8c7edf6ef4caf2eb03966584d434cef02ca6fa62f8e854330e194"],"state_sha256":"c6dc8d3a79de46a24f00746f0003b50613360ce4b4a37cbffe2c129a0fbec4c7"}