{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TMUMKAGZU6PAAGAFKRLHB7VYPM","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":"9d0dd412819ae7df038c26d4939f80cbc98984c71f80cfc4262600e39fce0215","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-08T19:27:43Z","title_canon_sha256":"38df2d35aee1525186e1ca839c44a3c00877d60c4900bf76631488c1167bfc37"},"schema_version":"1.0","source":{"id":"1602.02705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02705","created_at":"2026-05-18T00:19:31Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02705v1","created_at":"2026-05-18T00:19:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02705","created_at":"2026-05-18T00:19:31Z"},{"alias_kind":"pith_short_12","alias_value":"TMUMKAGZU6PA","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TMUMKAGZU6PAAGAF","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TMUMKAGZ","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:9b0b1366aa05a1af168765c38e34612feabc0ac8bfb366d7aa2c4dd6213e32a8","target":"graph","created_at":"2026-05-18T00:19:31Z","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":"Let N and p be two prime numbers > 3 such that p divides N-1. We estimate the p-rank of the class group of Q(N^(1/p)) in terms of the discrete logarithm, with values un F_p, of certain units. Using the Gross--Koblitz formula and identities on the N-adic Gamma function, we explicitly compute these logarithms. A special case (for which we don't have an elementary proof) of our formula is the following: assume there are some integers $a$, $b$ such that N = (a^p+b^p)/(a+b). Then (a+b)*\\prod_{k=1}^{(N-1)/2} k^{8k} is a p-th power modulo N. Furthermore we give a new proof which doesn't use modular f","authors_text":"Emmanuel Lecouturier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-08T19:27:43Z","title":"Sur le p-rang du groupe des classes de Q(N^1/p)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02705","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":"sha256:6f456f717264f9b02617ba567cb0540d052574583de24869e62876077c303c7f","target":"record","created_at":"2026-05-18T00:19:31Z","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":"9d0dd412819ae7df038c26d4939f80cbc98984c71f80cfc4262600e39fce0215","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-08T19:27:43Z","title_canon_sha256":"38df2d35aee1525186e1ca839c44a3c00877d60c4900bf76631488c1167bfc37"},"schema_version":"1.0","source":{"id":"1602.02705","kind":"arxiv","version":1}},"canonical_sha256":"9b28c500d9a79e001805545670feb87b0ee6676b4b9ca00b4d2b648df7717662","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b28c500d9a79e001805545670feb87b0ee6676b4b9ca00b4d2b648df7717662","first_computed_at":"2026-05-18T00:19:31.228626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:31.228626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U3g7fTHd/jViejJm10u/nrYa10DMaduszHds8GslU5hwELJI4SU5ALR4AuUwsGJodn8WGl3qyu6Z7q+KALaNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:31.229491Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f456f717264f9b02617ba567cb0540d052574583de24869e62876077c303c7f","sha256:9b0b1366aa05a1af168765c38e34612feabc0ac8bfb366d7aa2c4dd6213e32a8"],"state_sha256":"14b852e5a3476501f42240c598905847f4e5068e3d717dbda0905cbea0f9304b"}