{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HQQV3SMXQFOOYZU33AUSNOHLBH","short_pith_number":"pith:HQQV3SMX","schema_version":"1.0","canonical_sha256":"3c215dc997815cec669bd82926b8eb09f4623fd28851cf89c96f3b72b7bab089","source":{"kind":"arxiv","id":"1803.06095","version":3},"attestation_state":"computed","paper":{"title":"On the Iwasawa asymptotic class number formula for $\\mathbb{Z}_p^r\\rtimes\\mathbb{Z}_p$-extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dingli Liang, Meng Fai Lim","submitted_at":"2018-03-16T07:12:54Z","abstract_excerpt":"Let $p$ be an odd prime and $F_{\\infty,\\infty}$ a $p$-adic Lie extension of a number field $F$ with Galois group isomorphic to $\\mathbb{Z}_p^r\\rtimes\\mathbb{Z}_p$, $r\\geq 1$. Under certain assumptions, we prove an asymptotic formula for the growth of $p$-exponents of the class groups in the said $p$-adic Lie extension. This generalizes a previous result of Lei, where he establishes such a formula in the case $r=1$. An important and new ingredient towards extending Lei's result rests on an asymptotic formula for a finitely generated (not necessarily torsion) $\\mathbb{Z}_p[[\\mathbb{Z}_p^r]]$-mod"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.06095","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-16T07:12:54Z","cross_cats_sorted":[],"title_canon_sha256":"f441769a72efb544d67a88ff225f589f9ed0c62219f113d2a24d756084b68bd5","abstract_canon_sha256":"485f10c9fed7bc4497bef77cfef03bec4d9ecdf3e643518a0ee450f7c1f75141"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:32.683887Z","signature_b64":"A+MKyCbkI1z8f4+GPTfqgJ9TRzF2U1hQBI1TyN9UeM5fXtKRzbLJOU+WwjXoKfMQKZlS6co3Oe/0yvzzBpobAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c215dc997815cec669bd82926b8eb09f4623fd28851cf89c96f3b72b7bab089","last_reissued_at":"2026-05-17T23:44:32.683209Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:32.683209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Iwasawa asymptotic class number formula for $\\mathbb{Z}_p^r\\rtimes\\mathbb{Z}_p$-extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dingli Liang, Meng Fai Lim","submitted_at":"2018-03-16T07:12:54Z","abstract_excerpt":"Let $p$ be an odd prime and $F_{\\infty,\\infty}$ a $p$-adic Lie extension of a number field $F$ with Galois group isomorphic to $\\mathbb{Z}_p^r\\rtimes\\mathbb{Z}_p$, $r\\geq 1$. Under certain assumptions, we prove an asymptotic formula for the growth of $p$-exponents of the class groups in the said $p$-adic Lie extension. This generalizes a previous result of Lei, where he establishes such a formula in the case $r=1$. An important and new ingredient towards extending Lei's result rests on an asymptotic formula for a finitely generated (not necessarily torsion) $\\mathbb{Z}_p[[\\mathbb{Z}_p^r]]$-mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06095","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.06095","created_at":"2026-05-17T23:44:32.683334+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.06095v3","created_at":"2026-05-17T23:44:32.683334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06095","created_at":"2026-05-17T23:44:32.683334+00:00"},{"alias_kind":"pith_short_12","alias_value":"HQQV3SMXQFOO","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HQQV3SMXQFOOYZU3","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HQQV3SMX","created_at":"2026-05-18T12:32:28.185984+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HQQV3SMXQFOOYZU33AUSNOHLBH","json":"https://pith.science/pith/HQQV3SMXQFOOYZU33AUSNOHLBH.json","graph_json":"https://pith.science/api/pith-number/HQQV3SMXQFOOYZU33AUSNOHLBH/graph.json","events_json":"https://pith.science/api/pith-number/HQQV3SMXQFOOYZU33AUSNOHLBH/events.json","paper":"https://pith.science/paper/HQQV3SMX"},"agent_actions":{"view_html":"https://pith.science/pith/HQQV3SMXQFOOYZU33AUSNOHLBH","download_json":"https://pith.science/pith/HQQV3SMXQFOOYZU33AUSNOHLBH.json","view_paper":"https://pith.science/paper/HQQV3SMX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.06095&json=true","fetch_graph":"https://pith.science/api/pith-number/HQQV3SMXQFOOYZU33AUSNOHLBH/graph.json","fetch_events":"https://pith.science/api/pith-number/HQQV3SMXQFOOYZU33AUSNOHLBH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HQQV3SMXQFOOYZU33AUSNOHLBH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HQQV3SMXQFOOYZU33AUSNOHLBH/action/storage_attestation","attest_author":"https://pith.science/pith/HQQV3SMXQFOOYZU33AUSNOHLBH/action/author_attestation","sign_citation":"https://pith.science/pith/HQQV3SMXQFOOYZU33AUSNOHLBH/action/citation_signature","submit_replication":"https://pith.science/pith/HQQV3SMXQFOOYZU33AUSNOHLBH/action/replication_record"}},"created_at":"2026-05-17T23:44:32.683334+00:00","updated_at":"2026-05-17T23:44:32.683334+00:00"}