{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:6BOHOQOIYANZCW3ZENKY6AOKCY","short_pith_number":"pith:6BOHOQOI","schema_version":"1.0","canonical_sha256":"f05c7741c8c01b915b7923558f01ca161c63ea5ddf0e0198eaae4be28cfa912f","source":{"kind":"arxiv","id":"2505.24064","version":2},"attestation_state":"computed","paper":{"title":"Multivariable period rings of $p$-adic false Tate curve extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yijun Yuan","submitted_at":"2025-05-29T23:16:46Z","abstract_excerpt":"Let $p\\geq 3$ be a prime number and $K$ be a finite extension of $\\mathbf{Q}_p$ with uniformizer $\\pi_K$. In this article, we introduce two multivariable period rings $\\mathbf{A}_{\\mathfrak{F},K}^{\\operatorname{np}}$ and $\\mathbf{A}_{\\mathfrak{F},K}^{\\operatorname{np},\\operatorname{c}}$ for the \\'etale $(\\varphi,\\Gamma_{\\mathfrak{F},K})$-modules of $p$-adic false Tate curve extension $K\\left(\\pi_K^{1/p^\\infty},\\zeta_{p^\\infty}\\right)$. Various properties of these rings are studied and as applications, we show that $(\\varphi,\\Gamma_{\\mathfrak{F},K})$-modules over these rings bridge $(\\varphi,\\G"},"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":"2505.24064","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-05-29T23:16:46Z","cross_cats_sorted":[],"title_canon_sha256":"d26dc08ea0c4da7fc40f910d51adbc85b96aeb0ada6b831459a5935c40a2f22b","abstract_canon_sha256":"a2368dad94c9a808ccb323951db371dcc744dd385e8e33cb83be1b67c1a6416c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:51.708670Z","signature_b64":"+/mLyfrsWNIqaLdLe8NClPqRe86+4XZLaDR0Ijl6yRH7L5mLjBdL391nVH6NzKsqiHv6wluhjFTUQZFrFdnaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f05c7741c8c01b915b7923558f01ca161c63ea5ddf0e0198eaae4be28cfa912f","last_reissued_at":"2026-07-05T11:34:51.708180Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:51.708180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multivariable period rings of $p$-adic false Tate curve extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yijun Yuan","submitted_at":"2025-05-29T23:16:46Z","abstract_excerpt":"Let $p\\geq 3$ be a prime number and $K$ be a finite extension of $\\mathbf{Q}_p$ with uniformizer $\\pi_K$. In this article, we introduce two multivariable period rings $\\mathbf{A}_{\\mathfrak{F},K}^{\\operatorname{np}}$ and $\\mathbf{A}_{\\mathfrak{F},K}^{\\operatorname{np},\\operatorname{c}}$ for the \\'etale $(\\varphi,\\Gamma_{\\mathfrak{F},K})$-modules of $p$-adic false Tate curve extension $K\\left(\\pi_K^{1/p^\\infty},\\zeta_{p^\\infty}\\right)$. Various properties of these rings are studied and as applications, we show that $(\\varphi,\\Gamma_{\\mathfrak{F},K})$-modules over these rings bridge $(\\varphi,\\G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24064","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.24064/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2505.24064","created_at":"2026-07-05T11:34:51.708236+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.24064v2","created_at":"2026-07-05T11:34:51.708236+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24064","created_at":"2026-07-05T11:34:51.708236+00:00"},{"alias_kind":"pith_short_12","alias_value":"6BOHOQOIYANZ","created_at":"2026-07-05T11:34:51.708236+00:00"},{"alias_kind":"pith_short_16","alias_value":"6BOHOQOIYANZCW3Z","created_at":"2026-07-05T11:34:51.708236+00:00"},{"alias_kind":"pith_short_8","alias_value":"6BOHOQOI","created_at":"2026-07-05T11:34:51.708236+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/6BOHOQOIYANZCW3ZENKY6AOKCY","json":"https://pith.science/pith/6BOHOQOIYANZCW3ZENKY6AOKCY.json","graph_json":"https://pith.science/api/pith-number/6BOHOQOIYANZCW3ZENKY6AOKCY/graph.json","events_json":"https://pith.science/api/pith-number/6BOHOQOIYANZCW3ZENKY6AOKCY/events.json","paper":"https://pith.science/paper/6BOHOQOI"},"agent_actions":{"view_html":"https://pith.science/pith/6BOHOQOIYANZCW3ZENKY6AOKCY","download_json":"https://pith.science/pith/6BOHOQOIYANZCW3ZENKY6AOKCY.json","view_paper":"https://pith.science/paper/6BOHOQOI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.24064&json=true","fetch_graph":"https://pith.science/api/pith-number/6BOHOQOIYANZCW3ZENKY6AOKCY/graph.json","fetch_events":"https://pith.science/api/pith-number/6BOHOQOIYANZCW3ZENKY6AOKCY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6BOHOQOIYANZCW3ZENKY6AOKCY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6BOHOQOIYANZCW3ZENKY6AOKCY/action/storage_attestation","attest_author":"https://pith.science/pith/6BOHOQOIYANZCW3ZENKY6AOKCY/action/author_attestation","sign_citation":"https://pith.science/pith/6BOHOQOIYANZCW3ZENKY6AOKCY/action/citation_signature","submit_replication":"https://pith.science/pith/6BOHOQOIYANZCW3ZENKY6AOKCY/action/replication_record"}},"created_at":"2026-07-05T11:34:51.708236+00:00","updated_at":"2026-07-05T11:34:51.708236+00:00"}