{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OPODXW56XFQFRGT4QQOCDFH23U","short_pith_number":"pith:OPODXW56","schema_version":"1.0","canonical_sha256":"73dc3bdbbeb960589a7c841c2194fadd00efafbf494398d2ef7aefe018abd3d7","source":{"kind":"arxiv","id":"1207.6424","version":2},"attestation_state":"computed","paper":{"title":"Formal vector spaces over a local field of positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jared Weinstein","submitted_at":"2012-07-26T22:19:08Z","abstract_excerpt":"Let $O$ be the ring of power series in one variable over a finite field, with $K$ its fraction field. We introduce the notion of a \"formal $K$-vector space\"; this is a certain kind of $K$-vector space object in the category of formal schemes. This concept runs parallel to the established notion of a formal $O$-module, but in many ways formal $K$-vector spaces are much simpler objects. Our main result concerns the Lubin-Tate tower, which plays a vital role in the local Langlands correspondence for $GL_n(K)$. Let $A_m$ be the complete local ring parametrizing deformations of a fixed formal $O$-m"},"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":"1207.6424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-26T22:19:08Z","cross_cats_sorted":[],"title_canon_sha256":"8dbfcf7d9d5cb3750b3ca12923b90d9fa95afebbf00840a127fc9e818c11c9d5","abstract_canon_sha256":"899ab918d31256d889965aa1f5fa4078aec01af47cc09cd7ffc1d87225a4252d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:13.767615Z","signature_b64":"Eai5LWwy3QxgqhidNgieoYHhf2nL9m0LPJHolYSeub5ibwdZiGk/7GqRaFMSIGMxjHBgzaZrGC1Zm2OpPt/fBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73dc3bdbbeb960589a7c841c2194fadd00efafbf494398d2ef7aefe018abd3d7","last_reissued_at":"2026-05-18T03:29:13.766927Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:13.766927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Formal vector spaces over a local field of positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jared Weinstein","submitted_at":"2012-07-26T22:19:08Z","abstract_excerpt":"Let $O$ be the ring of power series in one variable over a finite field, with $K$ its fraction field. We introduce the notion of a \"formal $K$-vector space\"; this is a certain kind of $K$-vector space object in the category of formal schemes. This concept runs parallel to the established notion of a formal $O$-module, but in many ways formal $K$-vector spaces are much simpler objects. Our main result concerns the Lubin-Tate tower, which plays a vital role in the local Langlands correspondence for $GL_n(K)$. Let $A_m$ be the complete local ring parametrizing deformations of a fixed formal $O$-m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6424","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":""},"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":"1207.6424","created_at":"2026-05-18T03:29:13.767061+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.6424v2","created_at":"2026-05-18T03:29:13.767061+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6424","created_at":"2026-05-18T03:29:13.767061+00:00"},{"alias_kind":"pith_short_12","alias_value":"OPODXW56XFQF","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OPODXW56XFQFRGT4","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OPODXW56","created_at":"2026-05-18T12:27:16.716162+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/OPODXW56XFQFRGT4QQOCDFH23U","json":"https://pith.science/pith/OPODXW56XFQFRGT4QQOCDFH23U.json","graph_json":"https://pith.science/api/pith-number/OPODXW56XFQFRGT4QQOCDFH23U/graph.json","events_json":"https://pith.science/api/pith-number/OPODXW56XFQFRGT4QQOCDFH23U/events.json","paper":"https://pith.science/paper/OPODXW56"},"agent_actions":{"view_html":"https://pith.science/pith/OPODXW56XFQFRGT4QQOCDFH23U","download_json":"https://pith.science/pith/OPODXW56XFQFRGT4QQOCDFH23U.json","view_paper":"https://pith.science/paper/OPODXW56","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.6424&json=true","fetch_graph":"https://pith.science/api/pith-number/OPODXW56XFQFRGT4QQOCDFH23U/graph.json","fetch_events":"https://pith.science/api/pith-number/OPODXW56XFQFRGT4QQOCDFH23U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OPODXW56XFQFRGT4QQOCDFH23U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OPODXW56XFQFRGT4QQOCDFH23U/action/storage_attestation","attest_author":"https://pith.science/pith/OPODXW56XFQFRGT4QQOCDFH23U/action/author_attestation","sign_citation":"https://pith.science/pith/OPODXW56XFQFRGT4QQOCDFH23U/action/citation_signature","submit_replication":"https://pith.science/pith/OPODXW56XFQFRGT4QQOCDFH23U/action/replication_record"}},"created_at":"2026-05-18T03:29:13.767061+00:00","updated_at":"2026-05-18T03:29:13.767061+00:00"}