{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:W4UAEZEP6QN6OM6F7KEPBREMQZ","short_pith_number":"pith:W4UAEZEP","schema_version":"1.0","canonical_sha256":"b72802648ff41be733c5fa88f0c48c8663eca0ed71f351c8e57cdf2645a0dcc0","source":{"kind":"arxiv","id":"2309.09049","version":2},"attestation_state":"computed","paper":{"title":"Totally Ramified Maximal Tori and Bruhat-Tits theory","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Stephen DeBacker","submitted_at":"2023-09-16T17:15:45Z","abstract_excerpt":"Suppose $k$ is a nonarchimedean local field, $K$ is a maximally unramified extension of $k$, and $\\mathbf{G}$ is a connected reductive $k$-group. If $\\mathbf{T}$ is a $K$-minisotropic maximal $k$-torus in $\\mathbf{G}$, then we use Bruhat-Tits theory to describe the stable classes in the $\\mathbf{G}$-orbit of $\\mathbf{T}$, the rational classes in the $\\mathbf{G}$-orbit of $\\mathbf{T}$, and the $k$-embeddings, up to rational conjugacy, into $\\mathbf{G}$ of $\\mathbf{T}$. We also provide, via Bruhat-Tits theory, a complete and explicit description of: the rational conjugacy classes of $K$-minisotr"},"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":"2309.09049","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RT","submitted_at":"2023-09-16T17:15:45Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"1bd23a25a70e974b579381e59c67490e8b8fa1207798d2f249758fafa5670e47","abstract_canon_sha256":"6f0f078f7f0c5ca8db8c5bb764c733249983738a4e984b617e581e1c21b6bf46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:06:55.036693Z","signature_b64":"3vZlBN90ljZkr8I+RhxugBBBJgJVXhGPXmutQmc/e9zHCvuAk0DaEfQzlVie/RIjVMVgOSNQQ1XCwjH21oHwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b72802648ff41be733c5fa88f0c48c8663eca0ed71f351c8e57cdf2645a0dcc0","last_reissued_at":"2026-07-05T09:06:55.036211Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:06:55.036211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Totally Ramified Maximal Tori and Bruhat-Tits theory","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Stephen DeBacker","submitted_at":"2023-09-16T17:15:45Z","abstract_excerpt":"Suppose $k$ is a nonarchimedean local field, $K$ is a maximally unramified extension of $k$, and $\\mathbf{G}$ is a connected reductive $k$-group. If $\\mathbf{T}$ is a $K$-minisotropic maximal $k$-torus in $\\mathbf{G}$, then we use Bruhat-Tits theory to describe the stable classes in the $\\mathbf{G}$-orbit of $\\mathbf{T}$, the rational classes in the $\\mathbf{G}$-orbit of $\\mathbf{T}$, and the $k$-embeddings, up to rational conjugacy, into $\\mathbf{G}$ of $\\mathbf{T}$. We also provide, via Bruhat-Tits theory, a complete and explicit description of: the rational conjugacy classes of $K$-minisotr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.09049","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/2309.09049/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":"2309.09049","created_at":"2026-07-05T09:06:55.036264+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.09049v2","created_at":"2026-07-05T09:06:55.036264+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.09049","created_at":"2026-07-05T09:06:55.036264+00:00"},{"alias_kind":"pith_short_12","alias_value":"W4UAEZEP6QN6","created_at":"2026-07-05T09:06:55.036264+00:00"},{"alias_kind":"pith_short_16","alias_value":"W4UAEZEP6QN6OM6F","created_at":"2026-07-05T09:06:55.036264+00:00"},{"alias_kind":"pith_short_8","alias_value":"W4UAEZEP","created_at":"2026-07-05T09:06:55.036264+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.07780","citing_title":"Langlands parameters for Moy-Prasad types","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W4UAEZEP6QN6OM6F7KEPBREMQZ","json":"https://pith.science/pith/W4UAEZEP6QN6OM6F7KEPBREMQZ.json","graph_json":"https://pith.science/api/pith-number/W4UAEZEP6QN6OM6F7KEPBREMQZ/graph.json","events_json":"https://pith.science/api/pith-number/W4UAEZEP6QN6OM6F7KEPBREMQZ/events.json","paper":"https://pith.science/paper/W4UAEZEP"},"agent_actions":{"view_html":"https://pith.science/pith/W4UAEZEP6QN6OM6F7KEPBREMQZ","download_json":"https://pith.science/pith/W4UAEZEP6QN6OM6F7KEPBREMQZ.json","view_paper":"https://pith.science/paper/W4UAEZEP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.09049&json=true","fetch_graph":"https://pith.science/api/pith-number/W4UAEZEP6QN6OM6F7KEPBREMQZ/graph.json","fetch_events":"https://pith.science/api/pith-number/W4UAEZEP6QN6OM6F7KEPBREMQZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W4UAEZEP6QN6OM6F7KEPBREMQZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W4UAEZEP6QN6OM6F7KEPBREMQZ/action/storage_attestation","attest_author":"https://pith.science/pith/W4UAEZEP6QN6OM6F7KEPBREMQZ/action/author_attestation","sign_citation":"https://pith.science/pith/W4UAEZEP6QN6OM6F7KEPBREMQZ/action/citation_signature","submit_replication":"https://pith.science/pith/W4UAEZEP6QN6OM6F7KEPBREMQZ/action/replication_record"}},"created_at":"2026-07-05T09:06:55.036264+00:00","updated_at":"2026-07-05T09:06:55.036264+00:00"}