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Let $G = \\G(K_\\mathcal{S})$, $\\Gamma = \\G(\\OO)$ and $\\pi:G \\rightarrow G/\\Gamma$ the quotient map. We describe the closures of the locally divergent orbits ${T\\pi(g)}$ %in $G/\\Gamma$ where $T$ is a maximal $K_\\mathcal{S}$-split torus in $G$. If $\\# S = 2$ then the closure $\\overline{T\\pi(g)}$ is a finite union of $T$-orbits stratified in terms of parabol"},"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":"1801.02497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-05T10:53:37Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"bdb05e04cf2a77b1e99ac5b998d84e331c5e7dffca7931bf1b9767f25f3a7cce","abstract_canon_sha256":"089058685e7f969d74ddcb6fc9bc64e5e37ae441044f2ef4b099bdd554e378a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:31.368695Z","signature_b64":"ac62lCp7LGBsSV+Etwwp0m1GhkNBO0DN7BQeQQrZ7o0Nz3Ibhx+r08rnouEHDZsUxfgWC/BBKE/joyPUDsdIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"213403a80af28604ca5b80d48f774fdac50b4c1cfc4aea46a6fb786d6ef021bb","last_reissued_at":"2026-05-18T00:26:31.367952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:31.367952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closures of locally divergent orbits of maximal tori and values of homogeneous forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"George Tomanov","submitted_at":"2018-01-05T10:53:37Z","abstract_excerpt":"Let $\\G$ be a semisimple algebraic group over a number field $K$, $\\mathcal{S}$ a finite set of places of $K$, $K_\\mathcal{S}$ the direct product of the completions $K_v, v \\in \\mathcal{S}$, and $\\OO$ the ring of $\\mathcal{S}$-integers of $K$. Let $G = \\G(K_\\mathcal{S})$, $\\Gamma = \\G(\\OO)$ and $\\pi:G \\rightarrow G/\\Gamma$ the quotient map. We describe the closures of the locally divergent orbits ${T\\pi(g)}$ %in $G/\\Gamma$ where $T$ is a maximal $K_\\mathcal{S}$-split torus in $G$. If $\\# S = 2$ then the closure $\\overline{T\\pi(g)}$ is a finite union of $T$-orbits stratified in terms of parabol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02497","kind":"arxiv","version":1},"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":"1801.02497","created_at":"2026-05-18T00:26:31.368078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.02497v1","created_at":"2026-05-18T00:26:31.368078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02497","created_at":"2026-05-18T00:26:31.368078+00:00"},{"alias_kind":"pith_short_12","alias_value":"EE2AHKAK6KDA","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EE2AHKAK6KDAJSS3","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EE2AHKAK","created_at":"2026-05-18T12:32:22.470017+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/EE2AHKAK6KDAJSS3QDKI652P3L","json":"https://pith.science/pith/EE2AHKAK6KDAJSS3QDKI652P3L.json","graph_json":"https://pith.science/api/pith-number/EE2AHKAK6KDAJSS3QDKI652P3L/graph.json","events_json":"https://pith.science/api/pith-number/EE2AHKAK6KDAJSS3QDKI652P3L/events.json","paper":"https://pith.science/paper/EE2AHKAK"},"agent_actions":{"view_html":"https://pith.science/pith/EE2AHKAK6KDAJSS3QDKI652P3L","download_json":"https://pith.science/pith/EE2AHKAK6KDAJSS3QDKI652P3L.json","view_paper":"https://pith.science/paper/EE2AHKAK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.02497&json=true","fetch_graph":"https://pith.science/api/pith-number/EE2AHKAK6KDAJSS3QDKI652P3L/graph.json","fetch_events":"https://pith.science/api/pith-number/EE2AHKAK6KDAJSS3QDKI652P3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EE2AHKAK6KDAJSS3QDKI652P3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EE2AHKAK6KDAJSS3QDKI652P3L/action/storage_attestation","attest_author":"https://pith.science/pith/EE2AHKAK6KDAJSS3QDKI652P3L/action/author_attestation","sign_citation":"https://pith.science/pith/EE2AHKAK6KDAJSS3QDKI652P3L/action/citation_signature","submit_replication":"https://pith.science/pith/EE2AHKAK6KDAJSS3QDKI652P3L/action/replication_record"}},"created_at":"2026-05-18T00:26:31.368078+00:00","updated_at":"2026-05-18T00:26:31.368078+00:00"}