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Denote $G = \\G(K_\\mathcal{S})$, $T = \\te(K_\\mathcal{S})$ and $\\Gamma = \\G(\\OO)$. Let $T\\pi(g)$ be a locally divergent orbit for the action of $T$ on $G/\\Gamma$ by left translations. We prove: ($1$) if $\\# S = 2$ then the closure $\\overline{T\\pi(g)}$ is a union of finitely"},"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":"1502.02297","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-08T20:25:04Z","cross_cats_sorted":[],"title_canon_sha256":"5e083f25c6e485e7c5c7fead9d04c8e3658b0fd21546ae7d543593383b6653d5","abstract_canon_sha256":"834cb6ba1c02529e8f46a8c0b0385519a482091987fbd9442aa2e4a91af13154"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:46.948397Z","signature_b64":"zS8gwnLs4gd6x7VVitj2KkWFJsMNoyc15Lit5VhXmMXThjjkiEQKb/3QnewP3B0fDxqtSDaxlDSwATDIgd68Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8883012a12c51f6b097cc48d08ffb7fdb9c2bdd46a5e78cc96ef3c52ab974667","last_reissued_at":"2026-05-18T00:21:46.947692Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:46.947692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Locally divergent orbits of maximal tori and values of forms at integral points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"George Tomanov","submitted_at":"2015-02-08T20:25:04Z","abstract_excerpt":"Let $\\G$ be a semisimple algebraic group defined over a number field $K$, $\\te$ a maximal $K$-split torus of $\\G$, $\\mathcal{S}$ a finite set of valuations of $K$ containing the archimedean ones, $\\OO$ the ring of $\\mathcal{S}$-integers of $K$ and $K_\\mathcal{S}$ the direct product of the completions $K_v, v \\in \\mathcal{S}$. Denote $G = \\G(K_\\mathcal{S})$, $T = \\te(K_\\mathcal{S})$ and $\\Gamma = \\G(\\OO)$. Let $T\\pi(g)$ be a locally divergent orbit for the action of $T$ on $G/\\Gamma$ by left translations. We prove: ($1$) if $\\# S = 2$ then the closure $\\overline{T\\pi(g)}$ is a union of finitely"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02297","kind":"arxiv","version":5},"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":"1502.02297","created_at":"2026-05-18T00:21:46.947810+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.02297v5","created_at":"2026-05-18T00:21:46.947810+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02297","created_at":"2026-05-18T00:21:46.947810+00:00"},{"alias_kind":"pith_short_12","alias_value":"RCBQCKQSYUPW","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RCBQCKQSYUPWWCL4","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RCBQCKQS","created_at":"2026-05-18T12:29:39.896362+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/RCBQCKQSYUPWWCL4YSGQR75X7W","json":"https://pith.science/pith/RCBQCKQSYUPWWCL4YSGQR75X7W.json","graph_json":"https://pith.science/api/pith-number/RCBQCKQSYUPWWCL4YSGQR75X7W/graph.json","events_json":"https://pith.science/api/pith-number/RCBQCKQSYUPWWCL4YSGQR75X7W/events.json","paper":"https://pith.science/paper/RCBQCKQS"},"agent_actions":{"view_html":"https://pith.science/pith/RCBQCKQSYUPWWCL4YSGQR75X7W","download_json":"https://pith.science/pith/RCBQCKQSYUPWWCL4YSGQR75X7W.json","view_paper":"https://pith.science/paper/RCBQCKQS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.02297&json=true","fetch_graph":"https://pith.science/api/pith-number/RCBQCKQSYUPWWCL4YSGQR75X7W/graph.json","fetch_events":"https://pith.science/api/pith-number/RCBQCKQSYUPWWCL4YSGQR75X7W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RCBQCKQSYUPWWCL4YSGQR75X7W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RCBQCKQSYUPWWCL4YSGQR75X7W/action/storage_attestation","attest_author":"https://pith.science/pith/RCBQCKQSYUPWWCL4YSGQR75X7W/action/author_attestation","sign_citation":"https://pith.science/pith/RCBQCKQSYUPWWCL4YSGQR75X7W/action/citation_signature","submit_replication":"https://pith.science/pith/RCBQCKQSYUPWWCL4YSGQR75X7W/action/replication_record"}},"created_at":"2026-05-18T00:21:46.947810+00:00","updated_at":"2026-05-18T00:21:46.947810+00:00"}