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We define a certain closed subgroup~$\\GOS$ of $\\Ga_S = \\prod_{v \\in S} \\Ga_{K_v}$ that contains $\\Ga_{\\theints}$, and prove that $\\Ga_{\\theints}$ is a superrigid lattice in~$\\GOS$, by which we mean that finite-dimensional representations $\\alpha\\colon \\Ga_{\\theints} \\to \\GL_n(\\real)$ more-or-less extend to representations of~$\\GOS$.\n  The subgroup~$\\GOS$ may be a proper subgroup "},"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":"math/9611219","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"1996-11-19T00:00:00Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"4ae68e4f633a8d69715774b2cda7bf7a723161e67506ac81a121ec872d2f2df8","abstract_canon_sha256":"862ed128d7c4bbf5c325aba68ee725fd02876cf3547c331f2db1829235e770d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:46.879695Z","signature_b64":"hKruerHvotcqlOgZP1EIN2v/PGABmuV/9i9kPZUfoUG6oMtoNkgtvX0yA6yTF8CJfW+jZaxwxjY7PScKVmBHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b15f30be3d21ac5ffb254d2ab66765348799dbecaa451f61ba7009f57df5dd8","last_reissued_at":"2026-05-18T01:05:46.879250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:46.879250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Archimedean superrigidity of solvable S-arithmetic groups","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Dave Witte","submitted_at":"1996-11-19T00:00:00Z","abstract_excerpt":"Let $\\Ga$ be a connected, solvable linear algebraic group over a number field~$K$, let $S$ be a finite set of places of~$K$ that contains all the infinite places, and let $\\theints$ be the ring of $S$-integers of~$K$. We define a certain closed subgroup~$\\GOS$ of $\\Ga_S = \\prod_{v \\in S} \\Ga_{K_v}$ that contains $\\Ga_{\\theints}$, and prove that $\\Ga_{\\theints}$ is a superrigid lattice in~$\\GOS$, by which we mean that finite-dimensional representations $\\alpha\\colon \\Ga_{\\theints} \\to \\GL_n(\\real)$ more-or-less extend to representations of~$\\GOS$.\n  The subgroup~$\\GOS$ may be a proper subgroup "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9611219","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":"math/9611219","created_at":"2026-05-18T01:05:46.879326+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9611219v1","created_at":"2026-05-18T01:05:46.879326+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9611219","created_at":"2026-05-18T01:05:46.879326+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMK7GC7D2INM","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMK7GC7D2INML75S","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMK7GC7D","created_at":"2026-05-18T12:25:48.327863+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/LMK7GC7D2INML75SKTJKWZTWKN","json":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN.json","graph_json":"https://pith.science/api/pith-number/LMK7GC7D2INML75SKTJKWZTWKN/graph.json","events_json":"https://pith.science/api/pith-number/LMK7GC7D2INML75SKTJKWZTWKN/events.json","paper":"https://pith.science/paper/LMK7GC7D"},"agent_actions":{"view_html":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN","download_json":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN.json","view_paper":"https://pith.science/paper/LMK7GC7D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9611219&json=true","fetch_graph":"https://pith.science/api/pith-number/LMK7GC7D2INML75SKTJKWZTWKN/graph.json","fetch_events":"https://pith.science/api/pith-number/LMK7GC7D2INML75SKTJKWZTWKN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN/action/storage_attestation","attest_author":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN/action/author_attestation","sign_citation":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN/action/citation_signature","submit_replication":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN/action/replication_record"}},"created_at":"2026-05-18T01:05:46.879326+00:00","updated_at":"2026-05-18T01:05:46.879326+00:00"}