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This confirms a conjecture on Zimmer's program for these manifolds."},"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":"1601.02314","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-01-11T03:48:46Z","cross_cats_sorted":["math.AT","math.DS"],"title_canon_sha256":"9804c5faf5350fe9eed05803564f8386979297da8736cd295b9e27cf79428ac5","abstract_canon_sha256":"f9b3a800ccfda1873976010c0a6c31b6f43b3396d105b1fa0265ef6e33001447"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:06.740635Z","signature_b64":"NByKb6hivwU2uXk+8N/YlEm+kNdLqn22RjtZnERRgEDYKsYTrzgvCjgGit4tKiEtxAjJnEcjN2LalAUc9RYpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20a82918f8b90db7dad7366b8d835d5fced39596d807056a1fca847a9a1c8402","last_reissued_at":"2026-05-18T01:23:06.740174Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:06.740174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix group actions on product of spheres and Zimmer's program","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.DS"],"primary_cat":"math.GT","authors_text":"Shengkui Ye","submitted_at":"2016-01-11T03:48:46Z","abstract_excerpt":"Let SL(n,Z) be the special linear group over integers and $M =S^r_1 \\times S^r_2,T^r_1 \\times S^r_2$ , or $T^r_0 \\times S^r_1 \\times S^r_2$, products of spheres and tori. We prove that any group action of SL(n,Z) on $M^r$ by diffeomorphims or piecewise linear homeomorphisms is trivial if $r<n-1$. This confirms a conjecture on Zimmer's program for these manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02314","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":"1601.02314","created_at":"2026-05-18T01:23:06.740256+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.02314v1","created_at":"2026-05-18T01:23:06.740256+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02314","created_at":"2026-05-18T01:23:06.740256+00:00"},{"alias_kind":"pith_short_12","alias_value":"ECUCSGHYXEG3","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"ECUCSGHYXEG3PWWX","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"ECUCSGHY","created_at":"2026-05-18T12:30:12.583610+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/ECUCSGHYXEG3PWWXGZVY3A25L7","json":"https://pith.science/pith/ECUCSGHYXEG3PWWXGZVY3A25L7.json","graph_json":"https://pith.science/api/pith-number/ECUCSGHYXEG3PWWXGZVY3A25L7/graph.json","events_json":"https://pith.science/api/pith-number/ECUCSGHYXEG3PWWXGZVY3A25L7/events.json","paper":"https://pith.science/paper/ECUCSGHY"},"agent_actions":{"view_html":"https://pith.science/pith/ECUCSGHYXEG3PWWXGZVY3A25L7","download_json":"https://pith.science/pith/ECUCSGHYXEG3PWWXGZVY3A25L7.json","view_paper":"https://pith.science/paper/ECUCSGHY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.02314&json=true","fetch_graph":"https://pith.science/api/pith-number/ECUCSGHYXEG3PWWXGZVY3A25L7/graph.json","fetch_events":"https://pith.science/api/pith-number/ECUCSGHYXEG3PWWXGZVY3A25L7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ECUCSGHYXEG3PWWXGZVY3A25L7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ECUCSGHYXEG3PWWXGZVY3A25L7/action/storage_attestation","attest_author":"https://pith.science/pith/ECUCSGHYXEG3PWWXGZVY3A25L7/action/author_attestation","sign_citation":"https://pith.science/pith/ECUCSGHYXEG3PWWXGZVY3A25L7/action/citation_signature","submit_replication":"https://pith.science/pith/ECUCSGHYXEG3PWWXGZVY3A25L7/action/replication_record"}},"created_at":"2026-05-18T01:23:06.740256+00:00","updated_at":"2026-05-18T01:23:06.740256+00:00"}