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If $\\pi_1(M)$ is almost solvable, M is finitely covered by a torus bundle over the circle. Furthermore, there exist infinitely many hyperbolic 3-manifolds that do not support dynamically coherent partially hyperbolic diffeomorphisms; this list includes the Weeks manifold.\n  If f is a stro"},"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":"1001.1029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-01-07T06:34:50Z","cross_cats_sorted":[],"title_canon_sha256":"c81fbce12fdb29ef8df209420756ad6844be7bc3b56ac795cf9c2a398b72ab6f","abstract_canon_sha256":"1eaa5d8226416ccda7a9ad0567cc8277f856a0cb4743e1af4be7f7dc58317ff5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:04.190613Z","signature_b64":"4u1X0e2evCPS/Ed47Cd6keBrS9es4Rdj2PEZ1Xg3CbS5szUcyC5Fz8w+GC8y1Hl3oXsBD29J/HALRl06m38YBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a7b9b5c0c80f3a9b12888ed3be9f59bfdcd3af851e707eb352edfdfc5e114d0","last_reissued_at":"2026-05-18T02:10:04.190267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:04.190267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On 3-manifolds that support partially hyperbolic diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kamlesh Parwani","submitted_at":"2010-01-07T06:34:50Z","abstract_excerpt":"Let M be a closed 3-manifold that supports a partially hyperbolic diffeomorphism f. If $\\pi_1(M)$ is nilpotent, the induced action of f on $H_1(M, R)$ is partially hyperbolic. If $\\pi_1(M)$ is almost nilpotent or if $\\pi_1(M)$ has subexponential growth, M is finitely covered by a circle bundle over the torus. If $\\pi_1(M)$ is almost solvable, M is finitely covered by a torus bundle over the circle. Furthermore, there exist infinitely many hyperbolic 3-manifolds that do not support dynamically coherent partially hyperbolic diffeomorphisms; this list includes the Weeks manifold.\n  If f is a stro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1029","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":"1001.1029","created_at":"2026-05-18T02:10:04.190323+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.1029v1","created_at":"2026-05-18T02:10:04.190323+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1029","created_at":"2026-05-18T02:10:04.190323+00:00"},{"alias_kind":"pith_short_12","alias_value":"HJ5ZWXAMQDZ2","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"HJ5ZWXAMQDZ2TMJI","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"HJ5ZWXAM","created_at":"2026-05-18T12:26:07.630475+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/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP","json":"https://pith.science/pith/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP.json","graph_json":"https://pith.science/api/pith-number/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP/graph.json","events_json":"https://pith.science/api/pith-number/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP/events.json","paper":"https://pith.science/paper/HJ5ZWXAM"},"agent_actions":{"view_html":"https://pith.science/pith/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP","download_json":"https://pith.science/pith/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP.json","view_paper":"https://pith.science/paper/HJ5ZWXAM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.1029&json=true","fetch_graph":"https://pith.science/api/pith-number/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP/graph.json","fetch_events":"https://pith.science/api/pith-number/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP/action/storage_attestation","attest_author":"https://pith.science/pith/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP/action/author_attestation","sign_citation":"https://pith.science/pith/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP/action/citation_signature","submit_replication":"https://pith.science/pith/HJ5ZWXAMQDZ2TMJIRDWTX2PVTP/action/replication_record"}},"created_at":"2026-05-18T02:10:04.190323+00:00","updated_at":"2026-05-18T02:10:04.190323+00:00"}