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Otherwise, F admits a pair of transverse very full genuine laminations.\n  In the second case, M satisfies the weak geometrization conjecture - either its fundamental group contains Z+Z or it is word-hyperbolic. Moreover, if M is atoroidal, the mapping class group of M is finite, and any automorphism homotopic to the identity is isotopi"},"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/0210148","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2002-10-10T00:53:52Z","cross_cats_sorted":[],"title_canon_sha256":"351c3a58ae148be00b0b27832c55602cad512a8dba6669f94eb75db7fb5e247e","abstract_canon_sha256":"1c8ac26408bd2d3e1662e63af55fb5972af875185bafced10eb6a72025388813"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:29.398585Z","signature_b64":"t1Iz8wCIQRtjS2iLYGOHC3kaPc9E/zqGtSkVuX4ti7jQmtnPUYXBQgbA2LDL76RuNHCLhj5vY7AAOA9cvYHSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"268e43d36999308c373b9a8e2c4de741004d1de9da09cf65c9e9c1bedd3fe7bf","last_reissued_at":"2026-05-18T01:38:29.397919Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:29.397919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Promoting Essential Laminations","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Danny Calegari","submitted_at":"2002-10-10T00:53:52Z","abstract_excerpt":"We show that every co--orientable taut foliation F of an orientable, atoroidal 3-manifold admits a transverse essential lamination. 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