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Using this criterion, we generalize a theorem of Jones by proving that if $M$ is a full factor and $\\sigma : G \\rightarrow \\mathrm{Aut}(M)$ is an outer action of a discrete group $G$ whose image in $\\mathrm{Out}(M)$ is discrete then the crossed product von Neumann algebra $M \\rtimes_\\sigma G$ is also a full factor. We apply this result to prove the following conjecture of Tomatsu-Ueda: the continuous core of a type $\\mathrm{III}_1$ factor $M$ is fu"},"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":"1605.09613","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-31T13:10:40Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1298724c8fb7eccdd4d41fc9f21c28f6862d2e1bf69c2539db36899abe7708f3","abstract_canon_sha256":"2ee29e8e483ae2b48d82424ea0a5dd7ff2ab86013649f56fab60346c55d83ea0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:55.164916Z","signature_b64":"sgybj2iRB1G7BazGfcs4LH4I4xW8WyPZQaX1Vhd+D7JW7iPFyvd6yiYZTU1aOrklR9f+2O2wtY2RXCZqfo1zCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7207a90cc29102548e7cea64d345c3c851c5c98a2f3f695b6a00659000af5fe","last_reissued_at":"2026-05-18T00:58:55.164258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:55.164258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral gap characterization of full type III factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Amine Marrakchi","submitted_at":"2016-05-31T13:10:40Z","abstract_excerpt":"We give a spectral gap characterization of fullness for type $\\mathrm{III}$ factors which is the analog of a theorem of Connes in the tracial case. 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