{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:64QHVEGMFEICKSHHZ2TE2NC4HS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2ee29e8e483ae2b48d82424ea0a5dd7ff2ab86013649f56fab60346c55d83ea0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-31T13:10:40Z","title_canon_sha256":"1298724c8fb7eccdd4d41fc9f21c28f6862d2e1bf69c2539db36899abe7708f3"},"schema_version":"1.0","source":{"id":"1605.09613","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09613","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09613v5","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09613","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"64QHVEGMFEIC","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"64QHVEGMFEICKSHH","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"64QHVEGM","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:3d50580d8ea1cb51ce57558f4b6021430d959b2fa75af1afa9742e6b31d6ea71","target":"graph","created_at":"2026-05-18T00:58:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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. 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","authors_text":"Amine Marrakchi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-31T13:10:40Z","title":"Spectral gap characterization of full type III factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09613","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:62e2ae59dbd1935965c60c91043648592c1a5b88e5970cc40253765616f28475","target":"record","created_at":"2026-05-18T00:58:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2ee29e8e483ae2b48d82424ea0a5dd7ff2ab86013649f56fab60346c55d83ea0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-31T13:10:40Z","title_canon_sha256":"1298724c8fb7eccdd4d41fc9f21c28f6862d2e1bf69c2539db36899abe7708f3"},"schema_version":"1.0","source":{"id":"1605.09613","kind":"arxiv","version":5}},"canonical_sha256":"f7207a90cc29102548e7cea64d345c3c851c5c98a2f3f695b6a00659000af5fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7207a90cc29102548e7cea64d345c3c851c5c98a2f3f695b6a00659000af5fe","first_computed_at":"2026-05-18T00:58:55.164258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:55.164258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sgybj2iRB1G7BazGfcs4LH4I4xW8WyPZQaX1Vhd+D7JW7iPFyvd6yiYZTU1aOrklR9f+2O2wtY2RXCZqfo1zCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:55.164916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.09613","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62e2ae59dbd1935965c60c91043648592c1a5b88e5970cc40253765616f28475","sha256:3d50580d8ea1cb51ce57558f4b6021430d959b2fa75af1afa9742e6b31d6ea71"],"state_sha256":"cf5d6218c7d4e077641b1f4d4898c0b3ae34d03587cbd5aaaf337a744ee7abb0"}