{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2O2CXUHJSNSOEQMWUWLY5L34LS","short_pith_number":"pith:2O2CXUHJ","schema_version":"1.0","canonical_sha256":"d3b42bd0e99364e24196a5978eaf7c5c9cbe040ecea125fcfc402e10cc378e08","source":{"kind":"arxiv","id":"1412.2418","version":2},"attestation_state":"computed","paper":{"title":"A characterization of fullness of continuous cores of type III$_1$ free product factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Reiji Tomatsu, Yoshimichi Ueda","submitted_at":"2014-12-08T00:27:54Z","abstract_excerpt":"We prove that, for any type III$_1$ free product factor, its continuous core is full if and only if its $\\tau$-invariant is the usual topology on the real line. This trivially implies, as a particular case, the same result for free Araki--Woods factors. Moreover, our method shows the same result for full (generalized) Bernoulli crossed product factors of type III$_1$."},"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":"1412.2418","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-08T00:27:54Z","cross_cats_sorted":[],"title_canon_sha256":"3db020543ebf59fdebc6c1d8adc8ec2a9da52832531da5b728c0a28aaab5c2f6","abstract_canon_sha256":"5537701bb89d7cdcaa8b56faaff44e8eddebd3be41ff804257b68fb59d0cf642"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:53.826413Z","signature_b64":"m6s92JH8mMiH/GfQcMXvNMdxGkHxI3Sk/rf+9nHYP5pLgFt0afRDNOJ0nA+Pfr8zYJ0VX3VH3G4Ix5xuCxfoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3b42bd0e99364e24196a5978eaf7c5c9cbe040ecea125fcfc402e10cc378e08","last_reissued_at":"2026-05-17T23:45:53.825870Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:53.825870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characterization of fullness of continuous cores of type III$_1$ free product factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Reiji Tomatsu, Yoshimichi Ueda","submitted_at":"2014-12-08T00:27:54Z","abstract_excerpt":"We prove that, for any type III$_1$ free product factor, its continuous core is full if and only if its $\\tau$-invariant is the usual topology on the real line. This trivially implies, as a particular case, the same result for free Araki--Woods factors. Moreover, our method shows the same result for full (generalized) Bernoulli crossed product factors of type III$_1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2418","kind":"arxiv","version":2},"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":"1412.2418","created_at":"2026-05-17T23:45:53.825950+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.2418v2","created_at":"2026-05-17T23:45:53.825950+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2418","created_at":"2026-05-17T23:45:53.825950+00:00"},{"alias_kind":"pith_short_12","alias_value":"2O2CXUHJSNSO","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2O2CXUHJSNSOEQMW","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2O2CXUHJ","created_at":"2026-05-18T12:28:11.866339+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/2O2CXUHJSNSOEQMWUWLY5L34LS","json":"https://pith.science/pith/2O2CXUHJSNSOEQMWUWLY5L34LS.json","graph_json":"https://pith.science/api/pith-number/2O2CXUHJSNSOEQMWUWLY5L34LS/graph.json","events_json":"https://pith.science/api/pith-number/2O2CXUHJSNSOEQMWUWLY5L34LS/events.json","paper":"https://pith.science/paper/2O2CXUHJ"},"agent_actions":{"view_html":"https://pith.science/pith/2O2CXUHJSNSOEQMWUWLY5L34LS","download_json":"https://pith.science/pith/2O2CXUHJSNSOEQMWUWLY5L34LS.json","view_paper":"https://pith.science/paper/2O2CXUHJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.2418&json=true","fetch_graph":"https://pith.science/api/pith-number/2O2CXUHJSNSOEQMWUWLY5L34LS/graph.json","fetch_events":"https://pith.science/api/pith-number/2O2CXUHJSNSOEQMWUWLY5L34LS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2O2CXUHJSNSOEQMWUWLY5L34LS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2O2CXUHJSNSOEQMWUWLY5L34LS/action/storage_attestation","attest_author":"https://pith.science/pith/2O2CXUHJSNSOEQMWUWLY5L34LS/action/author_attestation","sign_citation":"https://pith.science/pith/2O2CXUHJSNSOEQMWUWLY5L34LS/action/citation_signature","submit_replication":"https://pith.science/pith/2O2CXUHJSNSOEQMWUWLY5L34LS/action/replication_record"}},"created_at":"2026-05-17T23:45:53.825950+00:00","updated_at":"2026-05-17T23:45:53.825950+00:00"}