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Given two unital inclusions $B_i\\subseteq M_i$ of von Neumann algebras, we examine groupoid normalisers for the tensor product inclusion $B_1\\ \\overline{\\otimes}\\ B_2\\subseteq M_1\\ \\overline{\\otimes}\\ M_2$ establishing the formula $$ \\mathcal{GN}_{M_1\\,\\overline{\\otimes}\\,M_2}(B_1\\ \\overline{\\otimes}\\ B_2)''=\\mathcal{GN}_{M_1}(B_1)''\\ \\overline{\\otimes}\\ \\mathcal{GN}_{M_2}(B_2)'' $$ when one i"},"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":"1004.0851","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-04-06T13:43:02Z","cross_cats_sorted":[],"title_canon_sha256":"7bd22f20b74355b2e02f39faa8b15e571b2375895121631a471cfa7fd56bd155","abstract_canon_sha256":"a564af3ba9c6470cdbe3bcc84437d8ac6c6c7d8035bd25989679f3722d9f84b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:46.002777Z","signature_b64":"afaj4NMcN3pssfAjESKT2kj1pYQKLbQdGOXAYaGS4FunfzHpimmfgX4w6G9qty93upTczcbfua0Raya46u7VBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03029a66125f97b7b0da46ba72749629420f3785e13c344b01406c81d9e22d9e","last_reissued_at":"2026-05-18T01:34:46.002156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:46.002156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Groupoid normalisers of tensor products: infinite von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Junsheng Fang, Roger R. 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Given two unital inclusions $B_i\\subseteq M_i$ of von Neumann algebras, we examine groupoid normalisers for the tensor product inclusion $B_1\\ \\overline{\\otimes}\\ B_2\\subseteq M_1\\ \\overline{\\otimes}\\ M_2$ establishing the formula $$ \\mathcal{GN}_{M_1\\,\\overline{\\otimes}\\,M_2}(B_1\\ \\overline{\\otimes}\\ B_2)''=\\mathcal{GN}_{M_1}(B_1)''\\ \\overline{\\otimes}\\ \\mathcal{GN}_{M_2}(B_2)'' $$ when one i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0851","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":"1004.0851","created_at":"2026-05-18T01:34:46.002241+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.0851v1","created_at":"2026-05-18T01:34:46.002241+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0851","created_at":"2026-05-18T01:34:46.002241+00:00"},{"alias_kind":"pith_short_12","alias_value":"AMBJUZQSL6L3","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"AMBJUZQSL6L3PMG2","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"AMBJUZQS","created_at":"2026-05-18T12:26:05.355336+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/AMBJUZQSL6L3PMG2I25HE5EWFF","json":"https://pith.science/pith/AMBJUZQSL6L3PMG2I25HE5EWFF.json","graph_json":"https://pith.science/api/pith-number/AMBJUZQSL6L3PMG2I25HE5EWFF/graph.json","events_json":"https://pith.science/api/pith-number/AMBJUZQSL6L3PMG2I25HE5EWFF/events.json","paper":"https://pith.science/paper/AMBJUZQS"},"agent_actions":{"view_html":"https://pith.science/pith/AMBJUZQSL6L3PMG2I25HE5EWFF","download_json":"https://pith.science/pith/AMBJUZQSL6L3PMG2I25HE5EWFF.json","view_paper":"https://pith.science/paper/AMBJUZQS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.0851&json=true","fetch_graph":"https://pith.science/api/pith-number/AMBJUZQSL6L3PMG2I25HE5EWFF/graph.json","fetch_events":"https://pith.science/api/pith-number/AMBJUZQSL6L3PMG2I25HE5EWFF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AMBJUZQSL6L3PMG2I25HE5EWFF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AMBJUZQSL6L3PMG2I25HE5EWFF/action/storage_attestation","attest_author":"https://pith.science/pith/AMBJUZQSL6L3PMG2I25HE5EWFF/action/author_attestation","sign_citation":"https://pith.science/pith/AMBJUZQSL6L3PMG2I25HE5EWFF/action/citation_signature","submit_replication":"https://pith.science/pith/AMBJUZQSL6L3PMG2I25HE5EWFF/action/replication_record"}},"created_at":"2026-05-18T01:34:46.002241+00:00","updated_at":"2026-05-18T01:34:46.002241+00:00"}