{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:F2335WO24YUNMTW2NF7FWB4BR2","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":"98b3578d1ad2171de7028b237f8bc429ed7d8183143a2088fae5131420b5f8b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-01-09T13:37:34Z","title_canon_sha256":"cc91dfd9223fd1900f0f875d117f1bd0678d0666748e24993b4520c80fc7a5b7"},"schema_version":"1.0","source":{"id":"1401.1997","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1997","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1997v2","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1997","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"F2335WO24YUN","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F2335WO24YUNMTW2","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F2335WO2","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:3385a001372c6711686f3eaa2bec7d0c24c9e5b271b7e5a66a8147b8f6f84b0a","target":"graph","created_at":"2026-05-18T01:34:45Z","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":"For completely contractive Banach algebras $A$ and $B$ (respectively operator algebras $A$ and $B$), the necessary and sufficient conditions for the operator space projective tensor product $A\\widehat{\\otimes}B$ (respectively the Haagerup tensor product $A\\otimes^{h}B$) to be Arens regular are obtained. Using the non-commutative Grothendieck's inequality, we show that, for $C^*$-algebras $A$ and $B$, the Arens regularity of Banach algebras\n  $A\\otimes^{h}B$, $A\\ot^{\\gamma} B$, $A\\ot^{s} B$ and $A\\widehat{\\otimes}B$ are equivalent, where $\\otimes^h$, $\\otimes^{\\gamma}$, $\\ot^s$ and $\\widehat{\\o","authors_text":"Ajay Kumar, Vandana Rajpal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-01-09T13:37:34Z","title":"Arens regularity of projective tensor products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1997","kind":"arxiv","version":2},"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":"sha256:0814f19355625e065a226859642624c0447865bd5ec70b3200442bb17845218a","target":"record","created_at":"2026-05-18T01:34:45Z","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":"98b3578d1ad2171de7028b237f8bc429ed7d8183143a2088fae5131420b5f8b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-01-09T13:37:34Z","title_canon_sha256":"cc91dfd9223fd1900f0f875d117f1bd0678d0666748e24993b4520c80fc7a5b7"},"schema_version":"1.0","source":{"id":"1401.1997","kind":"arxiv","version":2}},"canonical_sha256":"2eb7bed9dae628d64eda697e5b07818e90049024eea8f7e14632a0603134cfd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2eb7bed9dae628d64eda697e5b07818e90049024eea8f7e14632a0603134cfd0","first_computed_at":"2026-05-18T01:34:45.734132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:45.734132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wRZR86PFGWfpTJyR+6/3WZGGNDleYY4M4/C2gY3Ad0d/QYm1f8VV4JIWIh/L0d/bW2tcX/aykMieYQfqMoXbBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:45.734616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1997","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0814f19355625e065a226859642624c0447865bd5ec70b3200442bb17845218a","sha256:3385a001372c6711686f3eaa2bec7d0c24c9e5b271b7e5a66a8147b8f6f84b0a"],"state_sha256":"61c4f701862f13a1ae06654890d2cef7b0736ea7435fbc9f72962b19239d16bc"}