{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:K6HVXB3MDRSOXYU5APINHRE4YP","short_pith_number":"pith:K6HVXB3M","schema_version":"1.0","canonical_sha256":"578f5b876c1c64ebe29d03d0d3c49cc3df5bc5b11e33d19e2d2599ce66d244d1","source":{"kind":"arxiv","id":"1403.5958","version":1},"attestation_state":"computed","paper":{"title":"The Bidual of a Radical Operator algebra can be Semisimple","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Charles John Read","submitted_at":"2014-03-24T14:09:49Z","abstract_excerpt":"The paper of S. Gulick [Sidney (Denny) L. Gulick, Commutativity and ideals in the biduals of topological algebras, Pacific J. Math 18 No. 1, 1966] contains some good mathematics, but it also contains an error. It claims that for a Banach algebra A, the intersection of the Jacobson radical of A** with A is precisely the radical of A (this is claimed for either of the Arens products on A** - in itself a reasonable claim, because A is always contained in the topological centre of A**, so a fixed a in A lies in the radical of A** with the first Arens product, if and only if it lies in the radical "},"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":"1403.5958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-03-24T14:09:49Z","cross_cats_sorted":[],"title_canon_sha256":"efc16353ec3315127ec56fc8cc95f2d9a81151708740efbe70acdf095c5bdea1","abstract_canon_sha256":"b11bf32a155a4026bca1e1fefd9dbc00ea082709c3ef43785d6d3d78ce832980"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:24.223453Z","signature_b64":"FkPIEgeZhw+BPRv5NM/xT+emjiisoZruBqpAKheaGlUQJd0foChXQxORXJkmonwG7gLMlb8jbajooPDdmvPVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"578f5b876c1c64ebe29d03d0d3c49cc3df5bc5b11e33d19e2d2599ce66d244d1","last_reissued_at":"2026-05-18T01:22:24.222740Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:24.222740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Bidual of a Radical Operator algebra can be Semisimple","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Charles John Read","submitted_at":"2014-03-24T14:09:49Z","abstract_excerpt":"The paper of S. Gulick [Sidney (Denny) L. Gulick, Commutativity and ideals in the biduals of topological algebras, Pacific J. Math 18 No. 1, 1966] contains some good mathematics, but it also contains an error. It claims that for a Banach algebra A, the intersection of the Jacobson radical of A** with A is precisely the radical of A (this is claimed for either of the Arens products on A** - in itself a reasonable claim, because A is always contained in the topological centre of A**, so a fixed a in A lies in the radical of A** with the first Arens product, if and only if it lies in the radical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5958","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":"1403.5958","created_at":"2026-05-18T01:22:24.222847+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.5958v1","created_at":"2026-05-18T01:22:24.222847+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5958","created_at":"2026-05-18T01:22:24.222847+00:00"},{"alias_kind":"pith_short_12","alias_value":"K6HVXB3MDRSO","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"K6HVXB3MDRSOXYU5","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"K6HVXB3M","created_at":"2026-05-18T12:28:35.611951+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/K6HVXB3MDRSOXYU5APINHRE4YP","json":"https://pith.science/pith/K6HVXB3MDRSOXYU5APINHRE4YP.json","graph_json":"https://pith.science/api/pith-number/K6HVXB3MDRSOXYU5APINHRE4YP/graph.json","events_json":"https://pith.science/api/pith-number/K6HVXB3MDRSOXYU5APINHRE4YP/events.json","paper":"https://pith.science/paper/K6HVXB3M"},"agent_actions":{"view_html":"https://pith.science/pith/K6HVXB3MDRSOXYU5APINHRE4YP","download_json":"https://pith.science/pith/K6HVXB3MDRSOXYU5APINHRE4YP.json","view_paper":"https://pith.science/paper/K6HVXB3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.5958&json=true","fetch_graph":"https://pith.science/api/pith-number/K6HVXB3MDRSOXYU5APINHRE4YP/graph.json","fetch_events":"https://pith.science/api/pith-number/K6HVXB3MDRSOXYU5APINHRE4YP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K6HVXB3MDRSOXYU5APINHRE4YP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K6HVXB3MDRSOXYU5APINHRE4YP/action/storage_attestation","attest_author":"https://pith.science/pith/K6HVXB3MDRSOXYU5APINHRE4YP/action/author_attestation","sign_citation":"https://pith.science/pith/K6HVXB3MDRSOXYU5APINHRE4YP/action/citation_signature","submit_replication":"https://pith.science/pith/K6HVXB3MDRSOXYU5APINHRE4YP/action/replication_record"}},"created_at":"2026-05-18T01:22:24.222847+00:00","updated_at":"2026-05-18T01:22:24.222847+00:00"}