{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OAFGQKNAD23Z2C2SUHV254FXKQ","short_pith_number":"pith:OAFGQKNA","schema_version":"1.0","canonical_sha256":"700a6829a01eb79d0b52a1ebaef0b7542ef118e56bb8cac2aa51b6705bf2ce27","source":{"kind":"arxiv","id":"1208.4576","version":1},"attestation_state":"computed","paper":{"title":"Topological radicals, II. Applications to spectral theory of multiplication operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Victor S. Shulman, Yuri V. Turovskii","submitted_at":"2012-08-22T19:00:30Z","abstract_excerpt":"We develop the spectral radius technique and the theory of tensor radicals. As applications we obtain numerous results on mutiplication operators in Banach algebras and Operator bimodules."},"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":"1208.4576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-22T19:00:30Z","cross_cats_sorted":[],"title_canon_sha256":"7db4b7ac418c670f0d67730d39e5e73405bf7042036a9259e13e99cfa47808e4","abstract_canon_sha256":"1c654a0fab7828ba0c6395c9d2ee89b47c0b02aa81c3662441977bb57eefa724"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:13.991965Z","signature_b64":"SL1Tn0GFLMBZAt8vBQR/LuBaWsakCEOTMiJbMz5wLkWD8HvdgGE2XpRqBqJh5YTVSGNTyd6rkkrqKuVAnobiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"700a6829a01eb79d0b52a1ebaef0b7542ef118e56bb8cac2aa51b6705bf2ce27","last_reissued_at":"2026-05-18T03:48:13.991246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:13.991246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological radicals, II. Applications to spectral theory of multiplication operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Victor S. Shulman, Yuri V. Turovskii","submitted_at":"2012-08-22T19:00:30Z","abstract_excerpt":"We develop the spectral radius technique and the theory of tensor radicals. As applications we obtain numerous results on mutiplication operators in Banach algebras and Operator bimodules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4576","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":"1208.4576","created_at":"2026-05-18T03:48:13.991345+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.4576v1","created_at":"2026-05-18T03:48:13.991345+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4576","created_at":"2026-05-18T03:48:13.991345+00:00"},{"alias_kind":"pith_short_12","alias_value":"OAFGQKNAD23Z","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OAFGQKNAD23Z2C2S","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OAFGQKNA","created_at":"2026-05-18T12:27:16.716162+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/OAFGQKNAD23Z2C2SUHV254FXKQ","json":"https://pith.science/pith/OAFGQKNAD23Z2C2SUHV254FXKQ.json","graph_json":"https://pith.science/api/pith-number/OAFGQKNAD23Z2C2SUHV254FXKQ/graph.json","events_json":"https://pith.science/api/pith-number/OAFGQKNAD23Z2C2SUHV254FXKQ/events.json","paper":"https://pith.science/paper/OAFGQKNA"},"agent_actions":{"view_html":"https://pith.science/pith/OAFGQKNAD23Z2C2SUHV254FXKQ","download_json":"https://pith.science/pith/OAFGQKNAD23Z2C2SUHV254FXKQ.json","view_paper":"https://pith.science/paper/OAFGQKNA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.4576&json=true","fetch_graph":"https://pith.science/api/pith-number/OAFGQKNAD23Z2C2SUHV254FXKQ/graph.json","fetch_events":"https://pith.science/api/pith-number/OAFGQKNAD23Z2C2SUHV254FXKQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OAFGQKNAD23Z2C2SUHV254FXKQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OAFGQKNAD23Z2C2SUHV254FXKQ/action/storage_attestation","attest_author":"https://pith.science/pith/OAFGQKNAD23Z2C2SUHV254FXKQ/action/author_attestation","sign_citation":"https://pith.science/pith/OAFGQKNAD23Z2C2SUHV254FXKQ/action/citation_signature","submit_replication":"https://pith.science/pith/OAFGQKNAD23Z2C2SUHV254FXKQ/action/replication_record"}},"created_at":"2026-05-18T03:48:13.991345+00:00","updated_at":"2026-05-18T03:48:13.991345+00:00"}