{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OAFGQKNAD23Z2C2SUHV254FXKQ","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":"1c654a0fab7828ba0c6395c9d2ee89b47c0b02aa81c3662441977bb57eefa724","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-22T19:00:30Z","title_canon_sha256":"7db4b7ac418c670f0d67730d39e5e73405bf7042036a9259e13e99cfa47808e4"},"schema_version":"1.0","source":{"id":"1208.4576","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4576","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4576v1","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4576","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"pith_short_12","alias_value":"OAFGQKNAD23Z","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OAFGQKNAD23Z2C2S","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OAFGQKNA","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:3bba4521c75be2fdf146c53fb8495756a7bf9f8bc8cb99e413096ecf5e6a7a94","target":"graph","created_at":"2026-05-18T03:48:13Z","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":"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.","authors_text":"Victor S. Shulman, Yuri V. Turovskii","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-22T19:00:30Z","title":"Topological radicals, II. Applications to spectral theory of multiplication operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4576","kind":"arxiv","version":1},"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":"sha256:2ce9c14b4e6e21972251a928bcc8cd76e7f5e84fe45ddd755ba6c47c742e4962","target":"record","created_at":"2026-05-18T03:48:13Z","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":"1c654a0fab7828ba0c6395c9d2ee89b47c0b02aa81c3662441977bb57eefa724","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-22T19:00:30Z","title_canon_sha256":"7db4b7ac418c670f0d67730d39e5e73405bf7042036a9259e13e99cfa47808e4"},"schema_version":"1.0","source":{"id":"1208.4576","kind":"arxiv","version":1}},"canonical_sha256":"700a6829a01eb79d0b52a1ebaef0b7542ef118e56bb8cac2aa51b6705bf2ce27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"700a6829a01eb79d0b52a1ebaef0b7542ef118e56bb8cac2aa51b6705bf2ce27","first_computed_at":"2026-05-18T03:48:13.991246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:13.991246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SL1Tn0GFLMBZAt8vBQR/LuBaWsakCEOTMiJbMz5wLkWD8HvdgGE2XpRqBqJh5YTVSGNTyd6rkkrqKuVAnobiAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:13.991965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4576","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ce9c14b4e6e21972251a928bcc8cd76e7f5e84fe45ddd755ba6c47c742e4962","sha256:3bba4521c75be2fdf146c53fb8495756a7bf9f8bc8cb99e413096ecf5e6a7a94"],"state_sha256":"1593f19de09b1788b400d314b9b1f693d18c6fac15c199a277fd9a7c2b6faaa8"}