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Moreover, we characterize the uniqueness of the solutions.","weakest_assumption":"The setup assumes unital complex Banach algebras and a Banach module with continuous actions; if the module is not complete or the algebras lack units the spectral intersection condition and the derived solvability criteria may fail to apply or require substantial reformulation."}},"verdict_id":"6fde2743-c421-4d5d-8a46-0a8629173bb5"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f4d0e46c4f8a9a3b6849cbcd43dcc683274854bb4a9fa7cd974f7409393ff956","target":"record","created_at":"2026-05-18T02:44:47Z","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":"c3006fbd42c4c609a3c6c714c55007f53ab76fd1e23c3404f1ed96ab36dcd781","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-05-13T12:14:17Z","title_canon_sha256":"be58ae6d582c93919243789d2e1e6fabcada1b75a41d7edcd970f9930e0c7ac6"},"schema_version":"1.0","source":{"id":"2605.13419","kind":"arxiv","version":1}},"canonical_sha256":"c149bdb3c2491e755612e6d21eefbe6f1aa31fc1fa510944341de02399278d96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c149bdb3c2491e755612e6d21eefbe6f1aa31fc1fa510944341de02399278d96","first_computed_at":"2026-05-18T02:44:47.350276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:47.350276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2NMfo/dPkhD8d43+7ocZB823VpSn5HwpVvAsLqblwcb8rxIxSe1mNeeZirakJKMTIUd1kMcOEHVI4WYUQvCECQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:47.350886Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13419","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4d0e46c4f8a9a3b6849cbcd43dcc683274854bb4a9fa7cd974f7409393ff956","sha256:cce865b8181f8464916fc378450fc80235719ffd8f47bdced2c0112f6704b7cd","sha256:d0df36a2ad0468249920075445315526218d3a4ff28e7e32d7bcad2a726f3083"],"state_sha256":"ea65288b93ef04e202f1d0095766129421002922d40a74d3f612a84e1820b1cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v4t6NPVKGhLLou27SYVAPY2LzocBfxiP99Ziu1cZkuUFJXZqm316yU4DhpL1y3W4B0ZGDmSyHm/8DnZn6tE2BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T02:10:25.242186Z","bundle_sha256":"5e6dffe854e1c66d798a81438aa53dc72f6204d366a66c6ce181620d5a533ed2"}}