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For weight zero, we prove that the Rota--Baxter operators are precisely the linear maps P satisfying P^2=0 and Image(P)⊂m/m^2. For nonzero weight, a standard rescaling reduces the classification to weight one. In this case, the operators split into two disjoint families according to the value of P(1)∈{0,−1}. On the maximal ideal m/m^2, such operators induce an endomorphism L satisfying L^2+L=0, equivalently, −L is idempotent. We further show that each family is isomorphic to the variety of idempotent matrices.","weakest_assumption":"The claim that a standard rescaling reduces the nonzero-weight case to weight one without loss of generality, and that the resulting operators on m/m^2 always induce an endomorphism L with L^2 + L = 0, as stated in the abstract."}},"verdict_id":"6d7c89b4-b2fb-4a73-abcb-18e3e8a55ae7"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:07ace3f10d38b3135bf7c6d2ec74aa04c7bb97933afee012e0224ba69c014e2b","target":"record","created_at":"2026-05-20T00:01:11Z","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":"f09db64623fa0caf027c896fd105f82e761bad3de10b166e7eb35b89e416f2b5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2026-05-15T06:46:50Z","title_canon_sha256":"b4817561624d3d6896b5dec05cd02f4969254a5b3fbb5d5169dadd2ba3cbcd5a"},"schema_version":"1.0","source":{"id":"2605.15670","kind":"arxiv","version":1}},"canonical_sha256":"264a3da7c8afedc76a4cbaa33e8389ed7c8cb9f220efc0506e7b4dabe23689a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"264a3da7c8afedc76a4cbaa33e8389ed7c8cb9f220efc0506e7b4dabe23689a7","first_computed_at":"2026-05-20T00:01:11.355884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:11.355884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zXuAycmvMAQE3WCdUI/NX1kvkVycKabncqYW3ut0Ju0Tw+NgDA4dZ4/qjq9l6AzVA6jkr7nvXr786T5IzA/LCg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:11.356634Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15670","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07ace3f10d38b3135bf7c6d2ec74aa04c7bb97933afee012e0224ba69c014e2b","sha256:e94053dd08bddf07233e8d91e364641b00775b4a4d89cfc878038dfd7162c21a"],"state_sha256":"ef94a71ad6e0b4a658d83bc89a821c5a1e279402bc25150d1538b628dabf28a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+8hf+jc0MSyq5I9/i1WP5v223loElYRK9lYTQDXBw9XeGGphjvKOTK9IlXG+LnnQUKMp/uqIMQdGzhnFi4WZBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:58:10.527430Z","bundle_sha256":"768a1f4451f934e9ac0b720722fd6539f4cbdda047a4c67c194064b2b09a31c5"}}