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In this paper, we prove the stability of a cubic derivation with direct method. We also employ a fixed point method to establish of the stability and the superstability for cubic derivations."},"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":"1301.2888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-14T08:59:50Z","cross_cats_sorted":[],"title_canon_sha256":"bad9e7f896724193be0f8c463490530895f48c226f60f7462e5d837b2e375277","abstract_canon_sha256":"8eefcfbe6768d659bb0b8a1a74e9ad737a768ff73ec6976d4b14e029c6b94140"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:34.802417Z","signature_b64":"ykBwqLjzfliA2Y/y7izLx2/ch8Y8lwz7LQlYnx45cV+MFR7KKDmx3VvByZwAaDwGYarya7l3gR9CnPn70q8NAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee3e93aaa8bfa2fef82f98cdb7c252eec5311ded3c1d043b95c9987307b62aea","last_reissued_at":"2026-05-18T03:36:34.801721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:34.801721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cubic Derivations on Banach Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abasalt Bodaghi","submitted_at":"2013-01-14T08:59:50Z","abstract_excerpt":"Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. 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