A cubic counterexample to three C*-algebraic polynomial inequalities

One degree-three matrix construction refutes Krishna's C*-algebraic Schoenberg, de Bruin–Sharma and Kushel–Tyaglov conjectures. The ordered deletion derivative factors for every complex matrix argument, including noncommuting arguments. Both adjoint versions of each proposed inequality fail through exact negative quadratic forms. Lean proves the factorization and all six Hermitian failures. The common construction counts as one outcome; classical scalar results are unaffected. AI-assisted preprint by Myeongjin Kang, with no affiliation. Internal AI review is not external journal peer review. The accompanying Lean certificate covers the precise scoped main statement; inspect the formal endpoint, assumptions and provenance in the supporting package. Prior-art investigations are documented bounded searches, not worldwide-priority certification. Original prose is offered under CC BY 4.0 and original code/Lean under MIT; third-party rights and existing notices are preserved. The public supporting ZIP contains original proof sources and verification evidence, with bibliographic links and hashes instead of redistributed third-party source manuscripts. Recorded prior-art/source-access limits: Independent primary/citing/companion search found no prior refutation or subsuming negative theorem. Subscription indexes and systematic worldwide coverage unavailable. Parent addendum corrects ancillary review alternative-coefficient arithmetic, stale script docstring and an optional tautological loop; unchanged complete literal-source Lean and paper unaffected. No absolute priority guarantee.