A Hermitian counterexample to C*-algebraic Novak positivity

We construct four self-adjoint inputs with two coordinates in M_2(C) for which the literal exponential-defined Novak kernel is Hermitian but not positive semidefinite. An explicit quadratic form equals cos(pi*sqrt(15))-3 and is at most -2. This refutes Krishna's C*-algebraic extension; the scalar and commutative Novak theorems are unaffected. The matrix construction and exact failure are proved in Lean. 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: No prior full source-conjecture refutation found in inspected primary/citing literature. Classical radial-kernel mechanisms credited; Semantic Scholar corpus is incomplete, subscription indexes and systematic non-English search unavailable. Independent numerical precision/index-comment errors reconciled by parent addendum. No absolute worldwide priority certified.