Xiaohua Yang

Meng Li, Xiaohua Yang, Jie Liu et al.

Context. Metamorphic Testing addresses the test-oracle problem in scientific computing, but classical Mutation Score operates on syntactic AST mutations and misses domain semantics. Objective. We propose the Semantic Mutation Score (SMS), built on five domain-semantic operators (Conservation Erosion, Operator Substitution, Hyperparameter, Trajectory Flip, Structural Injection). SMS degenerates almost everywhere to MS in a characterised limit, so any SMS-based conclusion remains consistent with prior mutation-testing literature in the classical regime. Method. A 12-PUT x 5-MP design over four single-output float-to-float classes (numeric, probabilistic, surrogate, machine-learning) is paired with a three-layer attribution classifier separating true semantic faults from tolerance, OOD, statistical, and artefact categories. A same-source / cross-source ablation under an identical prompt isolates the LLM-source-diversity contribution. LLM-generated mutants are compared against a default-configuration cosmic-ray syntactic pool at the AST-normalised level. Results. The pre-registered large-effect threshold for Cliff's delta is not met under the point-estimate criterion; the observed effect lies in the medium-effect range. Cross-source pooling under an identical prompt does not appreciably shift delta, indicating that LLM identity is not the lever within this design. AST-level overlap between LLM-generated and default cosmic-ray syntactic mutants is small; the Hyperparameter, Structural Injection, and Trajectory Flip classes are unreachable under default first-order syntactic configurations. Conclusion. SMS is a backward-compatible adequacy metric for domain-semantic metamorphic-relation sets in scientific computing. The first-order unreachability evidence is independent of the effect-size question.

Meng Li, Xiaohua Yang, Jie Liu et al.

Context. Metamorphic Testing is recognised in IEEE/ISO software-testing standards and increasingly recommended for AI systems, but its progress is bottlenecked by metamorphic relation (MR) identification: existing approaches (structured frameworks, mining and evolutionary pipelines, LLM-assisted methods, MetaPattern catalogues) share an inductive grounding that leaves three foundational questions open: origin, closure, and transferability. Objective. We propose a framework whose downstream step from program-induced operator algebra to MetaPattern set is mechanical and provable, while the upstream curation of the algebra is a stated empirical hypothesis with explicit scope precondition. Method. NOETHER is a two-layer framework. The upstream layer is an eight-block decomposition over recurrent mathematical structures (symmetry, order, self-adjoint, time-reversal, limit, qualitative-dynamics, method-comparison, relational equivalence). The downstream CONSTRUCT-MP algorithm produces a MetaPattern set with algebraic-closure (Theorem 1) and polynomial-time decidability (Theorem 2) guarantees. We test the framework on three operator-algebraic domains. Results. On Boltzmann reactor physics NOETHER systematises a prior inductive catalogue; on equivariant ML it derives executable MRs for rotation invariance, adjoint duality, and training-trajectory reversibility; on relational query optimisers it exercises the relational-equivalence block. The central falsifiable prediction (L*-blindness on homogeneity-preserving mutators) holds on the in-scope substrate. The absolute-completeness conjecture (Theorem 1') is falsified on PWR core diffusion via two pairwise-independent counterexamples that identify five Translate-extension dimensions. Conclusion. Induction is relocated from per-program MR sampling to a per-domain algebraic layer; the downstream step is deductive and mechanical.