A Generative Closure Grammar for Quantized Physical Structure

We report a small generative grammar, abstracted from thirty-five known physical cases, which expands from primitive seeds into a quotient space of structural types. Known quantized physics occupies a subset of the generated slots; the remainder are ranked and resolved by external search. The method is intended to make systematic failure informative: where the grammar cannot distinguish structures that physics distinguishes, a missing primitive is exposed and its signature can be determined before consulting the literature. One such case is documented: an exhaustive synthesis over 4680 operator chains, plus static analysis of every operator, established that no composition could depend on the symmetry square. The required operator signature was fixed before any literature search, and only afterwards identified as Kramers degeneracy. Also included: a blind reconstruction of the Bekenstein-Hawking factor 1/4 from Euclidean regularity alone, without inserting S = A/4; a three-source decomposition of the Hawking spectrum; and a complete error history documenting ten cases where the method failed and what each failure corrected. No result reported here was previously unknown. The claim is methodological, and the claim ladder (proved / demonstrated / conjectured / open) is stated explicitly. A sealed prediction concerning the Altland-Zirnbauer classification was hashed and committed before any such test was run. Code and frozen test suite included; everything runs offline with Python 3 and sympy.