nx_tex_gate.nx

nx_tex_gate.nx -- REFEREE for the sovereign LaTeX-math -> MathML renderer (nx_tex). Proves the renderer is CORRECT + produces WELL-FORMED MathML on a battery of hand-verified Known-Answer Tests, and degrades GRACEFULLY on bad input. GREEN iff every check holds. CHECKS (all on REAL tx_render output, nothing hand-faked): A. EXACT-MATHML KATs (11): each LaTeX input must render byte-for-byte to the hand-verified expected MathML. Covers: x^2 (msup), \frac{a}{b} (mfrac), \sqrt{x+1} (msqrt over mrow), \sum_{i=1}^{n} i (munderover, sum-style limits), \int_{0}^{\infty} x (msubsup, integral limits + greek \infty), \alpha+\beta (greek entities), the BM25-style \frac{f}{f+k} (the exact shape of the ranker the wiki search uses), a_i^2 (msubsup -- sub AND sup on one base, NOT nested), a relations chain (\le \neq \approx as proper <mo> entities), and \left( a+b \right) (fenced mrow). B. WELL-FORMEDNESS: every KAT output passes a balanced-tag check (a tag stack: every opener is closed by the matching closer in order, no underflow, empty at end) AND is wrapped in a single <math>...</math>. This is asserted INDEPENDENTLY of the exact-string check, so even a future renderer change that still produces balanced output is verified structurally. C. NEGATIVE CONTROL (graceful degradation): an UNSUPPORTED command (\badcmd{x}) must NOT crash and must yield balanced MathML containing an <merror> fallback (no malformed bytes). A second teeth case proves the well-formedness checker has TEETH: a deliberately UNBALANCED string (<math><mrow></math>) must be REJECTED by the checker (else greens are fabricatable). VERIFICATION DOCTRINE: MathML is a STANDARD (non-novel) format. The renderer is sovereign; rigor comes from these hand-verified expected-MathML KATs + the balanced-tag well-formedness proof. A 3rd-party structural cross-check (latexml / node+mathjax) is the NEXT rigor step -- this gate probes for those tools and logs the cross-check as PENDING when (as here) none is runnable. We do NOT claim a 3rd-party comparison was made. Evidence -> knowledge/status/tex_gate.log. Sovereign: imports nx_tex + nx_framed_append + nx_syscalls. license_tier: ORIGINAL