Structural Cosmology and Euclid: Explicit Benchmark Conditions and Decision Rules for a Growth-Suppression Test - v1.1 Numerical Decision Kernel and Prior-Exposure Record

This v1.1 methods update advances the product-independent numerical decision component of the v1.0 growth-suppression protocol. It retains the conditional 5–7 percent phenomenological benchmark, reference conditions, and conservative chi-square rejection rule. It supplies a candidate kernel using exact rational linear algebra and real-ball enclosures for the chi-square tail and quantile. Numerical decisions require consistent separation by the probability and quantile enclosures; unresolved calculations stop without a scientific verdict. A plan and code/input hashes were recorded before a single new synthetic regression run. All 14,418 archived boundary inputs were numerically resolved. Among the 231 cases where the historical double-precision implementations S and A disagreed, the new kernel classified 150 as rejected and 81 as not rejected. Additional analytic controls, invalid-input tests, and quantile checks passed within their stated scope. Two separately planned post-run checks verified the delivered input encoding and an end-to-end unresolved stop at the precision cap, without changing the kernel. These checks do not constitute third-party verification, general implementation validation, an observational comparison, or a Euclid forecast. The update provides an uncompleted prior-exposure and freeze-record form. No author's exposure declaration or signature is inferred. Product selection, estimator/response/covariance validation, the reference-solver and response pipeline, product-specific numerical error propagation, full freeze F, and overall validation V remain incomplete; third-party T has not been performed. The manuscript is an incremental update to be read with v1.0. Publication of this methods update does not establish completion of the exposure declaration or full freeze F. Four figures illustrate the decision workflow, boundary decisions of S, A and N, the 231 disagreements, and the quantile brackets and precision-cap stop. They plot archived results only; the plotted distance uses the midpoint of the stored quantile bracket. The accompanying evidence archive contains the implementation, inputs, saved results, execution records, provenance materials, and checksums.