GAUSS-INSPIRED COMPUTATIONAL STATE-SPACE ATLAS FOR PARAMETRIC MODEL FAMILIES

Ernst Chladni’s plate experiments motivate a computational architecture for parameterized solution families, not a claim that unrelated physical domains share one universal vibration law [1,2]. Version 0.8 preserves the central OUXSPACE idea—precompute and validate reusable local structure, then answer a new question through a bounded transfer–evaluate–return step—while correcting the remaining formal and reproducibility weaknesses identified in review. The atlas is now explicitly typed as query space X_Q → chart selector s(q) → chart coordinates Z_i → domain state U_i → observable space Y_i, with F_i reserved for the local forward model, τ_ij for true within-stratum chart transitions, and κ_ij for cross-stratum coupling/coarse-graining. Fail-closed use is operationalized through calibrated support/nonconformity scores, uncertainty thresholds, abstention, false-accept/false-reject reporting and risk–coverage curves. The OUXSPACE-11S/33C and OUX-UMA-11B/33C representations remain research schemas: 33 is a declared coordinate-slot count, not proof of 33 independent physical dimensions; an empirical rank/identifiability test is required for every instantiated domain chart. A reproducible 2,000,000-case internal stress test is retained: 800,000 rectangular-plate, 600,000 hydrogenic and 600,000 synthetic diatomic cases, all passing a frozen 5×10⁻¹² relative-error tolerance with zero failures. The exact seed, parameter generators, executable harness, case-level error ledger and stream hashes are preserved in the companion package. These results establish internal numerical/software consistency only, not empirical prediction or computational superiority. The first independent gate remains P1: a frozen real-plate holdout with measured material properties, blind analysis, analytic/FEM/interpolation/reduced-basis/operator-learning baselines, quantitative uncertainty/OOD criteria, runtime and memory accounting. Atomic, molecular, biological, attosecond and digital-twin extensions are explicitly stage-gated future work. The 2–3% online-work figure is retained only as a defined engineering target f_online=C_query/C_direct at equal accuracy, not as a current result.