A Bounded Planetary Stability Vector Space and Monte Carlo Prioritization Framework Applied to the NASA Exoplanet Archive: Identification of LHS 1140 b as a Structurally Robust Terrestrial Candidate

A bounded planetary stability framework is constructed from the NASA Exoplanet Archive by defining a class-normalized state vector \( (R,H,M,S) \) and a windowed scalar projection, \( \Phi_p \), interpreted as planetary homeostatic potential. Planetary ripeness is defined as a time-weighted residence functional within this bounded stability window, separating instantaneous structural placement from accumulated incubation time. A five-tier pipeline enforces observability discipline and reproducibility. Tier 1 constructs the archive-scale stability space using robust normalization within radius classes. Tier 2 applies strict thermodynamic and temporal gates based on insolation, equilibrium temperature, orbital eccentricity, and stellar age. Tier 3 derives bulk diagnostics including density, surface gravity, and escape-velocity proxies without imputation. Tier 4 incorporates observational follow-up feasibility using distance, broadband photometry, and transit-depth proxies. Tier 5 propagates measurement uncertainties through Monte Carlo sampling (\( N_{\rm MC}=2\times10^4 \)), explicitly merging uncertainty fields from the NASA Planetary Systems table, resolving duplicate catalog entries using a deterministic completeness-aware selection rule, and applying conservative uncertainty floors only where published errors are absent. An initial degenerate Monte Carlo outcome is traced to missing uncertainty columns and resolved, producing non-degenerate credible intervals and a fully documented uncertainty model. Under the strict rocky configuration, the combined Tier 1–Tier 5 cascade reduces \( 39{,}386 \) archive rows to a single surviving candidate: LHS 1140 b. For this planet, the pipeline derives a bulk density of \( 5.95\,\mathrm{g\,cm^{-3}} \), an escape velocity of \( 1.80\,v_{\rm esc,\oplus} \), and a Tier 5 median Ripeness score of \( 0.947 \) with unity pass probability across all gates. These results demonstrate that a bounded, uncertainty-aware homeostatic stability framework can isolate structurally robust terrestrial exoplanet candidates directly from archival data.