Thermal-Phase Crystallization Optimizer: Search Formulation, Analytical Conditions and Reported Numerical Evidence

Abstract

The Thermal-Phase Crystallization Optimizer (TPCO) is a proposed population-search framework organized through solid, liquid and vapor metaphors. Its reported components combine neighbor attraction, boundary handling, heavy-tailed proposals, elite attraction, Gaussian resampling and greedy retention. These are algorithmic choices rather than a thermodynamic derivation. The stated bond score is identical across particles and produces a deterministic release threshold; deposition, phase membership, bound handling and evaluation accounting remain incompletely specified. A conditional finite-sample coverage argument distinguishes requirements for global search from properties established for the proposed finite-budget process. Source-reported CEC 2022 summaries at dimensions 10 and 20, rotation tests, engineering examples, ablations and a machine-learning example are retained without new experiments. Printed benchmark means place TPCO-T first on nine of twelve functions at each dimension among the six displayed methods. However, rank sums, Friedman statistics, critical differences and Sobol summaries are internally inconsistent, and the original implementation and run-level outputs are unavailable. These summaries therefore do not establish significance, global convergence, ergodicity, engineering feasibility or component causality. The contribution is the explicit search architecture, its mathematical limits and the experimental information required for a valid assessment.