Industrial bioleaching processes often suffer from suboptimal yields and monitoring gaps due to the extreme acidity and corrosiveness of the environment. This article presents a lightweight, web-based digital twin (DT) framework for semi-industrial bioleaching optimization, in tegrating low-cost RGB sensing (transformed to hue, saturation, and value space for robustness), IoT connectivity, and support vector machine (SVM) regression within a Unity-WebGL platform. To ensure industrial-grade reliability, the predictive pipeline utilizes a group-based three way split strategy to eliminate data leakage and ensure generalization to unseen experimental batches. While traditional random-split approaches often yield overfit results,our SVM-based regressorachievesageneralized R2 =0.55,providing stable and physically consistent predictions of copper concentration. A targeted ablation study demonstrates that noncontact optical sensing independently outperforms traditional pH probes (R2 = 0.52 vs. R2 = 0.42),offering critical operational resilience in corrosive media(pH <2.0). Model transparency is further validated through residual diagnostics and response surface analysis, confirming homoscedastic behavior and chemical consistency. Furthermore, a pilot evaluation indicates that the DT enables 57.3% faster anomaly detection than legacy supervisory control and data acquisition systems, facilitating proactive intervention. The framework’s decoupled WebGL architecture ensures zero-install deployment, offering a scalable blueprint for real-time bioprocess monitoring in data-scarce industrial environments.

The graph-based geometric constraint solving technique works in two steps. First the geometric problem is translated into a graph whose vertices represent the set of geometric elements and whose edges are the constraints. Then the constraint problem is solved by decomposing the graph into a collection of subgraphs each representing a standard problem which is solved by a dedicated equational solver. In this work we report on an algorithm to decompose biconnected tree-decomposable graphs representing either underor wellconstrained 2D geometric constraint problems. The algorithm recursively first computes a set of fundamental circuits in the graph then splits the graph into a set of subgraphs each sharing exactly three vertices with the fundamental circuit. Practical experiments show that the reported algorithm clearly outperforms the treedecomposition approach based on identifying subgraphs by applying specific decomposition rules.