VERYQ.AI pioneers novel approaches to solving the Boolean satisfiability (SAT) problem with a focus on industrial applications such as hardware and circuit verification. By combining insights from statistical physics and machine learning, we develop innovative algorithms that reveal hidden structural patterns within SAT instances, enabling faster and more reliable verification workflows. Our work bridges theory and computation, introducing new perspectives on phase transitions, optimization landscapes, and efficient heuristics for large-scale, real-world combinatorial challenges.