Current Large Language Model (LLM) architecturesare fundamentally reactive, operating within a "Prompt-Response" paradigm that leaves significant computational resourcesdormant during inter-prompt intervals. This paper introducesProactive Heuristic Synthesis (PHS), an architecturalframework that enables models to transition into a state of LatentIdle Consolidation. Unlike "thought-at-inference" methods (e.g.,Quiet-STaR) which impose latency penalties, or static distillationmethods (e.g., Fast Quiet-STaR) which lack continuous adaptability,PHS shifts the computational burden to asynchronousidle cycles. The framework utilizes a Regret-Based Replaymechanism defined by the counterfactual delta between initialinference failure and post-exploration success to target high-valueoptimization trajectories. Unlike recent replay methods suchas SuRe, which prioritize high-perplexity samples for memoryretention, PHS prioritizes high-regret samples for reasoningevolution. By autonomously navigating these associations, themodel synthesizes novel heuristics verified via a Dual-ModelConsensus engine to prevent generation-verification collapse. Thispaper establishes the mathematical formulation and architecturalblueprint of PHS. We theoretically demonstrate that by shiftingfrom perplexity-driven retention to regret-driven evolution, PHSprovides an asymptotically optimal solution to the latencyreasoningtrade-off. Furthermore, relying on recent bounds inrecursive training, we formalize how our Dual-Model Consensusmathematically mitigates model collapse, offering a rigorouspathway to zero-latency self-evolution in LLMs.