Beyond Prompt Optimization: Sparse Semantic Anchors for Open-Ended Exploration

This exploratory Project BOG preprint investigates sparse semantic anchors as a method for open-ended scientific exploration rather than merely shortening or optimizing prompts. Three human-designed A/B problem pairs were examined, followed by two identical minimal instructions: "ВЫЧИСЛЕНИЯ" (Computations) and "МАТИМАТИКА ФОРМУЛА" (Mathematics Formula). The resulting conversations developed distinct conceptual trajectories. The anchor-oriented dialogue explored physical traces, adaptive networks, and possible computation through environmental change. The conventional-prompt dialogue developed systems for recording, verifying, and distributing calculations. These observations suggest a research question: can sparse semantic signals, interacting with conversational history, help language models explore unexpected conceptual directions that were not explicitly specified by the user? The study is exploratory and qualitative. Differences in initial conditions, context carryover, and inconsistencies in generated mathematical models prevent causal claims of superiority or scientific discovery. Supporting materials include selected prompt-response evidence and a qualitative comparison dataset. This work is not peer reviewed.