spectral-random-walker

Random-walk guided exploration samples proof space by simulating walks on theorem adjacency graphs, identifying related theorems through co-visitation patterns—theorems frequently visited together in walk trajectories. This reveals hidden structural relationships in large theorem catalogs without exhaustive search.

Spectral-gap analysis measures how quickly random walks mix on a graph. A larger spectral gap indicates faster mixing, allowing accurate estimation of exploration time needed to discover theorem regions. This predicts comprehension difficulty and search efficiency.

Yes. Metropolis-Hastings sampling generates proof-path trajectories that respect the underlying theorem graph structure. This enables targeted exploration of high-probability proof regions and formation of comprehension clusters around theorem families.

Co-visitation clustering groups theorems that appear together in random-walk samples. These clusters form comprehension regions—semantic neighborhoods in theorem space where related results concentrate, enabling region-based search and localized reasoning.

Random-walk exploration scales to large theorem catalogs by avoiding exhaustive enumeration. Mixing-time estimation from spectral gaps determines sampling effort needed, making it practical for automated reasoning tasks across sizable proof databases.

Estimate mixing time upfront to predict exploration duration and set appropriate walk length. This avoids wasted sampling on poorly-mixed graphs and ensures comprehension discovery completes within acceptable computational budgets for agent-driven reasoning.