Project Sphere: Convergence-Weighted Hierarchical Search for Hallucination-Resistant LLM Reasoning

In multi-step LLM reasoning, an early unsupported step can propagate to the final answer. We propose Project Sphere, a search procedure that combines hallucination signals at the level of individual reasoning steps. Sphere expands a reasoning graph breadth-first, scores every node by a weighted combination of model confidence, knowledge-grounded entailment, and cross-path convergence weighted for source diversity, and deepens promising paths best-first. When a node's risk exceeds a threshold, Sphere spawns a bounded sub-sphere that resolves the doubtful step before merging its result back. We formalize the risk scores, give the algorithm with cost and termination analysis, show why correlated samples cap the value of agreement, and specify an evaluation protocol with four benchmarks, seven baselines, and ablations.