New Metric Measures Novelty of Formal Proof Techniques.

A novel method called PriorProof has been introduced to quantify the time-relative novelty of techniques employed in formal mathematical proofs, specifically within the Lean theorem prover. Unlike subjective human judgments about proof elegance or explanatory power, PriorProof focuses on a narrower, mechanically measurable construct: the nonstandardness of a proof's route at a specific point in time. The system operates by extracting the dependency footprint of an elaborated proof term and then calculating the weighted surprisal of this footprint. This calculation is performed against a hierarchically smoothed prior, which is built exclusively from an earlier quarterly snapshot of the Mathlib library. This approach eliminates the need for manual technique ontologies or human-labeled data, as statement retrieval is learned from proof-derived contrastive pairs, and the scored object is directly read from proof terms. In a blinded study involving topology experts, PriorProof demonstrated a 69.7% agreement with the majority of human raters on distinguishing novel from standard proof techniques. While a language model condition showed slightly higher agreement, the statistical difference was not significant at the given sample size. PriorProof is presented as a decomposable, time-anchored signal that offers an interpretable reliability indicator for assessing proof novelty.