PIR-JEPA: Joint Embedding Predictive Architecture as a Physics Manifold Prior for Out-of-Grammar Symbolic Law Discovery

Symbolic regression systems recover physical laws from data but are fundamentally limited by their search grammar: any law whose canonical form lies outside the hand-designed template set cannot be discovered regardless of loss function quality. PIR-JEPA addresses this grammar coverage problem by integrating a Joint Embedding Predictive Architecture physics manifold prior with a score-based diffusion candidate generator into the Physics Intermediate Representation (PIR) framework. The JEPA prior operates in latent expression space, biasing candidate generation toward physically plausible expression forms outside the hand-designed grammar. Candidates are scored additively — s_total = s_OT + 0.2·s_JEPA — so no grammar candidate is ever hard-rejected. Validated on a purpose-designed out-of-grammar benchmark task, oog_damped_oscillator (F = −kx − bv|v|, quadratic drag), where the v|v| term is provably outside all current PIR-Bench grammar templates. Baseline PIR achieves 0% discovery rate (MAE = 0.808); PIR-JEPA achieves 80% DR (4/5 seeds) with 100× MAE reduction (MAE = 0.008). A V-JEPA ablation (100 vs 50 candidates) produces identical 80% DR, confirming that sampling width is not the bottleneck — diffusion manifold coverage is the path to 100% DR. All 20 in-grammar PIR-Bench tasks maintain 100% DR with JEPA active. A key property of JEPA exploration is hidden physics sensitivity: JEPA runtime on in-grammar tasks scales with expression class density in latent space. Kepler's law requires ~40 min/seed vs 0.8 min baseline — because the diffusion sampler generates a dense catalogue of near-Kepler modifications (r^(3/2+δ), r^(3/2)log r, etc.) corresponding to dark matter, fifth force, and extra dimension corrections. The scoring margin Δs between rank-1 and rank-2 candidates is a sensitivity metric for detecting deviations from known physics without prior knowledge of the deviation's form. Related records: PIR Architecture v3 (DOI: 10.5281/zenodo.19130847), PIR-Bench v3.1 (DOI: 10.5281/zenodo.19130521), PhysicsGPT v3 (DOI: 10.5281/zenodo.19130163).