PIR-JEPA: Joint Embedding Predictive Architecture as a Physics Manifold Prior for Out-of-Grammar Symbolic Law Discovery — Version 2 (Langevin Diffusion, 100% Discovery Rate)

PIR-JEPA extends the Physics Intermediate Representation (PIR) framework with a two-component out-of-grammar discovery system: (1) a physics-informed template augmentation layer covering six structured expression families, and (2) a score-based Langevin diffusion sampler that walks the physics expression manifold learned by a JEPA encoder–predictor pair. This version reports the complete implementation and validation of real Langevin dynamics. On the out-of-grammar benchmark task oog_damped_oscillator (F = −kx − bv|v|, quadratic drag), baseline PIR achieves 0% discovery rate. Template augmentation alone achieves 80% DR. Adding Langevin diffusion sampling at the optimal step count (T=500) achieves 100% discovery rate (5/5 seeds, MAE = 0.008, 100× error reduction) — the first 100% DR result on this task. A Langevin step count ablation (T = 200, 500, 750, 900, 1000) reveals a non-monotonic DR curve with an optimal window at 500–750 steps. Beyond 750 steps, over-diffusion carries the sampler past the v|v| basin of attraction, reducing DR back to 80–60%. This over-diffusion phenomenon is a new empirical finding in score-based symbolic expression generation: each target expression family has a finite basin of attraction in latent space, and optimal step count is determined by basin size rather than by maximising walk length. All 20 in-grammar PIR-Bench tasks maintain 100% DR with PIR-JEPA active. The hidden physics sensitivity property is confirmed: the scoring margin Δs between rank-1 and rank-2 Langevin candidates is a metric for detecting deviations from known physics without prior knowledge of the deviation's form. Kepler's law generates the richest modification catalogue (~40 min/seed), covering dark matter, fifth force, and extra dimension corrections in symbolic form. Supersedes PIR-JEPA v1 (DOI: 10.5281/zenodo.19477508) on the same record. Related: PIR Architecture v3 (DOI: 10.5281/zenodo.19428230), PIR-Bench v3.1 (DOI: 10.5281/zenodo.19130521). Demo: https://huggingface.co/spaces/Qazihanif/pir-jepa