Automated Hidden Physics Detection in Galaxy Rotation Curves via Symbolic Regression with Langevin-Diffusion Expression Priors

PIR-JEPA SPARC: Automated Hidden Physics Detection in Galaxy Rotation Curves This paper applies PIR-JEPA (Physics Intermediate Representation with JEPA-based Langevin diffusion expression priors) to the SPARC galaxy rotation curve dataset (Lelli, McGaugh & Schombert 2016, 175 disk galaxies). The analysis proceeds in three stages, each adding a layer of evidence. Stage 1 — Pipeline Delta-s detection (v1): 143/175 galaxies identified as Kepler-failing. 88/143 (61.5%) flagged as hidden physics candidates via Delta-s < 0.15. Mean Delta-s = 0.143. Strongest candidates: NGC 1705, UGC 12732 (flagged 3/3 seeds). Stage 2 — Real PIR-JEPA confirmation (v2): Real PIR-JEPA (base symbolic search, no synthetic sampler) run on top 12 candidates, 3 seeds each. 11/12 galaxies confirmed at 3/3 seeds; NGC 0024 at 2/3. Mean Delta-s = 0.042 across confirmed galaxies. The Delta-s hidden physics signal is genuine, not a pipeline artifact. Stage 3 — JEPA candidate scoring (v3): Direct scoring of JEPA-generated candidate expressions across all 12 top galaxies: log(|v_bar|+1) wins 10/12 galaxies (mean MAE = 0.093) log(|r|+1) wins 2/12 galaxies (CamB, UGC07323 — gas-dominated dwarfs with v_bar ≈ 0) Log candidates win 12/12 galaxies in total Grammar baseline 1/r²: mean MAE = 0.753; v_bar·r^(-1/2): mean MAE = 0.317 Physical interpretation: The dominance of log(|v_bar|+1) is consistent with the Radial Acceleration Relation (McGaugh et al. 2016): the hidden correction depends on baryonic velocity, not radius alone. The two log(r) outliers are physically explained by near-zero baryonic velocity in their outer regions, where the correction must become spatial. This is the first data-driven, grammar-free recovery of a RAR-consistent symbolic correction term from the SPARC dataset, without prior knowledge of MOND, NFW profiles, or the RAR itself. Related work: PIR-JEPA v2: https://doi.org/10.5281/zenodo.19477508 PIR Architecture v3: https://doi.org/10.5281/zenodo.19428230 PIR-JEPA LIGO v2: https://doi.org/10.5281/zenodo.19586642