Physics Intermediate Representation (PIR): A Structured Framework for Automated Physical Law Discovery from Data (Version 3.1)

Version 3.1 — April 2026. Reproducibility upgrade. The benchmark runner now computes the formal Discovery Confidence Score (Eq. 5) at write time, storing per-run components (A, S, R) and the composite DCS in each result JSON artifact. Table 1 is regenerated end-to-end from these embedded fields using the companion script aggregate_table1_v3_1.py. The full reproducibility chain — benchmark runner → per-run JSON → aggregator → Table 1 — is now scripted and available in the PIR repository. All 20 tasks retain 100% discovery rate. Numerical DCS values are at or above their v3 counterparts (mean Δ = +0.029, max +0.083, no regressions). Mean DCS across all 20 tasks: 0.840 (v3: 0.818). Additional changes in v3.1:- Accuracy (A) is now scale-invariant: A = max(0, 1 − RMSE/std(y))- Simplicity uses sympy.count_ops for canonical complexity measurement- Residual randomness (R) uses genuine autocorrelation over lags 1–5- Fixed a grammar-upgrade regression in planar_robot_fk_x/y (_is_robot_task predicate was over-broad, routing FK through the Jacobian compound-angle library)- Jacobian noise robustness sweep (σ ∈ {0.10, 0.20}) completed: 100% DR confirmed across all four Jacobian tasks Design constants unchanged: α=0.7, β=0.3, γ=0.2, γ_JEPA=0.2, Langevin T=500. Supersedes Version 3 (DOI: 10.5281/zenodo.19428230).