Physics Intermediate Representation (PIR): A Structured Framework for Automated Physical Law Discovery from Data — Version 3.2

PIR is a research framework for automated physical law discovery combining physics-aware symbolic search, soft dimensional consistency filtering, residual-driven refinement, sparse model selection, and a hybrid loss (MSE + Optimal Transport, alpha=0.7, beta=0.3). It produces typed scientific output objects (Equation, PIRDifferentialEquation, PIRHamiltonian, PIRLagrangian, PIRSystem) decoupling data-level discovery from knowledge-level reasoning. Version 3.2 (May 2026) additions over v3.1: 1. Section 9.3 — Head-to-head comparison with gplearn 0.4.3 on the full PIR-Bench-20 under an identical evaluation protocol (same datasets, same seeds, same success criterion, same DCS formula). Result: PIR 100% mean DR / DCS 0.838 vs gplearn 50% / 0.672. PIR wins on 14/20 tasks, tied on 6/20, gplearn wins on 0/20. Eight catastrophic gplearn failures (0% DR) on structurally demanding tasks (Lagrangians, FK, Jacobian, pendulum, inverse-square). Six perfect ties confirm the benchmark contains genuinely solvable tasks. This retires the standard SR baseline gap identified in v3.1 critique. 2. Section 11 Conclusion — Stale "noise ≤ 0.05" parenthetical removed; now consistent with Abstract, Table 1, Section 10.4, and Appendix A (all of which correctly reported sigma in {0.01, 0.05, 0.10, 0.20}). 3. PySR head-to-head and component ablation are documented as deferred to v3.3 (Python 3.13 / PythonCall.jl C-API incompatibility for PySR; benchmark-runner cache requires invalidation logic for component ablation). The Langevin-step ablation already published in v3.1 is unaffected. All Table 1 numbers, feature comparisons, and design constants are unchanged from v3.1. Bundle contents:- PIR_Architecture_v3_2.pdf — main paper (13 pages)- PIR_Architecture_v3_2.tex — LaTeX source- comparison_table.md, .csv, .json — gplearn comparison artifacts- run_gplearn_headtohead_v2.py — reproducibility script- aggregate_pysr_comparison.py — aggregation script Reproducibility: the gplearn comparison reruns end-to-end via the two included Python scripts on the public PIR codebase. Per-run JSON artifacts and provenance trail are preserved.