Physics Intermediate Representation (PIR): A Structured Framework for Automated Physical Law Discovery from Data — Version 3

PIR is a physics-constrained symbolic discovery framework that combines dimensional filtering, residual refinement, sparse model selection, and a hybrid MSE + Optimal Transport loss to recover typed, interpretable physical laws from data with 100% success on core benchmark tasks. Version: 3 (April 2026) Description: Version 3 extends the validated 9-task core (Version 2, March 2026) to a comprehensive 20-task benchmark suite, achieving 100% discovery rate across all tasks. Key additions and corrections relative to Version 2: New results: 11 additional validated benchmark tasks: full planar robot Jacobian (J11–J22, 100% DR confirmed at noise ≤ 0. 05, 15 runs each), double pendulum dynamics (θ1dot, θ2dot), harmonic oscillator ODE components (xdot, vdot), Lagrangian discovery, and structured Lagrangian discovery Mean DCS across all 20 tasks: 0. 818 (n=200, noise=0. 01, 5 seeds) Robot Jacobian tasks require trigonometric composition basis (sin (θ1+θ2), cos (θ1+θ2) ) ; confirmed with --no-dim-filter flag New architectural components: Euler-Lagrange residual construction formally documented: d/dt (∂L/∂q̇) − ∂L/∂q = 0, implemented in lagrangiandiscovery. py OT + Diffusion + JEPA triple-stack prior: score-based diffusion and JEPA physics manifold prior implemented in codebase (jepaₚrior. py, jepadiffusion. py). Important: these components are not yet activated in confirmed benchmark runs. All reported results use the OT hybrid loss (α=0. 7, β=0. 3) with flow matching prior (Fix C). Diffusion+JEPA ablation is the next publication milestone (PIR-JEPA paper) LangGraph-based autonomous coding agent (pirₐgent. py) with 21 tools documented as experiment execution infrastructure Scientist loop status formally documented: overnight sweep execution and multi-cycle theory validation implemented; production-grade NightLab orchestrator is future work Design constants (unchanged from Version 2): α=0. 7, β=0. 3 (OT loss weights) ; γ=0. 2 (soft dimensional penalty) ; 2% relative tolerance numerical equivalence criterion; asₚowersdict () for exponent extraction; soft scoring only — no hard candidate rejection Version history: V1 (2026-03-22): 7/9 tasks, pre-fix. V2 (2026-03-26): 9/9 tasks, Fix A–C. V3 (2026-04-05): 20/20 tasks, Jacobian + Lagrangian + triple-stack documentation.