PIR: Physics Intermediate Representation for Automated Discovery of Physical Laws

We present PIR (Physics Intermediate Representation), a classical symbolicregression engine for automated discovery of physical laws from data. PIR uses amonomial-basis log-linearization gate (F3) to detect power-law structure, combinedwith pairwise structure decomposition, RANSAC, sparse regression, and an Occamcomplexity penalty. On the Feynman Symbolic Regression Benchmark (Tier A, blindprotocol), PIR recovers 12/44 equations exactly (zero wobble across seeds, v3.4). Asecondary 12/44 equations are recovered in correct functional form withtranscendental constants folded as decimals (FORM_NUMERIC), reported separatelyand never summed into the primary figure. We characterize two hard structural limits: atranscendental wall (F2 class, 0/18 recovery, mechanism proven) and a log-spacefailure mode for sum-of-products laws (closed negative result). These negatives are asinformative as the positives: they define PIR's recovery envelope precisely and point toconcrete next steps. v3.4.1 correction: Section 2.2 previously described a hybrid optimal-transportscoring loss as part of the method. That component was not active in the reportedconfiguration (use_ot_loss=False). Section 2.2 has been rewritten to state whichengine components were and were not exercised. The comparison table alsomisstated the retracted formula-peeking figure as 19/44; the correct retractedfigure is 27.3%. No result changes: the headline remains 12/44 EXACT + 12/44FORM_NUMERIC.