Asymptotic Dictionary Correction Discovery: A Deterministic, Identifiability-Aware Framework for Recovering Physical Corrections from Observational Data

We present ADCD (Asymptotic Dictionary Correction Discovery), a deterministic framework for recovering structured corrections to known physical laws from noisy data. Given a classical baseline, ADCD searches for the residual correction that vanishes exactly at the classical limit, using three interlocking mechanisms: algebraically regularized primitives that enforce asymptotic vanishing as an exact algebraic identity; a five-dimensional (MLT$\Theta$Q) Buckingham-$\pi$ engine that auto-derives dimensionless ratio arguments without manual specification; and a Phenomenon-Specific Taxonomy encoding peer-reviewed functional priors for each physics domain. A four-step validation protocol—budget disclosure, positive control, BIC-based ablation control, and determinism check—issues one of two verdicts: IDENTIFIABLE or WITHHELD. On three canonical scenarios at historical low-signal windows, Screened Coulomb ($\Delta$BIC = 30.65, exact symbolic match) and Entropy Expansion ($\Delta$BIC = 14.70, class-level match) are IDENTIFIABLE; Time Dilation at $v \le 0.3c$ is WITHHELD because the 4.8% correction is indistinguishable from 1% noise—the intended, epistemically honest behavior. All results are byte-exact deterministic.