PIR-JEPA LIGO: Symbolic Discovery of Gravitational Wave Laws and Post-Newtonian Corrections via Langevin-Diffusion Expression Priors

PIR-JEPA LIGO: Symbolic Discovery of Gravitational Wave Laws and Post-Newtonian Corrections This paper applies PIR-JEPA (Physics Intermediate Representation with JEPA-based Langevin diffusion expression priors) to synthetic gravitational wave data modelled on the LIGO/Virgo detection programme. A four-stage symbolic regression pipeline progresses from leading-order chirp frequency recovery through post-Newtonian correction detection to chirp mass identification as a hidden parameter. Four-stage pipeline: Stage 1: f (t) ~ tau^ (-3/8) — leading-order chirp frequency law Stage 2: h (t) ~ tau^ (-1/4) — GW strain amplitude envelope Stage 3: 1PN correction term beyond leading order (hidden physics target) Stage 4: Chirp mass Mc as hidden parameter across multiple synthetic events Key results: Stages 1-3: 100% hidden physics detection (3/3 seeds) under both white Gaussian noise and realistic aLIGO PSD noise Stage 4 white noise: 3/3 seeds flag Mc as hidden parameter Stage 4 aLIGO noise: 1/3 seeds (physically correct — Mc extraction from colored noise requires matched filtering) aLIGO colored noise improves MAE in Stages 1-3 (effective low-pass filtering) while increasing Delta-s separation The Delta-s metric does not distinguish between law recovery and correction detection — the desired behaviour for an agnostic hidden physics sensor v2 Update (April 2026): PSD Whitening Results Added Stage 4 (chirp mass Mc as hidden parameter) under aLIGO colored noise has been re-run with PSD whitening applied as pre-processing (dividing the frequency-domain signal by sqrt (Sₕ (f) ), the standard LIGO data analysis step). Whitening result: Stage 4 aLIGO recovers from 1/3 to 3/3 seeds flagged (MAE = 0. 21, mean Delta-s = 0. 025). Without whitening: MAE = 42, Delta-s = 0. 373, 1/3 seeds. The whitening confirms that the Stage 4 aLIGO failure in v1 was physically correct (not a pipeline bug), and that PSD whitening is the correct pre-processing step for Mc extraction from colored noise — mirroring its role in standard matched filtering. The updated table (Table 1) now includes a 9th row: Stage 4* aLIGO + whitening: 3/3 HP, MAE=0. 212, Delta-s=0. 025.