Cosmic Recoil as a Phenomenological Link Between Baryon Asymmetry and Dynamical Dark Energy

Version 2.2 (erratum and extension of v2.1, same day). Data results unchanged: DESI DR2 BAO + Pantheon+SH0ES + Planck distance priors give w0 = -0.866 ± 0.058, wa = -0.514 (+0.217/-0.224), Δχ² = -9.0 vs ΛCDM; free-displacement Klein-Gordon fit Φi/f = 1.80 (+0.71/-0.55); β = cW × 2.29°; displacement-independent relation βCMB = 21.3° cW √(1+w0) MPl/fΦ; energetic bound x²/6 on any dynamical displacement. The β-w0 relation is now credited to Choi, Lin, Visinelli and Yanagida (PRD 104, L101302, 2021), which derived it first; this work recovers it with a universal coefficient (2% scatter) and applies it to the DESI DR2 posterior. The historical exponent 40/3 is shown to be convention-dependent (13.3/13.0/12.2/11.9) and is no longer presented as a target. Corrections in v2.2. (i) The gravitational Pontryagin coupling ΦRR~ of a cosmologically rolling field produces an amplitude birefringence ν ~ 4kΦ̇/(fRMPl²) ~ 10-101 at 100 Hz: the quantity ΞGW ~ 0.04 quoted in versions ≤ 2.1 was not the Chern-Simons observable and is withdrawn; the Pontryagin term has no gravitational-wave signature. (ii) The live gravitational-wave channel is the Nieh-Yan term, which produces a velocity birefringence (Li-Rao-Zhao 2020) with MPV = 5.7 κN √(1+w0) H0 MPl/fN, a second displacement-independent relation; for fN = MPl the prediction MPV = 0.6 κN H0 is a factor ~7 below the GWTC-1+2 bound (Wu et al. 2022) and within reach of ET/CE; fN < 1017 GeV is already excluded. (iii) In the Dvali-Funcke completion (Direction H2) the index-theorem normalisation of the gravitational θ-term gives fθ = fR/384π², so the cosmological fit fixes fR = 384π² MPl, not MPl. (iv) Kill-or-confirm audit of H2 across the Dvali-Funcke window ΛG = 4-256 meV: no value excluded; the surviving prediction is a nearly massless lightest neutrino at the hard level, mν1hard < 0.35 meV. New script audit_H2_chi_top_gw.py and outputs in the supplement. The Harvey-Turner no-go is retained: no claim of deriving the cosmological-constant scale is made.