Late-time Recognition-Weighted Growth and the Hubble Tension

Background: Late-time structure probes and CMB inferences yield discrepant values of the Hubble constant when analyzed under standard GR growth kernels.

Objective: We test whether a recognition-based late-time kernel anchored by a global timescale τ* can reconcile low- and high-redshift determinations of H0 without altering early-universe physics.

Methods: We introduce a dimensionless ILG kernel w(k,a) = 1+φ^(-3/2)(ac/kτ*)^α, propagate it through BAO, RSD, weak lensing, supernova, and peculiar-velocity likelihoods, and quantify the impact on H0 and σ8 using the same nuisance priors as GR.

Results: Across the late-time dataset suite, the kernel yields H0 = 71.8 ±1.2 km s^(-1) Mpc^(-1) versus the GR baseline 68.8±1.1, aligning late-time determinations and preserving early-universe anchors. Relative to Planck's CMB-inferred anchor, the ILG late-time result is higher; we therefore frame the main outcome as improved late-time internal alignment while quantifying the residual tension with Planck. Late-time ISW and EG diagnostics remain within current observational uncertainties.

Conclusions: A recognition-weighted Poisson source can alleviate the Hubble tension while keeping the early-universe sector untouched, offering a parameter-fixed alternative to dark-energy extensions. Future wide-area surveys will test the predicted percent-level tilt in fσ8(k) and EG.