Structure Growth and the Early-Galaxy Population: A Mass-Dependent Seed Amplitude, Two Candidate Density-Evolution Mechanisms, and the Statistical Limits of Rare-Peak Selection

James Webb Space Telescope observations have identified galaxies and an accreting black hole at
redshifts implying they assembled substantial mass within a few hundred million years of
recombination, a tight timing budget in any cosmology. This paper tests whether that budget can be met using two candidate mechanisms already in Pixel Theory's toolbox: a small residual
scale-factor growth term, and a density-evolution term derived from applying apparent-horizon
thermodynamics to the framework's postulated G(c) dependence. Both are tested using a properly
mass-dependent seed perturbation amplitude and checked against a rigorous statistical ceiling on
how much preference for rare, high-density peaks can additionally buy. Results depend materially
on which of two distance-redshift fits is used and on the assumed halo mass scale; the more
nternally self-consistent fit closes the gap in most tested cases, the other does not.s
**Currency note added at deposit**: this paper's growth equation (Section 2.1) was built on a
residual small-expansion correction to an otherwise static metric. The project has since adopted
genuine metric expansion a(t) as the primary picture (see Paper 1, Paper 17), and this paper's own
internal note flags that its headline conditional-success conclusion in Section 6 likely does not
survive re-running with the correct, friction-included growth equation. It is deposited for
transparency and as a record of the mechanisms explored, not as a currently-endorsed result; see
Paper 17 for the corrected genuine-expansion cosmology this paper's growth equation should
eventually be re-run against.