The Geometric Growth Factor: Unifying the JWST Early Galaxies and the S8 Tension

We present a unified cosmological history based on the Axiomatic Physical Home-ostasis (APH) framework, resolving two apparently contradictory tensions in modern cos-mology: the unexpectedly rapid formation of massive galaxies at high redshift (observed byJWST) and the suppression of matter clustering at low redshift (the S8 tension). We derivethe Geometric Growth Factor DAP H (z), which modifies standard linear perturbationtheory by introducing Geometric Stiffness (β ≈ 1.91) as a resistance to gravitationalcollapse. We demonstrate that the early universe (z > 10) was seeded by non-associativetopological defects (Sedenion Seeds) formed during the S → O phase transition, acceler-ating early structure formation. Conversely, at late times (z < 1), the super-linear stiffnessof the vacuum acts as a Geometric Viscosity, suppressing the growth of structure andresolving the S8 tension. Finally, we predict the fractal dimension of the cosmic web tobe DF ≈ 2.48, confirming that large-scale structure is a ”Stiff Web” stabilized by vacuumtopology.