A Two-Fabric Readout Offset as Candidate Scaling Law for the Hubble and 𝑆8 Tensions

Paper K develops a Light Frame Cadence Theory (LFCT) candidate scaling law for the Hubble tension and the S8 tension based on a two-readout architecture operating on a single underlying fabric. The central proposal is that the discrepancy between early-universe and late-universe measurements arises from an accumulated readout offset governed by the structural constant epsilon = 1/pi^2 and a geometrically derived mode-counting rule Delta_n = n/4.

The paper derives the cadence-balance exponent Delta* = 1/4 from three independent geometric routes and assigns observable offsets according to the geometric dimensionality of the probe's readout. Spacing measurements engage one mode, path-integrated measurements engage two modes, and full projection-surface measurements engage all three modes. The resulting relation,

A_obs = A_light × (1 − epsilon)^Delta_n,

is applied to the Hubble tension, the S8 tension, and the CMB trough asymmetry.

Using current observational benchmarks, the framework predicts H0 = 72.98 km/s/Mpc from the Planck 2018 value of 67.36 km/s/Mpc, matching the SH0ES result within 0.06 sigma, and predicts S8 = 0.791 from the Planck value of 0.834, consistent with current weak-lensing measurements. The paper further identifies a structural 3/2 relationship between the Hubble and S8 offsets arising from the underlying mode-count assignments rather than from fitted parameters.

The work positions the cosmological tensions as different observational projections of one readout geometry. It develops the connection between the two-readout architecture, the cadence-balance exponent, the c²–c³ resolution framework, the π²/10 = c²/β₁ keystone identity, and the local cadence-shear field, while providing explicit observational tests capable of falsifying the proposed scaling law.