Independent FLRW Consistency Tests Three recent papers by Koksbang, Heinesen, and Clifton (arXiv:2604.05836, 2604.05822, statistic σ(z), its integral Ω(z), and a density estimator

Three recent papers by Koksbang, Heinesen, and Clifton (arXiv:2604.05836, 2604.05822, 2604.07244) derive model-independent consistency tests for FLRW cosmology — the CBL statistic σ(z), its integral Ω(z), and a density estimator (z) — and apply them to DESI DR2 + ℳ Pantheon+, finding 2–4σ deviations from flat ΛCDM. We compute the framework predictions for all three statistics from zero free parameters. The framework occupies a third class not considered by Heinesen-Clifton: neither Dyer-Roeder (optical only) nor standard backreaction (geometric), but c(t) H(t) with κ = −1 and Carreau-Yasuda brane rheology. This produces a ∝ characteristic comoving distance χ = L_AdS ln(1+z), giving Ω(z) > 0 at all z (sign consistent with DESI DR2 observations), σ(z) > 0 growing with z (positive and growing, consistent with observations), and (z) > Ω_m,0 (excess apparent density from suppressed d_A). The ℳ framework's logarithmic comoving distance is distinguishable from both Dyer-Roeder and backreaction signatures with DESI DR3 and Euclid. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.