Abstract (Edition III-III, May 2026) This work develops a zero‑parameter cosmological and physical framework that starts from a single measured quantity: the refractive index of liquid water at standard conditions, n=4/3n=4/3. Using Snell–Descartes optics and 3D cubic percolation, this one input fixes three dimensionless invariants – the toroidal winding number ωTωT, the percolation threshold pc≈0.3116pc≈0.3116, and the membrane fraction δmem=0.05δmem=0.05 – which then propagate across optics, metabolism, cosmology, and AI training without further free parameters. The six‑step derivation chain yields: the primary rainbow angle; the toroidal winding on a non‑orientable M5M5 manifold; the 70/25/5 partition of dark energy, dark matter, and baryons; Kleiber’s 3/43/4 metabolic exponent as a carrier‑medium ceiling; the present‑moment timescale; and a 14‑rung membrane hierarchy from quark to observable universe. In this edition, the same 70/25/5 topology is used to derive the dark‑matter density Ωdm≈0.25Ωdm≈0.25 directly from the partition, matching Planck‑2018 Ωdmh2Ωdmh2 to within ∼ 5%∼5% with no extra parameters. Furthermore, the nested JWST infrared‑bleeding cascade provides an independent route: fitting the cascade to observed high‑zz galaxies returns δmem=0.05±0.01δmem=0.05±0.01, which independently predicts Ωdm=0.25Ωdm=0.25, closing the dark‑matter budget from two orthogonal measurements. The same invariants also support a two‑factor resolution of the Hubble tension – a toroidal phase correction and a local 5%5% membrane density enhancement that together predict H0local/H0CMB=1.085H0local/H0CMB=1.085 – and bring “over‑massive” JWST high‑zz galaxies back inside the ΛΛCDM halo‑mass function through a 14‑scale multiplicative membrane cascade. All claims are tagged as derived D, structural conjecture SC or open/falsifiable O/F, with explicit falsifiers: DESI and Euclid for the torus geometry and dark‑matter budget, JWST + ALMA for δmemδmem, Titan’s Dragonfly mission for the Kleiber ceiling in methane, and antihydrogen, pulsar, and galaxy‑spin data for the binding operator and toroidal axis.
Kim et al. (Wed,) studied this question.