Eco : From n = 4/3 to pc = 0.3116

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.