Nonary Dynamic Geometry: A Treatise on the Discrete Architecture of Three-Dimensional Space

This treatise develops a geometric approach to understanding and explaining physics: from a three-dimensional space studied as a saturated base-9 Cosserat lattice, evolving in physics to a visco-elastic micropolar medium, with Kelvin–Voigt-type response and constitutive properties, that depends on its local state of deformation. Particles and fields are interpreted through the waves, defects and geometric configurations of this medium.The 9³ = 729-state cell—written ⟨999⟩ in NDG’s ordinal notation—serves as the geometric and topological reference for a neutral, unstrained state, from which physics happens and nature evolves. From four postulates and a declared constitutive identification, with no continuously fitted parameter, the dimensionless coefficients of this medium give: - the weak mixing angle as one deformation trajectory, from 2/9 (neutral lattice) through 144/625 (membrane strain) to the measured 0.2313;- the muon-to-electron mass ratio, 207 − 144/625 = 206.7696 (6 ppm), the fine-structure constant (0.2 ppm) and the Higgs vacuum expectation value (0.4%);- the proton magnetic moment, μp/μN = 8π/9 (0.011%), and the proton charge radius, 0.8412 fm from a Bessel cavity dilated by the auxetic strain 32/729 (0.04% from muonic hydrogen);- the B-DNA waveguide, with fill factor 0.540 (Franklin's 0.54) and a bandwidth (4/9)³ × 729 = 64 read against the 64 codons;- ΩΛ/Ωm = 54/25 (0.7%), ΩDM/Ωb = 340/63 (0.6%) and the spectral tilt ns = 0.9667 (0.4σ) against Planck 2018, the comparisons including DESI being given in the text with their tensions, and a form-dependent gravity law with the galactic acceleration scale cH0/2π. At planetary and satellite scales, a Bessel phase backbone of orbital spacings is fitted across eleven systems, with a scale R0 and a step k for each non-solar system, and compared with geometric sequences at identical nodes. For the solar system the step 7/40 follows from the stated geometric and constitutive identification; the five major Uranian moons, free of low-order resonances today, follow the backbone at 3.8% RMS (two parameters, consecutive nodes, p ≈ 0.004 under a log-uniform null). Falsifiable consequences include a neutrino mass sum of 0.06 eV with a massless lightest state (at the edge of the DESI DR2 + CMB bound, about 0.064 eV at 95% in ΛCDM), a dark-energy equation of state w = −77/81, a sonoluminescence collapse ratio of 9, and a density-dependent Hubble ratio reaching 13/12 in dense environments (conjecture). Each result states its status, hypotheses and refutation test; a cross-domain discriminant reaches 3.4σ under its null model. Version 2.2 (1,250 pages) supersedes the earlier versions, including v1.0, "Nonary dynamic geometry and physics". The LaTeX sources and companion verification scripts are included; the Master Table script recomputes the 72 entries with a closed numerical form through 170 identities and documents the status of the other 24.