Geometric matter density Omega_m = 1/pi: Confrontation with the CMB power spectrum, BAO distances, and matter clustering

We evaluate the cosmological prediction Ω_m = 1/π ≈ 0.3183, derived from the material yield limit of a five-dimensional dual-phase substrate with zero free parameters, against the Planck 2018 CMB power spectrum, DESI DR2 baryon acoustic oscillation distance ratios, and the BOSS/eBOSS linear matter power spectrum. Using the CLASS Boltzmann solver (v3.3.4) with no modifications, the geometric model reproduces the Planck ΛCDM TT, EE, and TE power spectra to χ²/dof < 0.01 at H₀ = 67.0 km/s/Mpc across all multipoles 30 ≤ ℓ ≤ 2500. Direct comparison against the Planck 2018 binned TT data yields χ²/N = 1.20 (83 bins) with a single amplitude parameter. The geometric impedance equation reproduces DESI DR2 BAO distances across seven redshift bins (χ² = 26.6, 12 observables). The clustering amplitudes σ₈ = 0.824 and S₈ = 0.849 match ΛCDM; a companion analysis shows that introducing a lattice sound speed c_s² = α³ yields S₈ = 0.775, resolving the S₈ tension with DES Y3 to 0.07σ. The framework reduces ΛCDM from six to five free parameters.

This deposit contains the article source (.tex), compiled article (.pdf), companion Google Colab notebook (.ipynb) reproducing all figures and tables, and a PDF print of the notebook. The notebook is fully self-contained and requires no local software installation.