The Partition of Cosmological Tensions: DESI DR1 BAO Resolved by H₀ Artifact and Ω_m Deficit Without Evolving Dark Energy

The ξ-Normalization Framework for Cosmological Distance Comparison Martin, E.D. (2026b) · Preface, Provenance, and Validation Record This paper is the second in a sequence that emerged from an empirical observation, not from a theoretical framework built in advance. The starting point was the Hubble tension itself: the well-documented ~5σ discrepancy between the SH0ES distance-ladder measurement of H₀ = 73.04 ± 1.04 km/s/Mpc and the Planck CMB inference of H₀ = 67.4 ± 0.5 km/s/Mpc. While investigating the structure of this discrepancy, it became apparent that the two pipelines express cosmological distances in ways that encode H₀ differently — one geometrically (Cepheid calibration), one through a full CMB likelihood. The normalized coordinate ξ = dc/dH was introduced as a diagnostic: a dimensionless representation of comoving distance that cancels explicit H₀-scaling for redshift-derived distances. This was not designed to make the tension disappear. It was designed to ask: what fraction of the apparent discrepancy is a property of the comparison conventions, and what fraction survives as a physical signal? What the Analysis Found — In the Order It Was Found ~93% of the raw H₀ tension statistic dissolves under ξ-normalization, consistent with the two pipelines using incompatible H₀-dependent distance conventions. The residual after normalization (~7%) decomposes into a matter density deficit (Ωm ≈ 0.295 vs Planck's 0.315) and a weak dark energy signal (w₀ ≠ −1 at ~1.81σ under conservative N/U bounds). DESI DR1 BAO subsequently reported Ωm = 0.295 ± 0.015 from a fully independent H₀-free measurement. This was not known when the framework was developed. Why Additional Framework Was Laid Out Before Submission Reviewers reasonably ask: Is ξ-normalization a tautology? Is the result H₀-frame-dependent? Does it preserve information? Does it add value over standard methods? To answer these questions rigorously, a supporting validation framework was developed (available in the companion repository abba-01/hubble-anisotropy): Proof Result Proof 1 Distance ratios are exactly preserved across all H₀ frames (residual = 0.00e+00), verified against GAIA DR3 parallax. Proof 2 ξ is monotone and continuous from stellar (pc) to CMB (Gpc) scales — no discontinuities. Proof 3 H₀ variation leaves ξ invariant (range 5.5×10⁻¹⁷); Ωm and w₀ variation changes ξ (ξ is a diagnostic, not a tautology). Proof 4 Round-trip μ → ξ → μ residual = 0.00e+00; uncertainty tracking matches GAIA DR3 precision exactly. Proof 5 ξ reduces per-SN H₀ scatter by 38% vs raw local H₀ estimates; z-dependent residuals confirm non-trivial physical content. This framework was not part of the original discovery. It was built afterward to give reviewers the tools to evaluate the claim on its merits without having to take any single step on faith. Pre-Registered Decisive Test Euclid DR1 (October 2026) represents the pre-registered decisive test. Independent measurements of Ωm, S8, and the w₀wa plane from Euclid will either confirm or refute the framework's predictions without any additional free parameters. Relation to Companion Work Item Reference Role Paper 1 Martin 2026a DOI: 10.5281/zenodo.19230366 Introduces ξ; demonstrates the ~93% frame-artifact finding on SH0ES/Pantheon+. N/U Algebra Martin 2025 DOI: 10.5281/zenodo.17172694 Conservative uncertainty propagation framework used for significance bounds. UHA Patent US Provisional 63/902,536 Encoding infrastructure (Morton encoder, CosmoID, TLV format). Scientific results require only ξ, not the full patent architecture. Keywords Hubble tension, cosmological tensions, distance normalization, xi coordinate, matter density, dark energy, BAO, S8 tension, frame artifacts, Omega_m, w0wa, DESI, Euclid, Pantheon+, UHA, N/U algebra Related Identifiers Is supplement to 10.5281/zenodo.19230366 (Paper 1) Is supplement to 10.5281/zenodo.17172694 (N/U Algebra) References 10.5281/zenodo.19232340 (UHA v2.0.0 pre-registration) License & Access License Creative Commons Attribution 4.0 International (CC BY 4.0) Access Open Access