The Ten Pillars of Dark Matter: A Geometric Alternative

This document presents a systematic ten-pillar synthesis of the dark matter problem within the Geometric Relay Programme (GRP), built on Minazzoli’s Entangled Relativity action Lₘ²/R. The cold dark matter hypothesis is supported by a broad network of observational pillars: galaxy rotation curves, CMB acoustic peaks, baryon acoustic oscillations, structure formation, the matter power spectrum, gravitational lensing, the Bullet Cluster, the cusp/core problem, the baryon fraction in clusters, the abundance of large-scale structure, and the stability of fundamental constants. The purpose of this synthesis is not to claim that dark matter particles are excluded. The narrower question is whether particle dark matter is strictly necessary, or whether the same observational pillars admit a coherent geometric reinterpretation. Within the GRP, the central object is the relay tension R* = Omegaₘ - Omegab, interpreted as a cold geometric component emerging from the scalar relay field sigma. At the linear cosmological level, R* enters the Friedmann equation like cold dark matter, scales as (1+z) ³, and reproduces the same background expansion, growth factor, and matter power spectrum as Lambda-CDM. At galactic and non-linear scales, the same relay structure produces MOND-like fixed points, P4 saturation, core profiles, and discriminating departures from Lambda-CDM. The paper evaluates ten classical pillars of dark matter one by one: 1. galaxy rotation curves, 2. CMB acoustic peaks, 3. baryon acoustic oscillations, 4. structure formation and P (k), 5. gravitational lensing, 6. the Bullet Cluster, 7. cusp/core profiles, 8. baryon fraction in clusters, 9. abundance of large-scale structure, 10. stability of fundamental constants. Each pillar is assigned an epistemic status according to the GRP scale: A — derived or verified, B — structurally motivated but not fully derived, C — conjectural. The resulting synthesis gives seven pillars at status A and three at status A/B. The three A/B pillars — gravitational lensing, Bullet Cluster, and cusp/core profiles — share a common bottleneck: the absence of full N-body simulations with the relay field sigma (x) integrated into the gravitational solver. The gap is therefore identified as computational rather than conceptual. The document also lists explicit falsification criteria, including future measurements of S8, ultra-faint dwarf core profiles, cluster gravitational slip, M87* polarisation signatures, and compact-binary phase corrections. This synthesis closes the internal dark-matter sector of the Geometric Relay Programme. It argues that the standard observational evidence for dark matter admits a coherent, falsifiable, parameter-free geometric alternative. The conclusion is deliberately cautious: dark matter particles may exist, but their necessity is no longer automatic within this framework.