The Map Is Stretching: Cosmological Tensions as Artifacts of an Evolving Mercator Depth

In the extended Randall-Sundrum framework, the warping depth kL determines the conformal geometry through which all electromagnetic observations are made. If kL evolves over cosmic time — deepening from approximately 36 at recombination to 37 today, driven by black hole feeding of the d = 1 substrate — then observations at different redshifts are being read through different Mercator projections. This single effect produces the Hubble tension (different rulers at different epochs), the apparent cosmic acceleration (Mercator distortion mimicking dimming), and the evolving dark energy equation of state (w ≠ −1 as the projection derivative). The universe is not accelerating. The map is stretching. We show that one e-fold of kL change over 13.8 Gyr is quantitatively consistent with the Planck-SH0ES discrepancy (H₀ = 67.4 vs 73.0), the DESI DR2 evidence for evolving dark energy (2.8–4.2σ) [1], and the observed w₀ ≈ −0.8. The framework predicts that the apparent acceleration will continue to weaken as kL deepens further, and that the Hubble tension will grow with improvements in both CMB and local measurements. Hubble tension, evolving kL, Mercator projection, cosmic acceleration, dark energy, DESI, sound horizon, varying constants, Randall-Sundrum, cosmological constant