Three Histories Against the DESI Ruler: Evolving Dark Energy Helps, a Shrunk Ruler Alone Fails

Baryon acoustic oscillation measurements from the first DESI data release provide eleven precise distance determinations between redshifts 0.295 and 2.33. This paper scores three expansion histories against those eleven numbers, without refitting: the Planck standard history; the same early universe with an evolving dark-energy equation of state (w0 = −0.83, wa = −0.75); and a bounce-frame combination in which the sound horizon is shrunk to 135.65 Mpc, the value the local ladder requires, while the Hubble constant takes the SH0ES value of 73.04 km/s/Mpc and the physical matter density is held at the Planck value. The standard history gives a chi-squared of 18.77 for eleven points. Evolving dark energy improves this modestly to 15.34, a gain of 3.43. The shrunk-ruler combination fails decisively, with a chi-squared of 82.97 and every one of the eleven pulls positive: shrinking the ruler while raising the expansion rate over-predicts the transverse and line-of-sight distances in ruler units at nearly every redshift. The negative result is the finding: a smaller sound horizon is not by itself a resolution of the Hubble tension, because the same change that reconciles the microwave background with the ladder breaks the intervening baryon acoustic oscillation distances unless the late-time expansion shape changes with it. All results are computed from published data and stated assumptions; nothing here is measured.