The BAO standard ruler reads two lengths: DESI prefers r_d near 147 +/- 1 Mpc while Planck's ΛCDM inference gives 150.0 +/- 0.4, a 2.3σ mismatch in a computed quantity with no free parameters. The offset quietly powers the Hubble tension, since the CMB-calibrated ruler is what holds BAO to the low H₀, and every early-time patch that shortens it imports tuned new physics and pays in the damping tail.
The ruler's length follows from the primordial plasma's sound speed, c_s² = c²/[3(1+R_b)], with the baryon loading R_b in the denominator: an assumption about the acoustic medium, computed rather than measured. If the plasma's acoustic structure differs from that formula, every distance in cosmology is calibrated against a miscomputed length.
SCT modifies exactly the computed step: in the coherent acoustic regime the collision-thermalized plasma carries baryon loading in the numerator, c_s² = c²(1+R_b)/3, collision geometry enhancing acoustic pressure where ΛCDM books baryon inertia dragging it (P29, P30, P45), a genuine physical difference in the medium, not a parameter shift. Run through the full Boltzmann machinery, the modified sound speed yields r_d = 149.1 +/- 0.3 Mpc, landing between the contested anchors: 2.0σ from Planck, 2.1σ from DESI, reducing the inter-dataset tension from 2.3σ to about 1.1σ with the baryon loading itself independently derived from cascade geometry (R_b = 0.2545, 0.17σ from observation). The ruler disagreement becomes a measurement of the acoustic medium, and the same regime delivers the joint fits whose Bayesian comparison favors the two-parameter CAR over the 48-parameter standard chain. The CAR framework is Paper 16, From Chaos To Codified Acoustics, with the R_b derivation in Paper 17, From Chaos To Coalescent Parsimony.
Two premises and one derived constant carry the resolution, and the family follows: the H₀ that emerges from the CAR chain (70.4 +/- 0.4) splits the Hubble anchors the same way the ruler splits the distance anchors, one acoustic modification reconciling both ledgers.
PROVISIONAL: r_d = 149.1 and the CAR H₀ come from the modified CAMB pipeline pending independent third-party verification, with a known 28 Mpc discrepancy between the simple analytic integral and the full solver output flagged as unresolved in the registered ledger. The numbers are published predictions, not settled results.
The registered kill: DESI Year 5 measuring r_d above 150.5 or below 145.0 Mpc at 3σ falsifies the CAR value; within the band, the decisive test is the verification itself, since an independent Boltzmann run failing to reproduce 149.1 from the CAR sound speed would retire the provisional reconciliation. The companion derivation shares jeopardy: observed R_b outside 0.158 to 0.350 breaks the chain that feeds the ruler.