The BAO standard ruler is drifting between its users. Galaxy, quasar, and Lyman-α tracers return mildly different scales, and DESI prefers r_d near 147 Mpc where Planck's ΛCDM calibration gives 150.0 ± 0.4, a pull above 2σ (Aubourg 2015; Alam 2021; DESI 2024). A ruler that should be one number is behaving like a family of numbers.
The model computes a single sound horizon from early-universe physics and propagates it through a single global expansion history. Both halves are assumptions: one r_d for all tracers, one H(z) for all environments. Any genuine drift between tracers has nowhere to go except systematics or new dark-sector physics, and the proposed extensions each repair one dataset by straining another.
SCT modifies both halves, which is why this tension takes two mechanisms where most take one. The ruler itself is set by the CAR sound speed of Paper 16, From Chaos To Codified Acoustics: c_s² = (1 + R_b)/3, with the baryon loading R_b in the numerator because coherent acoustic superposition of comoving baryons enhances acoustic pressure rather than merely adding inertia (P45). With R_b = 0.2545 ± 0.032 derived from cascade geometry alone in Paper 17, From Chaos To Coalescent Parsimony, no BBN or CMB input, the modified CAMB run yields r_d = 149.1 ± 0.3 Mpc, sitting between the DESI and Planck inferences and cutting the inter-dataset tension roughly in half.
The carrying is the M5 half: dynamical Λ_eff(x,t) makes the expansion history mildly environment- and epoch-dependent (P17, P18, P19), so the angular-diameter-distance mapping that converts the ruler into an observed scale differs slightly between tracers sampling different redshifts and different density environments. The registered prediction is concrete: void-environment BAO tracers should return a D_A shifted from cluster-environment tracers by 0.1 to 0.3 percent at the same redshift. The drift between tracers is not noise to be modeled away; it is the ruler reporting the structure of the Λ_eff field it travels through.
PROVISIONAL (M6 component). The CAR-derived r_d = 149.1 Mpc carries the Paper 16 Section 2.3 caveat: a 28 Mpc gap stands between the simple analytic sound-horizon integral and the modified-CAMB output, most likely because the patch modifies c_s² in the perturbation equations but not the background routines. The value awaits independent third-party verification. The M5 environmental component is grounded separately.
Two registered kills. DESI Year 5 measuring r_d above 150.5 or below 145.0 Mpc at 3σ refutes the CAR ruler directly. Environment-split BAO finding void and cluster tracers consistent to better than 0.05 percent in D_A at the same redshift rules out the predicted 0.1 to 0.3 percent Λ_eff shift and removes the M5 half. Both legs must survive; either failing breaks the resolution.