MCMC chains results- updated

Working update note, 26 October 2026. A free-parameter MCMC comparison on the joint Planck + DESI DR2 BAO + PantheonPlus set is now complete and deposited here. The note does not revise the locked geometric identification, does not replace prior records, and does not claim a detection. The exercise does not crown a victor. It places two constructions in the same small region and, in doing so, opens sharper questions than a decisive ranking would have allowed. One construction is free to adjust along the entire trail; the other is fixed and can be examined only once the trail has been exposed. That both finish near one another is the observation. That the proximity itself generates the next precise questions is the use of the result. The work remains open. Further checks are still possible. Data and Einstein remain the standard against which any subsequent step will be measured. Companion to Zenodo record 23653695. Prior deposits are not replaced.