Chart formulae and the exact dependency ledger

Write $x=(t,\mathbf{x})$, $y=(s,\mathbf{y})$, and $x^{\prime }=(t^{\prime },{\mathbf{x}}^{\prime })$, and set

This is a space of observation triples in one supported chart; it is not the spacetime host.

All comparison quantities are expressed in one fixed system of units. In particular $\mu \epsilon$ and the scale ratios inside logarithms are dimensionless.