Verbal-postulate reconstruction obligations not discharged by this framework

This framework adopts the oriented time-oriented affine Minkowski space (Oriented time-oriented affine Minkowski space (the spacetime primitives)), its inertial frames and inertial charts (Inertial frames and inertial charts of the affine Minkowski model), and the assertion that inertial changes of description are governed by that geometry (Adopted inertial covariance of the model equations). The transformation law derived on this page is a conditional consequence of that adoption. This remark records the epistemic status of the starting point; it makes no further physical or mathematical claim.

In particular, the page does not claim to derive the model from the verbal postulates customarily used to motivate special relativity: Einstein's principle of relativity for mechanics and electrodynamics together with the constancy of the speed of light in vacuum (as paraphrased in Crowell, Section 2.4.1), nor from Crowell's postulates P1-P6 (causality, flatness, homogeneity/isotropy, inertial-frame existence/equivalence, and relativity of time) (Sections 2.1-2.4). A reconstruction from such verbal statements would still owe, at least, the following open steps.

1. A precise formal statement of homogeneity and isotropy of spacetime as symmetry assumptions, including the class of allowed coordinate changes.
2. An existence and modelling assumption that inertial frames exist, and that frames in uniform relative motion are related by transformations of constant velocity.
3. An operational definition of simultaneity and of the light-signal comparison, together with the assumptions needed to turn the light postulate into a statement about the quadratic interval.
4. A proof that the admissible coordinate changes form an affine group preserving a quadratic form of Lorentzian signature, with the conversion constant fixed.
5. A decision about global topology, since flatness alone does not exclude quotient spacetimes such as cylinders that admit no global inertial chart.

None of these steps is carried out here, cited as proved, or used as a logical premise. The framework's adoption of the geometry is a modelling assumption, and the obligations above are recorded as open work, not as established mathematical facts. In particular, no item on this page or on its companion page may treat this remark as a premise establishing the geometry, and no claim is made that the verbal postulate systems are logically equivalent to the affine model.