Matching those endpoints does not determine every interior point. An additional geometric or physical premise is required to set the normalized interior relation. Arbitrary unequal scale divisions do not automatically preserve the ordinary Pythagorean identity.

The source identifies Lorentz-compatible kinematics as one route to the required normalization, with homogeneity, isotropy, reciprocity, and transformation composition entering that argument. Those are substantive premises. The unit-bound interior cannot be presented as following from the endpoint checks alone.

This October revision separates a useful algebraic test from a complete derivation. It establishes why one product construction fails to provide the desired common bound and where the alternative introduces additional assumptions. The result is a conditional mathematical clarification within the motion program, rather than independent evidence that discrete counts uniquely force special relativity.