Intrinsic Clock Synchronisation and the Mathematical Necessity of a Unique Stationary Frame in Special Relativity

This paper presents a clock‑synchronisation procedure equivalent to the Poincaré–Einstein convention, treating time coordinates as ensembles of intrinsic proper‑time indications of abstract clocks distributed throughout space. Starting from Einstein’s postulates and an isolated moving inertial frame, the synchronisation rule is expressed as a sequence of operations on clocks and light signals rather than as an abstract algebraic construction. Under initial conventional synchronisation t'=x'/c the propagation time from the origin to the synchronised point emerges as a function of a derived parameter c+, that depends on the system’s relative velocity, yielding an expression algebraically equivalent to the one‑way light velocity associated with the Tangherlini transformation. The analysis suggests that the Lorentz transformation implicitly contains the structural components of the Tangherlini transformation, making the two operationally equivalent under general covariance. The Lorentz transformation remains intact and is necessary for the appearance of c+. It is shown that Lorentz‑transformed coordinates coincide with the intrinsic coordinates of an event in the moving system only for a unique stationary‑frame velocity, indicating a condition for coordinate consistency rather than a constraint on the underlying physics. In this formulation, relative simultaneity arises as a coordinate artefact tied to the synchronisation convention rather than a physical effect.