Discussion
The current framework (Beta 1) is a kinematical reformulation in (1+1) dimensions, not a complete dynamical theory. These are the principal directions in which it remains open — condensed from §6.7 of the manuscript.
Length contraction already follows from the derived Lorentz transformation at the coordinate-kinematic level. What is missing is a bundle-intrinsic, dynamical derivation: extending the construction from a single wave excitation to coherent ensembles of internal clocks bound by interaction terms not yet specified, and showing that the moving equilibrium configuration is the contracted one.
The wavefunction ψ(x, θ, t) is a complex scalar. There is no spinor bundle, no spin-½ structure, and no fermionic statistics in the framework as it stands.
The treatment covers a single-mode wave excitation on a single bundle. Whether multiple particles share one bundle or are described by tensor products of separate bundles is not yet fixed — a choice that entanglement and many-body coherence will require.
Extension to (3+1)-dimensional kinematics, non-collinear configurations, and accelerated observers requires generalizing the local constraint and the bundle structure. Curved or non-trivial spacetime backgrounds are similarly outside the present scope.
The construction is purely kinematical: it does not derive QED amplitudes or cross-sections, and includes no mechanism for gravitational attraction. The same interaction sector would also supply the binding forces underlying dynamical length contraction, above.
Within its (1+1)-dimensional domain, Beta reproduces the standard relativistic predictions that follow from γ — energy-momentum relation, time dilation, relativistic momentum, photon propagation, velocity composition. The distinction from the standard formulation is structural, not numerical. Discriminating signatures would have to come from genuinely new domains, such as the internal-mode spectrum of the fiber.
Mass is discussed in geometric terms, but the model does not yet include an analogue of the equivalence principle, nor does it account for gravitational attraction. Whether inertial and gravitational mass coincide in all dynamical scenarios, and whether a gravity-like mechanism can be formulated from trajectory curvature or wave interference, remain open.
The internal circular dimension supports multiple harmonic wave modes, each in principle a possible rest mass; the current paper restricts the construction to the fundamental mode. Why higher modes are absent, unstable, or inaccessible is not solved here — nature shows only isolated mass values, with no evidence of a regular harmonic sequence. This is one of the framework's main open problems.
Each of these is a programmatic direction, not an established result. For a broader question — whether Beta adds anything beyond standard relativity at all — see Is Beta just a reparametrization? →. See Publications for the full manuscript, and get in touch with thoughts or relevant references.