The Beta Hypothesis is a geometric reconstruction of relativistic kinematics in which the underlying object is not a Minkowski spacetime, but a fiber bundle M = D1 × S1 — a one-dimensional base and a compact internal circular fiber — equipped with a local propagation constraint vx2 + vθ2 = c2 on the wavefield. The bundle and the constraint are common to all observers; the parametrisation of trajectories is relative to the internal clock of each observer. The Lorentzian structure of relativistic kinematics is not postulated at the outset: it arises as an emergent consistency structure when different observers, each using its own internal clock as time parameter, give mutually coherent descriptions of the same constrained bundle, with Lorentz invariance selected under the standard inertial-frame assumptions. The Minkowski metric is therefore not the geometry of the bundle itself, but the geometry of consistency among its multi-observer descriptions. A single operational definition of energy — the rate of wavefront crossings multiplied by ℏ — yields the Planck relation directly and, through the algebraic decomposition of the geometric dispersion, the de Broglie relation. Time dilation, relativistic momentum, and the identification of rest mass with an internal mono-harmonic frequency follow as kinematical consequences. The local constancy of photon propagation between massive observers follows from Postulate 1 in the massless limit; the topological rigidity of E0 = m0c2 selects SO(1,1) on (E, pxc), yielding the relativistic composition of collinear velocities. The construction is a kinematical reformulation, not a dynamical theory of interactions.