A Möbius-Scale Spinor Lift of Lorentz Kinematics: The Contained-Volume Law for Four-Momentum

Lorentz transformations are linear on Minkowski spacetime but induce Möbius maps on velocity, null-direction, celestial, and spinor ratios. Starting from this correspondence, we introduce the active model lift B = λA ∈ GL(2,ℂ), with A ∈ SL(2,ℂ), λ = κ exp(iθ), and κ > 0. The scalar factor leaves the projective Möbius action unchanged, while the momentum-spinor postulate gives P′ = κ²APA†. For a fixed domain with uniform scalar transfer and Lorentz map and homogeneous reference momentum density, P_(Ω,r) = C_r κ² V_Ω, hence P ∝ κ²V under a fixed projection and reference state. We distinguish the active modulus κ from the fixed physical reference constant κ₀ by κ(x) = κ₀ exp[δχ(x)]. The normalized limit κ/κ₀ → 1 recovers special relativity, followed by the standard Newtonian low-velocity limit. Under the proposed scale-length closure, κ₀ = ℓ_P²/(η_Q a_min²) only after a_min and η_Q have been fixed independently; modular mathematics alone does not determine its physical value. No numerical estimate of κ₀ is used in the derivation.