The Quantum Phase from the Euclidean Substratum: the Wick Signature Transition as the Single Foundational Posit of Absolute Frame Theory

Why is the physical action a phase, $e^{iS}$ (oscillatory, norm-preserving, interference-bearing), rather than a real weight, $e^{-S}$ (diffusive, dissipative)? This is the difference between a quantum and a merely statistical world, and in Absolute Frame Theory (AFT) it is the difference between the Lorentzian observable manifold $\mathcal{M}$ and the Euclidean substratum $\mathcal{A}$: the imaginary unit is introduced by the $\mathcal{M}$--$\mathcal{A}$ signature transition, the Wick rotation. We show that this transition is the single deepest posit beneath the AFT account of quantum theory---the same root from which the complex structure, the Born rule, parity violation, the arrow of time, and the Tsirelson bound were separately shown to follow---and we reduce it as far as a physical theory can reduce its own ground. The signature transition factorizes into three layers: the existence of a time direction (the sliding of the embedding interface), the orientation (the arrow, fixed by informational irreversibility), and the complex/unitary character (the $i$ and the phase). For the last and only open layer we prove three statements. First, the complex structure is not smuggled in: it is the real, antisymmetric generator of the first-order phase-space closure of a real oscillation, present in the real description before any imaginary unit is named. Second, we prove a theorem---for the free sector with uniform sliding---that the reconstructed evolution on $\mathcal{M}$ is unitary (the phase $e^{iS}$, with a single complex structure), and that no dissipative $e^{-S}$ sector is admissible: the positive Euclidean Laplacian $-\Delta_{\mathcal{A}}\ge0$ admits only oscillatory bounded substratum modes, the comoving frame is static, and Osterwalder--Schrader reconstruction delivers a positive Hamiltonian and unitary continuation. Third, that single complex structure acts compatibly across subsystems, $J_S\otimes\mathbb{1}=\mathbb{1}\otimes J_{S'}$---an operator identity, not a shared scalar sign---so the reconstructed theory is locally tomographic, complex rather than real (rebit). The phase is therefore forced by the single fact that $\mathcal{A}$ is Euclidean. That fact is not an arbitrary extra assumption: it is entailed by $\mathcal{A}$'s role as the atemporal, stable, deterministic ground (atemporality forbids a timelike direction; a bounded-below action requires positive-definiteness), hence the two-signature architecture reduces to one posit. Asking why $\mathcal{A}$ is Euclidean is asking the theory to derive its own ground---a foundational question of self-referential, not identifiability, character. The reduction is sharp: it does not derive the posit from its origins, but it shows the posit to be single, non-arbitrary, and necessary given the role. The open residual is thereby narrowed to two sectors, the interacting and the curved/horizon, the latter addressed by modular reflection positivity in the companion dynamical reconstruction.