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 M and the Euclidean substratum A: the imaginary unit is introduced by the M--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 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 -₀0 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, JS1=1 Jₒ'---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 A is Euclidean. That fact is not an arbitrary extra assumption: it is entailed by 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 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.
Patricio E. Valenzuela (Tue,) studied this question.