Quantum Theory as the Operational Shadow of the M--A Channel: a Substratum Reconstruction in Absolute Frame Theory

The reconstruction program of quantum foundations asks why nature is described by complex Hilbert spaces with the Born rule, and why its correlations stop at the Tsirelson bound rather than saturating the no-signaling limit. Absolute Frame Theory (AFT) embeds the observable four-dimensional manifold M in a continuous Euclidean substratum A carrying a pilot wave, with an information-bottleneck channel that projects A onto M and traces out an inaccessible fiber. We propose that finite-dimensional quantum theory is the operational shadow of that channel---the channel viewed from within M, restricted to its M-accessible, identifiable part---and we carry out the reconstruction in that reading. This is a program, not a completed theorem: we mark every claim as derived, as a structural correspondence, or as an open frontier, and we state plainly that AFT is not yet formulated as an operational-probabilistic theory in full rigor and that the complex Hilbert structure is here a mechanism (the analytic-signal representation of the channel's sampling), not a posit. Within those limits the reconstruction reduces the why-of-quantum-theory to a single physical fact---the M--A signature transition, the Euclidean-to-Lorentzian Wick rotation---of which the complex structure and the Born rule are the two faces. Concretely, a linear map carries both the complex generator and the conserved ||² density if and only if it is unitary. The same signature transition is, in AFT, the root of parity violation and of the arrow of time; quantum theory, parity violation, and time's arrow thus share one origin. The operator-level complex structure that makes the theory locally tomographic is supplied by the Osterwalder--Schrader reconstruction about that single Euclidean time---reflection positivity being a theorem for the free embedding sector and preserved, by a local Feynman--Kac argument, for static configurations---hence complex quantum theory is derived, not posited, in the static sector. The named open frontier is then the time-dependent and interacting reconstruction, while the Born measure ||² is shown to be the equivariant density of the reconstructed unitary and generic macroscopic matter is derived to be classical, leaving only the strict Dürr--Goldstein--Zanghì uniqueness open. That the embedding yields the Lorentzian signature, and with it emergent local Lorentz invariance, is established in a companion paper on emergent Lorentz invariance.