A geometric-modular-action question for the Bunch–Davies generalised free field on de Sitter

This companion note to Spectral Quantum Gravity (doi:10.5281/zenodo.20930664, v4.3.3) isolates, in self-contained form, the single question in algebraic quantum field theory to which that framework's Lorentzian-completion (emergent-time) problem reduces. The question: does the generalised free (Gaussian) field on four-dimensional de Sitter space whose two-point function is the de Sitter-invariant Bunch–Davies one — KMS-thermal at the Gibbons–Hawking temperature, with the maximal-analyticity (weak spectral) property of Bros–Epstein–Moschella — satisfy the Condition of Geometric Modular Action (Buchholz–Dreyer–Florig–Summers) for wedge regions, equivalently wedge duality? A positive answer closes a locality (micro-causality, at the wedge level) step in the emergent-gravity construction; a negative answer locates precisely where it fails. The note supplies the two inputs explicitly — the Bunch–Davies two-point function and the spectral condition — and records the reduction: Bros–Epstein–Moschella supply the de Sitter analogues of the Reeh–Schlieder and Bisognano–Wichmann theorems together with Gibbons–Hawking thermality, and for generalised free fields in d ≥ 4 the geometric-modular-action condition is equivalent to wedge duality and to covariance. The question can therefore be assessed entirely within algebraic and constructive QFT, independently of the originating framework. Two caveats are stated honestly: wedge duality is a strong but specific locality property, weaker than full micro-causality for every region; and the equivalence is a generalised-free-field (Gaussian-level) statement. This is a self-archived note posing an open question for the algebraic-QFT community, not a claimed result.