Realization Limits of the Bicomplex Signal Surface: Analytic Rigidity, Smooth Flexibility and Observation Monodromy

A prescribed power distribution on a two-component signal fixes the moduli of the components but leaves their phases free. Can this freedom realize an explicit ruled surface S in R3 through a fixed readout map? For the original assignment (|z1|2, |z2|2) = (cos t, 1 − cos t) the answer reveals a sharp distinction between analytic and smooth realizations. No readout that is real-analytic along the circle {z1 = 0} realizes S, whatever states are used; this excludes affine projections, polynomial maps and every polynomial in a bicomplex variable and its conjugates. Explicit C∞ readouts, however, do exist. The obstruction sits at a single geometric feature: the two edges of the source are forced onto one circle of states, while S maps them onto two different lines. Removing that feature restores analyticity: each half of the source has a real-analytic readout, and a modified power assignment has a quadratic one. The paper also identifies the carriers of the square-root monodromy of the observation field. It lives on a local system that is indecomposable over Z and splits after inverting 2, and it is distinct from both the fold involution and the normalization defect. The exceptional pullback of Z along any continuous planar map from a convex domain depends only on the domain; folds are seen instead by the comparison map that defines cohomological smoothness. Residual geometry (a parameter-free 3/4 resolution law, an explicit A3 completion, three projected curves) and the spectral estimates that remain valid are collected as well. This is the corrected successor to Geometric Realization of Bicomplex Signal Manifolds (ResearchGate record 408878000, files v11 and v12, doi:10.13140/RG.2.2.17048.15361). That record is kept unchanged; an appendix reviews every named statement of v12 and of its public description. The main corrections: no analytic readout exists, while C∞ readouts do; the formula i*Ψ!Z ≃ Z[−1] on the fold locus does not hold; the (2,2) deficiency claim for the original two-point operator H0 is replaced by the corrected operator treated in the companion paper (doi:10.5281/zenodo.23103056); and the sign reversal of √F is not an exchange of the sheets of a fold. Verification companion (exact and finite replays; Lean covers 33 selected theorems only and is not a formalization of the paper): doi:10.5281/zenodo.23103299.