Dark matter is usually introduced as a new particle species, a hidden sector, or a phenomenolog- ical fluid. I describe a different source-level possibility: dark stress-energy may arise from retained gauge-topological transgression data while the metric equation remains in Einstein form. The orga- nizing device is a complex two-sector equation whose real projection is the ordinary Einstein curva- ture response and whose imaginary projection records an independent gauge-topological consistency channel. If the selected two-sector carrier data are obstructed in the Poincare-Hopf/hairy-ball sense, a global nonvanishing carrier is unavailable and patch, transition, connection, and curvature data must be retained. Keeping only the minimal degree-four gauge Chern-Weil representative then se- lects the local Chern-Simons transgression current πΎβ = *πΆπ (π΄). Locality, covariance, symmetry, linearity in that current, and first-derivative order fix the leading non-trace rank-two source seat to β (ππΎπ). Thus the physical field equation can remain Gββ + Ξ gββ = 8ΟG (T^knownββ + T^topββ), T^topββ β (Ξ» / 8ΟG) β (β Kβ) The construction is not a modification of the Einstein tensor and does not postulate a fundamen- tal dark particle. Its counter-standard prediction is the loss of an arbitrary dark amplitude: the low-energy Chern-Weil/theta normalization gives π0 = 4ππΌπ, while observed amplitudes must be branch-dressed projections. For the π = 1 benchmark, present low-redshift consistency requires an order-one-or-smaller projected dressing, πsh β² 0. 715, excluding an unsuppressed universal propaga- tion map.
Guojun Pan (Mon,) studied this question.