# Reality revision 1.55 — multidimensional vector observers

The fixed skew-linear harmony engine is generalized from five coordinates to
arbitrary latent dimension `d`. It now exposes both the latent vector `x` and
its tangent vector `A x`, along with each calibrated three-dimensional
projection `P_j x` and projected velocity `P_j A x`.

The written result separates two questions. A single 3D observer has rank at
most three and therefore leaves at least `d-3` instantaneous directions hidden.
A simultaneous calibrated observer bank identifies the state exactly if and
only if the vertically stacked matrices have rank `d`. The executed coordinate
banks reach full rank for dimensions 4, 5, 6, and 8 and reconstruct frozen
states to numerical precision. An exact five-dimensional counterexample keeps
the projection unchanged while moving the latent state by one unit.

Multiple observers remove projection ambiguity, but they do not change the
intrinsic spectrum of the generator. A real `d`-dimensional skew generator has
at most `floor(d/2)` positive rotation frequencies. Dimensions 4 and 5 still
have capacity two; 6 and 7 have capacity three; dimensions 8 and 9 are the
first to have a count of four. Passing that count does not predict hydrogen's
wavelengths, intensities, transition rules, or physical dimensionality.

The evidence is written linear algebra and finite synthetic computation. It is
not a measurement of 4D/5D motion. The next physical gate must freeze a
transition operator and predict held-out spectral lines rather than selecting
dimension or frequencies after seeing them.