# Reality revision 1.46 — latent rotation matrices and inverse limits

Matter Harmony Lab 0.3.0 now builds explicit theoretical vector matrices for a
five-coordinate molecular state and its three-dimensional projection:

\[
X_5(t)=X_5(0)e^{t\Omega^T},\qquad
X_3(t)=X_5(t)P^T,\qquad
V_3(t)=X_5(t)\Omega^TP^T.
\]

The real skew-symmetric generator preserves five-dimensional norms. All 17
frozen C5--C7 alkane graphs receive position, velocity, and phase-interference
matrices, and n-heptane receives a 65-frame projected animation.

The key correction is identifiability. Mapping observed boiling and fusion
temperatures to angular coordinates reproduces all values to machine precision,
but independently shuffled values reproduce equally exactly. An arbitrary
uncoupled hidden-plane rotation causes zero visible change, while fixed-tick
plane rotations alias \(\omega\) with \(\omega+2\pi k/\Delta\). Static property
tables therefore do not uniquely determine hidden-dimensional rotations.

All 30 unit tests pass. A separately written implementation reproduces 68
property/frequency checks, 2,730 trajectory scalars, 124 hidden-invariance
states, and 205 fixed-tick alias pairs.

This is a mathematical construction and finite synthetic calculation using
reference property data, not a measured molecular trajectory, new force law,
or physical identification of fourth/fifth dimensions. The next test must
freeze a target-independent descriptor-to-generator law and evaluate a fresh
C8 or time-dependent/spectroscopic target without using that target to define
its frequency.