axis_C_robust

The module records multi-axis robustness for the dimension route in Recognition Science, from the revised paper on three-dimensional space from recognition cost. Spatial dimension is tied to a codimension formula $D = 2p + 1$ in the recognized-object dimension $p$; the case $p = 1$ yields $D = 3$.

Axis C is the coefficient-ring axis: whether changing the coefficient ring can move $D$ away from 3 after $p = 1$ is fixed. The robustness claim is a predicate-level interface, currently the constant true proposition, pending algebraic-topology formalization of coefficient-ring equivalences.

Only the arithmetical axis (varying $p$) is set up to move dimension; the coefficient-ring, tracked-invariant, and acyclicity axes are intended as stable once $p = 1$.

One-line tactic proof by trivial. The axis-C robustness predicate is defined as True, so the goal is immediate and no upstream lemmas are applied.

Feeds the bundled multi-axis robustness theorem, which states that only Axis P can move dimension away from 3, while Axes C, I, and A are stable at the theorem-surface level. That bundle is the formal counterpart of the robustness claim in the revised Three-Dimensional Space from Recognition Cost paper.

In the forcing chain this supports T8 ($D = 3$ spatial dimensions): once $p = 1$ is selected, coefficient-ring changes are recorded as not reopening the dimension. The structural True placeholder marks where a future algebraic-topology development of coefficient-ring equivalences would land without changing the surface API.