AxisCRobust

The module records multi-axis robustness for the dimension route in the revised Three-Dimensional Space from Recognition Cost paper. Three axes (coefficient ring, tracked invariants, acyclicity) are structural predicate interfaces for later algebraic-topology formalization. A fourth axis, the recognized-object dimension $p$, is arithmetical: the codimension formula becomes $D = 2p + 1$, so only changing $p$ moves the spatial dimension.

Upstream, spatial dimension is forced to $D = 3$ (T8/T9 linking). Constants modules expose D := 3 as that forced value. The present declaration does not re-derive that forcing; it only names the claim that coefficient-ring changes do not disturb it after $p = 1$ is fixed.

No proof. The declaration is a definition of a proposition equal to True. Downstream theorem surfaces discharge it by trivial. The mathematical content is deferred: the module header states that coefficient-ring equivalence is a predicate-level interface awaiting algebraic-topology formalization.

Feeds the Axis C robustness theorem surface and the bundled multi-axis robustness theorem. The bundle states that only Axis P can move dimension away from 3; Axes C, I, and A stay stable at the theorem-surface level. That packages the paper claim that the $D = 3$ conclusion (forcing chain T8, linking T9) is insensitive to coefficient-ring choice once $p = 1$. Without this interface the multi-axis statement cannot name C-stability separately from the arithmetical $p$-axis that actually changes $D = 2p + 1$.