axis_A_robust

The module records the robustness theorem from the revised paper Three-Dimensional Space from Recognition Cost. Content is intentionally structural: coefficient-ring, tracked-invariant, and acyclicity-axis equivalences are predicate-level interfaces for later algebraic-topology work. The only axis that moves dimension is arithmetical: changing the recognized-object dimension $p$ changes the codimension formula to $D = 2p + 1$.

Axis A is the acyclicity axis. Its robustness predicate states that substrate-acyclicity perturbations keep the $D = 3$ conclusion inside a fixed named $1$-acyclic class. Sibling axes C and I are likewise surface-stable; axis P is the dimension-selecting axis via the codimension formula.

This sits in the Foundation dimension-forcing route (T8 forces $D = 3$ spatial dimensions). The present declaration is the theorem-surface witness for axis A, not a full homology computation.

One-line tactic proof: trivial. The referenced predicate AxisARobust is defined as the constant proposition True, so the goal is immediate. No upstream lemmas are applied; the discharge is purely propositional.

Feeds the bundled multi-axis robustness theorem, which states that only axis P can move the dimension away from 3, while axes C, I, and A are stable at the theorem-surface level. That parent packages this result with the C and I surface theorems and the arithmetic fact that $p \neq 1$ forces codimension dimension off 3.

In the Recognition forcing chain this protects the T8 conclusion $D = 3$ against acyclicity-side perturbations of the substrate, while leaving open the deeper algebraic-topology formalization the module flags as future work. It is a structural lock on the dimension route, not a substitute for computing homology of the recognition complex.