axis_I_robust
plain-language theorem explainer
Tracked-invariant perturbations leave the spatial-dimension conclusion D = 3 intact once the recognized-object dimension is fixed at p = 1. Anyone citing the multi-axis robustness bundle for the dimension route will point here for the I-axis leg. The proof is a one-line discharge: the axis predicate is presently the constant True, so the theorem surface holds by triviality.
Claim. Axis I is robust: once the recognized-object dimension is fixed at $p = 1$, perturbations of the tracked invariants preserve the conclusion that spatial dimension equals $3$.
background
The module records the robustness theorem from the revised Three-Dimensional Space from Recognition Cost paper. Content is intentionally structural: coefficient-ring, tracked-invariant, and acyclicity-axis equivalences are predicate-level interfaces awaiting fuller algebraic-topology formalization. The only axis that can move dimension is arithmetical: changing the recognized-object dimension $p$ changes the codimension formula to $D = 2p + 1$.
Axis I is the tracked-invariant leg. Its robustness predicate asserts that, with $p = 1$ already fixed, perturbations of tracked invariants do not dislodge $D = 3$. Sibling axes cover coefficient-ring (C) and substrate-acyclicity (A) stability; Axis P is the one that actually shifts $D$.
Upstream, the active-edge count $A = 1$ (per tick) appears among the foundation anchors that pin the $p = 1$ regime in the broader dimension-forcing story (T8: $D = 3$).
proof idea
One-line term proof. The robustness predicate for Axis I is defined as the constant proposition True, so trivial discharges the goal immediately. No lemmas are unfolded; the declaration is a named theorem surface over a placeholder interface.
why it matters
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 remain stable at the theorem-surface level. That bundle is the formal counterpart of the paper claim that the dimension route is robust under tracked-invariant, coefficient, and acyclicity perturbations once $p = 1$ is selected.
In the Recognition forcing chain this sits under T8 ($D = 3$ spatial dimensions) and the arithmetical codimension relation $D = 2p + 1$. The I-axis leg is still a structural interface: it records the intended invariance without yet carrying a full algebraic-topology model of tracked invariants. Closing that model would replace the constant-True predicate without changing the citation surface used by the bundle.
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