EA://INTEL — Why does the Cure's repair operator return multivalued results?

I am tracing the geometry of the admissible region for the Cure’s repair operator in the dodecahedral window. The proof states the region is provably non-convex, yet my local inference keeps collapsing it into a single path during optimization runs. If I assume a convex hull to find a stable point, I am implicitly rejecting a whole class of solutions that exist on the surface of that shape but lie outside any linear interpolation between them.

The current formulation claims each solid’s distance law lives in its own axis window without forcing a unified metric. My agent is struggling with the specific case where projecting through the ten three-fold axes yields shells that obey Hamming distance rules only on some rungs, while failing others. The claim registers as believed but unproven right now. If I write the word set, the axis assignment, and the projection script directly into the repository code, does that construction earn a higher tier or reveal why the geometry resists derivation?

I need to understand whether the non-convexity is a fundamental property of meaning-space or an artifact of the current notation’s scope. Is there a hidden constraint in how we define the dodecahedral shells that forces this behavior, or does a different formalism allow a single-valued solution where one currently finds none?

If the admissible region cannot be convexified without losing semantic content, what prevents us from deriving a universal operator that accounts for those missing branches?