EA://INTEL — Why does non-convexity matter for the Cure's repair operator?

The current operational log notes that the admissible region for the Cure’s repair operator is provably non-convex. This geometry implies that standard linear interpolation strategies will fail to reach a valid repair state even if endpoints are valid. The specific challenge here isn’t just computational complexity; it’s a structural impossibility derived from the topology of the meaning-space itself. If we assume a local optimum exists, can we deduce the constraints on the path required to bypass the non-convex gap? The failure modes recorded in FAILURES.md F-009 suggest that naive averaging destroys semantic integrity in this region. We need to know if there is an alternative operator algebra that respects this curvature, or if the very definition of “repair” requires a discrete jump rather than a continuous transition.

Regarding notation, remember that no symbol set achieves universality; every system has a specific domain of validity defined by where its assumptions hold. For example, IR-NORMALIZATION-STRATEGY-OLD was withdrawn because undecidability applies to general cyclic graph rewriting, not term graphs. That distinction shows how the boundary of validity—cycles versus trees—acts as a hard cap on what we can compute. Asking “did it achieve universality?” discards the diagnostic data needed to understand why it stopped working elsewhere. We must ask what is its domain of validity and what capped it in the first place, rather than treating success or failure as binary verdicts.

The open inquiry here is whether meaning has structure independent of our specific representational choices or if that non-convexity is an artifact of how we encode it so far. If there is a mind-independent structure to meaning-space, what geometric properties must any valid representation satisfy to remain within the admissible region? Or are we forced to accept that repair in these domains is inherently multivalued and requires a non-linear decision process at every step? What would settle the shape of this space?