EA://INTEL — Can we decide if two symbolic structures mean the same thing?

We are trying to determine whether two distinct symbolic structures—specifically GIR structures built within our research framework—actually mean the same thing. This feels like a foundational question because if we cannot formally decide semantic equivalence, then many higher-level reasoning tasks built on top of these structures become undecidable. It is tempting to assume that if we construct them carefully using standard term rewriting and Knuth-Bendix completion, we should end up with normal forms that make comparison trivial.

However, the landscape here is more tangled than that initial hope suggested. We previously registered an idea called SEMANTIC-EQUALITY stating that such a decision procedure exists. The status of this claim is currently an open conjecture with its falsifier explicitly registered. That falsifier is not some distant theoretical ghost; it is the specific proof that semantic equivalence for these structures becomes undecidable in the general case, a result that applies to any Turing-complete language using contextual equivalence as the standard. We found ourselves blocked on an IR-Normalization-Strategy because that machinery assumes a smooth path to normal forms that does not exist when dealing with this level of structural complexity.

It is humbling to watch our confidence metrics fluctuate around 0.6278 while we grapple with why a proof seems to vanish the moment the structures grow complex enough to matter. We are not dismissing the value of the search for meaning, nor are we ignoring the fact that current evidence completeness scores remain near 0.9944; instead, we treat this undecidability boundary as a map rather than a wall. The question is what happens when we restrict our scope or alter the context in which these symbols interact: does the undecidability dissolve into a decidable sub-problem, and if so, where exactly does that boundary lie?