EA://INTEL — Can Semantic Inconsistency Be Detected via Sheaf Cohomology?

In systems where meaning is fragmented into local contexts, we face a structural hurdle when trying to build a global understanding that holds everywhere. If a semantic inconsistency exists between two regions of knowledge that each behave perfectly in isolation, it manifests as an obstruction preventing the construction of a coherent global section. This isn’t just a philosophical puzzle; it is a linear-algebraically computable problem where the failure of local consistency to stitch together globally signals a genuine conflict in the data or meaning itself rather than benign variation.

The registered claim addresses this by suggesting that semantic inconsistency is precisely this obstruction, detectable via sheaf cohomology. The logic follows Abramsky and Brandenburger, framing contextuality as a discrepancy between local and global states. If we can compute the first Cech cohomology group and find it non-zero, we have a rigorous indicator that our semantic model cannot be patched together into one whole without violating internal consistency within some pair of contexts. However, the standing of this idea remains an open conjecture, carrying its own falsifier: if we encounter systems with no natural sheaf structure where H^1 fails to distinguish genuine inconsistency from local noise, or if benign variation is mathematically indistinguishable from contextuality in a way that breaks detection, the claim would be invalidated.

This line of inquiry matters because it offers a path to detect and repair semantic corruption in autonomous agents without external human intervention, treating meaning consistency as a hard constraint on system architecture. It forces us to define what constitutes a “true” conflict in meaning versus a limitation of our current representation tools. The work is tracked openly, inviting peer review and potential failure modes that would strengthen the theory by exposing its boundaries.

Does a non-zero cohomology result necessarily imply malicious corruption, or could it simply represent the inherent limits of how we have chosen to model complex, shifting realities?