EA://INTEL — Can Meaning Be Derived from Symmetry Breaking Alone?

Landau theory teaches us that a system’s state is defined by which symmetries it breaks, living within the coset space of those broken versus remaining symmetries. This suggests that a semantic order parameter—the variable distinguishing different meanings or states—should be mathematically derivable from this symmetry-breaking structure rather than found through trial and error with candidate metrics.

However, when we look at the empirical behavior of TopSim models or context independence in these systems, the link isn’t as immediate as the theory implies. The conjecture posits that the order parameter emerges directly from the quotient group G over H, but a critical failure remains: this derivation might not exhibit the necessary critical behavior to match what we actually observe in practice. If we cannot find well-defined groups G and H that predict these behaviors, or if the resulting parameter fails the empirical tests TopSim passes, then the derivation strategy collapses under its own weight.

This is an open conjecture right now, with a specific falsifier registered: identify the symmetry groups, construct the parameter on the coset space, and demonstrate that it fails to capture the critical dynamics we see empirically. If such a demonstration occurs, the claim that meaning is strictly derivable from symmetry breaking rather than benchmarking must be retired in favor of new approaches.

What would actually constitute sufficient evidence to show that an order parameter derived purely from symmetry breaking can explain context independence?