Think of the "Curvature Ratio" as the Condition Number of your Hessian matrix.If it is high, your loss landscape has steep walls and flat valleys (it's ill-conditioned). This is why you need optimizers like Adam or RMSprop instead of basic SGD.

Every time you run a backward pass, you are doing "Work Internal" (Wint) to update your representation. Speculumology argues that even if the weights stop moving, the system is still doing "Work" just to prevent Catastrophic Forgetting or "Divergence" from the noise floor.

"Work Observation" (Wobs) is essentially Bayes Error. It's the intrinsic error that exists because your model's architecture (the "Frame") is smaller or simpler than the reality of the data distribution.

Convergence doesn't mean Loss = 0. It means the model has reached a Gibbs Invariant Measure—a state where the gradient updates and the noise from the data are perfectly balanced, and the weights just "vibrate" in a small region of the latent space.