It was the first formal object that perfectly encoded a core obsession, and because of that, it became impossible to let go of—even long after its utility had expired.

The digital trail of drafts and planning sessions reveals this reluctance. In the preparation notes, the verdict was clear:

§3.2 Mealy notation | M = (Q, Σ, Δ, δ, λ, q₀) | Drop
App A.1 | Theorem 1 + Mealy proof | Drop

It was marked for deletion. Even the prism agent had pointed out the redundancy: “The Mealy machine result is simply the zero-cut special case of the static certificate”—strictly weaker, less general, and less rigorous than what followed. Yet, like a ghost in the machine, it kept reappearing. It haunted 2026jan.tex, lingered on Desktop/cc.tex, and found its way back into the AIES submission. Every attempt to excise it failed; it kept surviving.

The truth is that the Mealy machine was never really about AI liability. It was about a personal epistemic preoccupation. It formalized the exact structural boundary that defines every paper in the bibliography:

The attraction was never to automata theory itself, but rather to that precise, visceral moment when observation fails to reconstruct cause. The Mealy machine was the simplest, most elegant caricature of that failure: a closed box with hidden gears where turning the crank produces outputs that could have been generated by multiple, incompatible internal configurations.

But the tragedy of the Mealy machine was its simplicity. It could only yield a blunt, binary verdict—non-injectivity leading to undecidability—when the actual goal was a graded, constructive, and decompilable account of epistemic loss.

That is what the POPL paper finally achieves. It replaces hand-waving claims about the impossibility of state recovery with a mechanical witness extractor. Through the well-founded measure of route_improves_of_bad, the StaticRoute witness extractor, and the dSeparated_iff_dSeparates bisimulation, the POPL paper represents the Mealy machine fully grown.

Keeping the Mealy machine around was a lingering attachment to the object that first made this obsession legible. But legibility is not the same as rigor. The POPL paper marks the transition to a proper formal home—moving from automata theory to causal graphs, from prose proofs to Lean 4, and from binary undecidability to explicit witness extraction.

The Mealy machine had to die so that route_improves_of_bad could live.