Formalize the decision-floor conjecture

Formalize and prove, under an appropriate computational substrate model, the decision-floor conjecture that resolving a fresh runtime choice among C alternatives incurs a worst-case dissipation of at least epsilon log C per cycle, and determine whether the overhead of general-purpose machines satisfies this bound.

Background

The paper conjectures that runtime choice itself has an energy floor: a machine resolving a fresh choice among C alternatives must dissipate at least epsilon log C per cycle in its decision path, in the worst case over choice sequences. The conjecture distinguishes choices actually delivered from merely provisioned capability and suggests that the relevant substrate-scale epsilon should be far above the Landauer limit.

The unresolved tasks are to identify a model in which this lower bound can be proved, to establish an appropriate rate axiom excluding arbitrarily slow adiabatic decisions, and to determine whether the measured overhead of general-purpose computing meets the conjectured floor.

References

The conjecture is that the floor at the substrate's scale is picojoules, not $kT$: a claim about switching, which needs a rate axiom in the manner of Axiom~\ref{ax:lat}, since an adiabatic decision path can be made as cheap as one likes by making it slow. Finding the model in which this is a theorem, and whether the general-purpose overhead measured by meets it, is open.

— The Price of Remembering: A Calibrated Energy Law for Computation  (2609.00744 - Bergach, 1 Sep 2026) in Conjecture 1 (Decision floor), Section 6, “Rent on Choice”