Losslessness of the Assumption-U restriction

Determine whether the imported Assumption-U restriction on budgeted protocol classes is without loss of generality, thereby establishing whether the restricted-class operational value coincides with the unrestricted operational value.

Background

The paper imports an Assumption-U restriction from its companion framework and imposes it on all protocol classes. The operational capital value is therefore defined relative to a restricted class of protocols rather than the unrestricted class.

If the restriction is not without loss of generality, the value obtained by the deletion-and-reoptimization counterfactual may differ from the unrestricted operational value. The authors explicitly identify this as an unresolved interpretation-level issue while maintaining that their theorems are valid on the restricted class.

References

Whether it holds without loss of generality is an open question there (Sec.~\ref{sec:setting-asterisk}).

— Thermodynamics of Learning: A Typed Four-Component Accounting of Memory, Fit, and Value  (2608.12791 - Sudo, 13 Aug 2026) in Section 2.1, Section 2.3.1, and Section 9 (Discussion and limitations)

Whether an enablement subject can be defined, and thereby yield a ledger decomposition of the gate domain, is open.

— Thermodynamics of Learning: A Typed Four-Component Accounting of Memory, Fit, and Value  (2608.12791 - Sudo, 13 Aug 2026) in Section 7.3, Remark 7.12; Section 9 (Discussion and limitations)