Sound static analysis for alternative investment rules

Establish the monotonicity and state conditions required for each of the five shipped QUDE investment rules to support the static affordability under-approximation and induction proved for Tacet's fixed_fraction rule.

Background

The formal metatheory covers only Tacet's fixed_fraction investment rule. The implementation also provides five QUDE-derived rules whose stakes depend on verdict history rather than solely on current wealth. Because the existing proof invariant tracks only current wealth, the paper does not establish that these alternative rules admit the same static reasoning. The authors explicitly leave open the condition an investment rule must satisfy for the induction to work.

References

The five shipped QUDE rules set their stakes from verdict history, and stating the condition an investment rule must satisfy for the induction to go through is open.

— Tacet: A Language and Type System for Automatic Statistical Validity Accounting  (2608.27451 - Abuah, 27 Aug 2026) in Section 4, Wealth Transformers, subsection “Scope of Equation (1)”; Section 7, Limitations and Threats to Validity, subsection “One investment rule”