Ordered execution under the full certification criterion

Establish whether the controlled elastoplastic oscillator’s response representation preserves the intervention law for held-out action orders, including the strict superiority of the full fused belief over the diagonal control, under a sufficiently trained shared step-factorized executor.

Background

The paper studies ordered execution by withholding the AB and BA transition edge while exposing the individual action primitives and other action sequences. A shared step-factorized executor can execute the held-out programs once trained with a sufficiently large budget, whereas a program-level executor fails on unseen adjacencies.

Nevertheless, the complete ordered-execution gate remains formally unresolved because two strict comparisons against the diagonal fused-information control fail. Thus the paper demonstrates substantial order-sensitive execution but does not establish the full conjunction required by its certification criterion.

References

Ordered execution Primitive order and transition edge Does the phrase preserve the intervention law? × OPEN

Beyond Multimodal Alignment: Certifying Physical Language through Response Substitution and Ordered Execution  (2608.19492 - Tan et al., 19 Aug 2026) in Appendix A, Table 1; Appendix C.5, Tables 3–4