What was already known
A monotone-slowdown theorem held for two-dimensional shear flows. The three-dimensional question was open because the one-dimensional profile argument does not extend to its two-dimensional cell problem.
AI involvement
ChatGPT 5.5 Plus suggested ansatzes and the orbit-average mechanism. Tran, Xin and Yu directed the search, made the construction rigorous and independently verified the resulting claims and proofs.
The model supplied the central orbit-average construction mechanism under a human-directed search; the authors established the rigorous theorem.
Importance
Refutes monotone slowdown in the stated three-dimensional G-equation model.
Limitations
The conclusion applies to the specified homogenized model and shear-flow class, not all combustion models. The precise final ansatz coefficients are not traced to a preserved model transcript.
Technical verification
The named authors explicitly report independent verification of all resulting claims and proofs, including the constructed counterexample. This is source-reported completed human checking, not an independent check here.
Formal checking
Independent author verification and rigorous written proof
- Checker
- Hung V. Tran, Jack Xin and Yifeng Yu
- Scope
- Theorem 1's smooth three-dimensional shear-flow counterexample and positive small-d speed change
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the periodic-orbit average, the variational selection argument and why the two-dimensional ODE slowdown mechanism does not transfer.
Correction and publication history
Refutes monotone slowdown in the stated three-dimensional G-equation model.
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