What was already known
Classical VLSI routing work left this terminal-only Manhattan complexity question open; related algorithms and approximations did not classify it.
AI involvement
GPT-5.6 Sol carried out central proof discovery under Zhu’s problem definition. Zhu reconstructed the argument, audited its boundaries and checked small instances.
The model performed central proof discovery for the weak NP-completeness claim within the human-designed project; the author reconstructed and selected the retained argument.
Importance
Would settle the exact terminal-only decision problem’s complexity.
Limitations
The claim is weak NP-completeness only. It does not allow Steiner points or cover general rectilinear routing. Small-instance checks and basic Lean lemmas do not verify the full reduction.
Technical verification
The author reports adversarial audit and exact small-instance checking, but the weak reduction and its complete-Manhattan-graph reverse implication are not in the completed Lean modules. The source does not establish a separately completed rigorous check of the full universal theorem.
Human understanding
Zhu explains the Partition gadget, cut-counting reverse implication, and why the claim is only weak NP-completeness.
Correction and publication history
Would settle the exact terminal-only decision problem’s complexity.
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