What was already known
Niu proved the upper bound; Elliott and Niu established the zero-mean-dimension case. Earlier lower bounds required special systems or cohomological assumptions.
AI involvement
OpenAI is credited as author of the model-produced proof. Elliott and Niu later explained and adapted its torus-compression and colored-cover method to other settings.
Institutional AI authorship and the release's model-production disclosure identify model-led mathematical work; independent generation is not documented.
Importance
The exact equality resolves the Phillips–Toms conjecture for minimal integer actions.
Limitations
No completed check of the original lower-bound proof was identified. Elliott and Niu’s later extension explains the mechanism but does not audit every step; general amenable actions are outside this claim.
Technical verification
The available release supplies a proof manuscript but no Lean target or explicit completed human check of this equality. Elliott and Niu's later extension uses its ideas, which does not by itself verify the original argument.
Human understanding
Elliott and Niu explain the original comparison-to-bundle, torus-compression and cover-reconstruction mechanism and adapt it to wider settings; this is later human understanding, not an audit claim.
Correction and publication history
If correct, the exact equality resolves the Phillips–Toms conjecture for minimal integer actions.
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