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@kim-em This PR now contains two tasks mostow_rigidity and mostow_rigidity_compact. The workspace for the former was generated successfully, but for the latter it contains several errors: see the ChallengeDeps.lean generated. Most notably, the section Topology is not ended, and variable (p q : ℕ) is dropped, leading to errors. Can you maybe ask Claude to fix these bugs?
(I should have also mentioned that open MeasureTheory is duplicated in Challenge.lean. Moreover, if I don't put mostow_rigidity in a separate namespace LeanEval.Geometry section, Challenge.lean will miss the line open LeanEval.Geometry and report errors like PO doesn't exist.)
Update: Since the bug hasn't been fixed, I have opted to remove the cocompact version to satisfy CI.
A few changes are needed before this is ready to merge:
Please put MatrixSum, pmOneMat, PO, their supporting declarations, and the associated instances in a problem-specific namespace such as LeanEval.Geometry.MostowRigidity. The current generic names and instances land directly in the shared LeanEval.Geometry namespace and risk collisions with future problems. Please name the instances as well.
Please make existence of fundamental domains explicit for both lattices. In Mathlib, MeasureTheory.covolume is defined to be 0 when no HasFundamentalDomain instance exists, so covolume Γ (PO n 1) ≠ ⊤ alone does not faithfully express finite covolume. Adding the corresponding HasFundamentalDomain hypotheses would close that gap.
Because the statement allows finite-covolume nonuniform lattices, this is the Mostow–Prasad theorem rather than only the original cocompact form of Mostow rigidity. Please cite Prasad, Strong rigidity of ℚ-rank 1 lattices, Invent. Math. 21 (1973), 255–286, in the file and manifest.
The standard strong-rigidity conclusion says that the given isomorphism f is induced by conjugation. The current conclusion only says that Γ and Λ are conjugate. Please either strengthen the conclusion to realize f, or clarify that the intentionally weaker isomorphic-iff-conjugate formulation is the benchmark target.
Also please add the missing final newline to the manifest.
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