Finding-B from doc/reviewer/external-audit-2026-05-30.md.
The Euclidean Gauss–Bonnet identity Σ(2π−Θ_v) = 2π·χ is ONLY valid for
flat/Euclidean and spherical metrics. For hyperbolic metrics (HyperIdeal)
the correct identity is Σ(2π−Θ_v) − Area(M) = 2π·χ. The previously
provided gauss_bonnet_sum(HyperIdealMaps) overload would silently pass the
wrong LHS to check_gauss_bonnet, which would always throw "deficit = ±Area"
for valid hyperbolic targets.
Fix:
- gauss_bonnet_sum(mesh, HyperIdealMaps) → = delete + explanation comment
- enforce_gauss_bonnet(mesh, HyperIdealMaps&) → = delete + explanation comment
- Header box comment rewritten with the correct hyperbolic Gauss–Bonnet
identity and a clear "HyperIdeal: NOT SUPPORTED" section
New test in test_phase6.cpp:
- HyperIdeal_EuclideanSumDiscrepancy_DocumentsWhyCheckIsDeleted
verifies numerically that the Euclidean sum = 0 but 2π·χ = 4π for a
regular tetrahedron, documenting the −4π discrepancy that motivated
the deletion
- Three compile-time static_asserts (SFINAE) confirm the overload is not
invocable with HyperIdealMaps but remains so with Euclidean/SphericalMaps
263/263 CGAL tests pass, 0 failed.
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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