CechFiltration

The Cech radius of a simplex: the true minimum-enclosing-ball radius of its vertices' coordinates, computed once per simplex and cached forever -- a deliberate departure from RipserCohomologyContext's "don't cache filtration values by default" doctrine, since (unlike VR's diameter, which insertionDiameter recomputes incrementally in O(d)) there is no incremental shortcut for a minimum-enclosing-ball radius: every filter check, sort, and filtrationOrdering comparison would otherwise re-run a full Miniball solve.

Caching is also a correctness safeguard, not just a speed one: Miniball is a randomized-incremental algorithm, so two separate calls on the identical input can in principle round differently and return bit-different radii. filtrationOrdering needs one consistent answer per simplex to stay a total order; caching guarantees that without needing to trust a third-party library's determinism.

Cech's own value over Vietoris-Rips is exactly this quantity: unlike VR's purely combinatorial max-pairwise- distance, the Cech radius needs the vertices' real coordinates and a minimum-enclosing-ball computation (Welzl's algorithm, via Miniball) -- not alpha.AlphaComplexDQP's dual active-set QP, which answers a different question (restricted-Delaunay membership, dependent on the whole point cloud, not just a simplex's own vertices).