Hierarchical Simplex Validity Checker

Ready to run simulation.
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Cayley-Menger Only
Hierarchical Face Validity

Rejection Breakdown

Dimension Total Trials Cayley Valid Hierarchy Valid Hierarchy % (Mean ± StdDev) p-value (d < d-1) Rejected at Face Dim 2 Rejected at Face Dim 3 Rejected at Face Dim 4 Rejected at Face Dim 5 Rejected at Face Dim 6 Rejected at Face Dim 7

Performance Timing (ms)

Dimension Cayley-Only Avg Hierarchical Avg Ratio Total Time

About This Simulation

This tool compares two methods of testing simplex validity:

  1. Cayley-Menger Only: Tests whether a simplex is valid using only the Cayley-Menger determinant of the highest dimension.
  2. Hierarchical Face Validity: Tests whether all faces of the simplex (including all lower-dimensional sub-faces) are valid.

For each dimension, the same set of random simplices is tested with both methods to compare the results.