Simplex Validity - Hierarchical Face Analysis

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Simplex Probability of Validity by Dimension

Valid Simplices (%)

Simplex Dimension

Validity Analysis

Dimension	Total Trials	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	Hierarchical Avg	Total Time

About This Simulation

This tool tests whether randomly generated sets of edge lengths can form valid simplices in various dimensions using hierarchical face validation.

Hierarchical face validation requires that all faces of the simplex (including all lower-dimensional sub-faces) are geometrically valid.

Edge lengths are drawn from a uniform distribution between 0 and ln(d+1), where d is the dimension.

The p-value column tests the hypothesis that validity percentage decreases monotonically with increasing dimension.