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Finite Point Set Hausdorff Witness API

Unordered finite point sets in dimension 2 or 3; each nonempty set has at most 128 distinct points, coordinates within plus/minus 1000000.

Unordered finite point sets in dimension 2 or 3; each nonempty set has at most 128 distinct points, coordinates within plus/minus 1000000. Matching dimensions required; repeated points within a set reject, points shared across sets are allowed. Compute both directed max-min squared Euclidean distances and their symmetric maximum. Every source point receives one exact nearest witness; nearest-distance ties choose the smallest target input index, attaining-source ties choose the smallest source input index, and equal directional maxima select A_TO_B for the symmetric witness. Witness indices are zero-based positions in the submitted arrays. Distances are invariant to point order; witness indices follow input order. At most 16384 pair distances and 49152 coordinate-square terms; no randomization. Exact calculations on submitted integer coordinates in one caller-declared consistent Cartesian unit. Squared distances and dot products are authoritative decimal strings; no square-root approximation is returned. No map lookup, provider call, external access, data inference or live action. Strict bounds and semantic checks run in the existing pre-quote validation path. Private JSON result retained for 30 days; USD 1.00 per one-time job. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

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