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Planar Proximity Graph Pair API

One combined relative-neighborhood/Gabriel graph offer from 1 through 48 distinct planar integer points.

One combined relative-neighborhood/Gabriel graph offer from 1 through 48 distinct planar integer points. For candidate pair i<j, RNG excludes the edge iff a third point k has d(i,k)^2<d(i,j)^2 AND d(j,k)^2<d(i,j)^2; Gabriel excludes iff (k-i) dot (k-j)<0. These are open-lune and open-diameter-disk conventions: equality on a boundary does not exclude. Collinear, right-angle, cocircular and equidistant points are accepted. Every pair receives a decision for each graph, plus the smallest-index strictly interior exclusion witness when one exists. Kept edges have null exclusion witnesses. Edges/pair decisions sort by (i,j), input indices start at zero; the single-point graph has no edges. At most 1128 pair distances and 51888 third-point tests, each assessing both graphs. 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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