Purdy's Inequality for Hyperplane Arrangements
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Statement
For an arrangement of hyperplanes in with intersection lines and intersection points where at least three hyperplanes meet, the refined form of Purdy's inequality expects . An explicit arrangement built from roots of unity violates it.
Context
the refined form for essential arrangements in projective three-space
A named inequality in the incidence-geometry tradition of Purdy, with a documented expected refinement for hyperplane arrangements.
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The acknowledgement credits the model with generating the computer programs used to carry out the symbolic computations over configurations of points and planes, which is how the violating arrangement was checked.
the refined form for essential arrangements in projective three-space
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Machine check · not human verification
machine: correctscope Reproduction by the VibeMathed site
The counterexample is an explicit root-of-unity arrangement whose point, line and plane counts the paper works out in closed form, so the violation is a finite check. arXiv preprint, not yet peer-reviewed.
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