Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
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Local rigidity of a nine-point distance configuration
_proof: The inverse function theorem and separated distance intervals turn an exact Jacobian minor into local similarity rigidity.
evidence/: The retained coordinates and full Jacobian minor are recomputed with exact arithmetic; the scope is local rigidity of one configuration.
The proof and exact finite evidence are author-recorded by Plasma AI, without independent review or Lean proof. The computation checks one configuration and its distance-equality Jacobian. It does not enumerate distance partitions or exclude any other connected component of the realization space.
This rules out a sufficiently small perturbative repair of the example in Problem 217. The research account keeps other finite-realization questions separate. No gap remains in this local statement. The global order-nine existence question remains open here.