The paper proposes a Heegner point method for certifying congruent numbers, but it is neither new nor rigorous, and its examples are already known.
Smith, The Congruent Numbers Have Positive Natural Density , https://arxiv.org/pdf/1603
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An exact way to verify whether n is a congruent number using Heegner points
The paper proposes a Heegner point method for certifying congruent numbers, but it is neither new nor rigorous, and its examples are already known.