How would you write a unit test that thoroughly verifies a custom equals() and hashCode() implementation satisfies its contract, and what testing libraries exist specifically for this purpose?

A thorough test suite should verify: reflexivity (x.equals(x)), symmetry (x.equals(y) implies y.equals(x)), consistency across multiple calls, correct handling of null and unrelated-type comparisons (both should return false, never throw), that equal objects produce identical hashCode() values, and ideally that meaningfully different field values correctly produce inequality -- rather than hand-writing all these checks manually and risking missing an edge case, the widely-used EqualsVerifier library automates comprehensive contract verification for a class's equals()/hashCode() implementation with a single fluent assertion, catching subtle violations (like forgetting a field, or a mutable-field risk) that manual tests might easily overlook.

// Using EqualsVerifier (a popular open-source testing library) for comprehensive automatic verification
import nl.jqno.equalsverifier.EqualsVerifier;

@Test
void equalsContract() {
    EqualsVerifier.forClass(Point.class).verify();
    // automatically checks reflexivity, symmetry, transitivity, null-safety,
    // hashCode consistency, and more -- catches subtle bugs a hand-written test might miss
}