I am wondering if anyone have tested the Dilithium Signature Verification result, from the different language implementation, following these steps:

1. Dilithium2:
   a. In C# implementation of bouncy castle, a key pair and signature are generated.
   b. In the official implementation in C, I got invalid signature.

2. Dilithium2:
   a. In the Java implementation, a key pair and signature are generated.
   b. In C# implementation of bouncy castle, I got invalid signature.

3. Dilithium3:
   a. In Rust implementation, a key pair and signature are generated.
   b. In C# implementation of bouncy castle, I got invalid signature.

While if I did the verification where the signature and key pair are generated, I got valid signature.

The implementations I tried out:
https://pq-crystals.org/dilithium/software.shtml

I tried the official implementations mentioned in the dilithium website, expecting that verification should happen no matter what developing language is used.