algs: Evaluate DocsChecker on real data

[andreygetmanov]

21.10
Validate papers ✅
Validate doc ✅

28.10
Validate anti-paper ✅
Validate anti-dic ❌

31.10:
Try reasoning models:
gpt o3, 04 mini

[DRMPN]

Result Table

https://docs.google.com/spreadsheets/d/1u9OdCDFkm4TXmCkXZr1iOOOVMqa1gJGCNzvwDCZgU7E/edit?usp=sharing