conclusive evidence; definite proof
Formal expression used in legal, journalistic, or argumentative contexts to emphasize that the evidence is solid and undeniable.
The prosecution could not present conclusive evidence.
Without definite proof, we cannot label him the culprit.
確実な証拠 is a more common and slightly less formal way to say 'reliable evidence'. 確たる証拠 has a stronger, more literary tone.
確たる is the attributive form of the classical adjective 確し (かくし), meaning 'certain' or 'firm'. Combined with 証拠 (evidence), it forms a set phrase meaning 'conclusive evidence'.