proof, evidence, certificate, testify, verify, guarantee, witness
證 centers on establishing truth or authenticity: providing proof, evidence, or testimony to verify a claim, and the resulting certificate or guarantee that serves as a witness.
證 combines 言 (words, speech) with 登, which likely contributes the sound and may suggest the idea of presenting or raising evidence. The character expresses using words to prove or testify.
Words (言) are used to climb (登) to the truth: presenting evidence or testimony to prove something, like a certificate that guarantees authenticity.
For ショウ, imagine a witness showing (ショウ) a certificate in court: show -> ショウ, and the words prove the truth.
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