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to mince; to cut fine; to chop up; to hash; to shred
to carve; to engrave; to chisel; to notch
to tick away (time); to beat out (e.g. rhythm); to record the passing moments
to etch (into one's mind); to remember distinctly
野菜を細かく刻んでスープに入れた。
I chopped the vegetables finely and put them in the soup.
この瞬間を心に深く刻んでおきたい。
I want to engrave this moment deep in my heart.
墓石に故人の名前を刻んでもらった。
I had the deceased's name carved on the tombstone.