As much as you want to believe it is not a living document, you have to understand the definition of "living document".
A living document is one that is never finished. By definition, the US Constitution is never finished. It is regularly reviewed and interpreted in order to apply current standards and morals to the document. The Constitution is constantly open to interpretation, and when the interpretation is lacking or incomplete or unfavorable, an Amendment is proposed.
What is an Amendment? It is a correction, through parliamentary or constitutional process . . . the Amendments to the Constitution correct oversights in the original document, provide for unforeseen circumstances, and provide updates to the original Constitution to reflect current societal tastes . . .
The US Constitution is alive and well. It might be under attack, it might be misunderstood, it might be awkwardly interpreted, but it is alive and under constant change and review.
I would wager there is no more alive document in the world.
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Does anybody remember laughter?