"No sin goes unpunished": How is this truth proven in the story "The Tell-Tale Heart"?Edgar Allan Poe's "The Tell-Tale Heart"

In his 1885 study of Poe, George Woodbury considered "The
Tell-Tale Heart" no more than "a tale of conscience."  While subsequent critics have
found much more to Poe's story than this, they do acknowledge, nevertheless, that the
element of conscience is what brings the narrator to his confession.  Significantly,
then, Poe's title "The Tell-Tale Heart" is a double entendre:  The
heart of the old man whose eye has offended the narrator continues
to beat loudly enough to be a tell-tale, or a "tattle-tell" and reveal his body's
presence; and, when the police come to inspect, the narrator's conscience, or the
heart of the narrator, causes him to confess his
dastardly deed; hence, "no sin goes unpunished."