With the delirious praise swirling around "Hamilton" since its Public Theater run in February, there was danger that Lin-Manuel Miranda's hip-hop masterwork would seem anticlimactic -- or at least overhyped -- at its Broadway premiere.

Instead, the show -- which tells early American history in its own time but shot through with multicultural urban sensibility -- is even more nuanced, more cohesive in individual performances and its more focused finale. Most important, Miranda and director Thomas Kail have fine-tuned it without losing a shiver of its audacity and thrill.

The musical -- written and composed by its star -- manages to be radical and satirical, yet good-hearted. It is sung-through like a pop opera. But it is driven by rap's nonstop verbal and rhythmic unpredictability and, somehow, proudly indebted to jazz, '60s pop, Gilbert & Sullivan patter songs and golden-age Broadway. The jagged, sly poetry and overlapping storytelling barrel through, dense and fast, except when choreographer Andy Blankenbuehler's lusciously visceral dancers shock us in slow motion.

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Miranda, who plays Hamilton with wit and an exquisitely endearing inelegance, doesn't preach. Yet he and the ingenious Kail embed knowing ideals about immigration, slavery, authenticity and love. More than once, with an enthusiasm rare outside the theater today, characters urge one another to "look around" at "how lucky we are to be alive right now."

As everyone surely knows by now, Miranda, inspired by Ron Chernow's biography, tells the story of this lost founding father, what rival Aaron Burr calls a "bastard orphan son of a whore." Remembered, if at all, for being killed in a duel by Burr and being the face on the $10 bill, Hamilton went from ambitious Caribbean teen to George Washington's right-hand man. He wrote most of the Federalist Papers, establishing the federal bank and having what may have been the first sex scandal in American politics.

However, this is anything but a one-man show. Every supporting character is a vivid personality, the virtuoso actors clearly having grand fun in Paul Tazewell's historical-yet-cool costumes and on David Korins' double-decker set with concentric turntables.

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Daveed Diggs remains an irresistible peacock as Lafayette and, later, Thomas Jefferson. Leslie Odom Jr. has added daring physical and vocal flair to his portrayal of Burr, as has Phillipa Soo as Hamilton's wife. Jonathan Groff is lovably evil as the deliciously snide King George, who sings a '60s revenge ditty, "I will kill your friends and family/to remind you of my love."

Early in the evening, Hamilton sings, "Don't be shocked when the history books remember me." Little did he know he'd make musical-theater history, too.