If one was a theater student in the early 2000s, there is a good chance one encountered David Auburn’s Pulitzer-winning play, Proof, a work of tidy structure, elegant rhyme and, not for nothing, commercial appeal. (For theater, anyway.) Auburn carefully calibrates the funny with the sad, balances credible realism with fugues of understated poetry. It was once described to me as a perfect play, in the formal sense, a template from which any budding playwright could draw inspiration should they want to write something smart but accessible, and endlessly producible. There’s even a grabby cliffhanger at the end of act one.

The sturdiness of Auburn’s construction can, it turns out, stand up to a lot. Evidence of that comes in the form of the director Thomas Kail’s new Broadway production, the first such revival in the play’s history and one that seriously tries its integrity. That the house is still standing at the end is a mighty testament to Auburn’s ingenious (and ingeniously simple) design.

This production is a star vehicle for Ayo Edebiri, an Emmy winner for The Bear, and Don Cheadle, a movie star who has done compelling work in features great, small and everywhere in between. Edebiri is the stubborn, sardonic Catherine, newly 25 and shuffling around the back yard of her father’s Chicago home, not so much spinning her wheels as she is content to be stuck idle in the mud. Cheadle is her late father, Robert, a great mind of mathematics who was severely waylaid by mental cataclysm in his latter days. Catherine worries that she has inherited all of her father’s illness, but perhaps only a little of his brilliance. Aspirations to follow in his career footsteps were put aside to become his caretaker; with that purpose gone, she spends her time speaking to his ghost and wondering if she’s going crazy herself.

At first, it seems that Edebiri has found her own successful take on the character. In the play’s opening scenes, she plays Catherine as a young adult arrested in petulant late-adolescence, perhaps a defensive posture against the forces of reality bearing down upon her. She is quippy and needy with her imaginary-friend dad, and amusingly aloof to his devoted former student Hal (Jin Ha), who is sifting through Robert’s journals in the hopes of finding some undiscovered remnant of his genius. Catherine treats her sister, type-A Manhattanite Claire (Kara Young), as a nagging mom figure, indignant to Claire’s attempts at coaxing Catherine toward a new and more productive life.

This is all done rather convincingly, Edebiri shrewdly approximating the slouch and gesture of a frustrated, awkward teen – or an adult who is frozen in that mode. But when the more dramatic, plot-advancing mechanics of the play churn into motion, Edebiri quickly loses her grasp on the performance, devolving into a jumble of stammers and tics that increasingly isolate us from Catherine’s humanity. It is as if she is becoming the living embodiment of Catherine’s most hyperbolic fears about her mental health, a cliche of addled behavior that stands in harsh contrast to the relative plainness and naturalism of Auburn’s writing.

Cheadle goes the opposite direction, barely betraying even a hint of Robert’s mental disturbance. He is curiously flat in the role, not adjectives one usually uses to describe a Cheadle performance. Perhaps he is nobly trying to offset Edebiri’s overstatement, but the pair never fuse together into the picture of generational legacy – both accepted and rebuked – that the play intends.

Thank goodness, then, for Young, a late-in-rehearsals replacement who brings a much-needed clarity to this fraught domestic scene. The two-time Tony winner (in back-to-back years, no less) is crisp and legible as the frustrated, guilty Claire, who has subsidized the lives of her father and sister but regrets her absence from the house in the most difficult years. It’s a dialed-in, no-frills performance, which is what the role, and the play, require. She keeps the thing afloat, as perhaps Claire did for her ailing family. Ha also has his effective moments as the sweet but calculating Hal, who must reconcile his attraction to Claire with his desire to exploit something of her father’s. (And, it turns out, of Claire’s.) Despite that strong support, though, it ultimately falls on Edebiri to hold the play’s center of gravity. She wobbles badly under that weight.

On the style front, Kail mostly gets out of the way of the text, though he does add a few embellishments, for better and worse. Kris Bowers’ original music is appropriately wistful and weary, poignantly scoring simple scene transitions. But strip lights that glow along the edges of Teresa L Williams’ otherwise sharply designed set during those transitions call to mind too many slick, fluorescent-lit productions that have made their way to New York from LED-happy London in recent years. Such cold flashiness is not needed here.

A few technical missteps are nonetheless minor compared with the serious performance troubles at the heart of Kail’s Proof. And yet, the unassuming strength of Auburn’s writing manages to shine through that onslaught of actorly miscalculation. We still crave answers to the play’s mild mysteries, still chuckle ruefully at its subtly recurring motifs. This production’s handwriting may be awfully messy, but the basic math of it all is sound as ever.