“This was never the way I planned” Katy Perry sang in Newark, New Jersey’s Prudential Center on Friday night. “I Kissed A Girl,” the song that put Ms. Perry on the map in 2007, was performed during the Egypt-portion of her elaborate ‘Prismatic’ tour. And the mega-tron literally depicted cobwebs.

To the vast majority of KatyCats, “I Kissed A Girl” is in fact ancient history. Even Ms. Perry seemed cautious of eluding her young fans, so she made sure to introduce the song as a treat for those who knew her “all the way back” (in 2008) on One Of The Boys, her debut album.

Two-thousand-and-ten’s Teenage Dream is the work that turned Ms. Perry into a household name. The music encompassed her flavor for wide-eyed mischief (“Daisy Dukes/ Bikinis on top”) and Mellencamp-meets-Madonna nostalgia (“Every February, you’ll be my Valentine”). Teenage Dream even tied a record with Michael Jackson’s Bad for having the most (five) No 1’s on an album.

But Prism, for all its balladry and tales of resilience, forces an artistic evolution that has not taken place. The album is the opposite of acute and nuanced. Simply, Ms. Perry isn’t letting go of the rainbow just yet. That’s okay. She’s allowed to have her birthday cake. But in a live format, this confusion manifested in strange ways.

Let’s begin with the positive: Ms. Perry’s confident, colorful celebration of femininity kicked off with “Roar.” There were flying guitarists (sadly neither of which was Eddie Van Halen or John Mayer). There were glass cages and trap doors; treadmill chases and an inflatable “smiling pile of poo” emoji, which one Dad sitting near me had a hard time coming to terms with.

Despite the physicality of the over two-hour performance, Ms. Perry seemed to do the bulk of the singing live, which was particularly impressive on her ballad “Love Me.”

A techno-inspired “Wide Awake” had Ms. Perry floating on a rotating triangle. The entire stage looked like a giant crpytogram in line with The Da Vinci Code – riveting and ridiculous – but still needling the question: how much of this is real?

Ms. Perry’s album Prism flirts with this discrepancy. She appears to ask her listeners to take her straight and with a grain of salt simultaneously. Her best songs of the night, to this reviewer, were of the grain-of-salt variety. Ms. Perry built her pop pyramid on the finger-in-mouth, drink-in-hand bravery that lubricates the brazen fun of “Dark Horse,” what with its glaring mythological errors (silly Katy, Aphrodite is Greek!) and its Baz Luhrrman-baiting music video.

The silhouette of palm fronds indicated what was to come. Ms. Perry rode in on a golden horse and Juicy J became a rapping sphinx. Then Kanye West’s disembodied “dirty mind” entered on “E.T.” The historical narrative gets a little thorny. Egypt to… cats. Safe to say, there was no one in the audience old enough to appreciate the homage to Mr. Mistoffelees that literally happened along with a cabaret-style “Hot N Cold.”

Old Deuteronomy herself reappeared in a flowing white cloak, brandishing a glittering acoustic guitar. This was the “down to earth” part of the show. Ms. Perry, in Jesus/Gandhi/Gandalf form, knelt to take a selfie with a fan. She urged us to spread the good word on Twitter and used that ploy as the unfortunate segue into “By The Grace Of God,” a song that hints at overcoming self-abuse.

During her rambling, baby-voiced soliloquy she congratulated New Jersey for being so authentic. “Because I want to be authentic!” she hummed. The disingenuous vibes may have stemmed from circumstances beyond her control, like the location. It’s impossible to trek to Newark in mid-July and ignore the city’s hard history of race riots and neglect, remnants of which are stingingly palpable in the five blocks between the train and the stadium. Let’s just say, it hardly puts one in the #instaGlam state of mind.

If authenticity is truly what Ms. Perry covets, she would do better to put down the Eckhart Tolle and revisit Cyndi Lauper. Throughout Ms. Perry’s career, critics have likened her more to Madonna. “I Kissed A Girl” was defended on the precedent of “Like A Virgin.” The hollow earthiness of Prism is given the benefit of the doubt on the grounds of Ray Of Light. But Ms. Perry is not a quick chameleon like Madonna. She exhibits more in common with Ms. Lauper, who never relinquished her vibrant ’80s girl-next-door brand. Instead, she translated it into a profusion of artistic pursuits.

Similarly, Ms. Perry never feels quite ready to kill off her goofy, cartoonish side. It keeps resurfacing in different hues. On this tour, when Ms. Perry emerged with a slime green wig and a smiley-face bra top, by the grace of God, I nearly wept. She pulled off a rollicking “This Is How We Do” in an inflatable jeep, with an inflatable taco and an inflatable handbag. “Last Friday Night,” “Teenage Dream” and “California Girls” were over before you could even say “Bikinis, zucchinis/ Martinis, no weenies,” alas, the mark of great pop jams.

In the end, the Achilles’ heel of the night was song placement. “Birthday Cake” should have begun the night’s celebration. What would be a better testament to birthdays than a concert starting with the night’s inevitable confetti rollout? The song also could have used the vigor of first-song status, especially since it has about as much risk as a tip-in-the-jar song you might hear at Coldstone Creamery.

“Roar,” the best song on Prism, should have come last – or at least second to last. “Firework” was the grand finale. The crappy little 3D glasses from the Cover Girl dispensers turned out to be the coolest special effect of the night, transforming the stadium into a dilating spiral of rainbows; the perfect readymade backdrop for Ms. Perry’s raison d’etre.

But if the night was about self-discovery, no song renders a more accurate picture of Ms. Perry than “Roar,” a song that makes room for her both her cute hiccuping and her robust belting. When Ms. Perry triumphantly unveiled the song at the 2013 Video Music Awards, she wore a boxing costume. Tonight, she wore a glowing cheerleader uniform. There is something about this song that lets Ms. Perry revel in two worlds. You can believe her to be the jock and the cheerleader, the loudmouth and the lion-tamer, all at once.

Set List for Katy Perry @ the Prudential Center | 7/11/14

Roar
Part of Me
Wide Awake
This Moment/Love Me
Dark Horse
E.T.
Legendary Lovers
I Kissed a Girl
Hot N Cold
International Smile
By the Grace of God
Legends Never Die
The One That Got Away/Thinking of You
Unconditionally
Walking on Air
It Takes Two
This Is How We Do/Last Friday Night
Teenage Dream
California Gurls

Encore

Birthday
Firework