If you only know one thing about the reunited Smashing Pumpkins, it's probably that they're not actually the Smashing Pumpkins—at least, not as you remember them. Billy Corgan is now the band's lone original member, and to many longtime fans, especially those who came of age to the band's alienation anthems in the '90s and still cling to their early impressions of what the band represented, that makes these new Smashing Pumpkins illegitimate. Never mind that Corgan had always been the near-exclusive creative force behind the band, writing (and usually recording) with scant input from his one-time band mates, and that he has every legal claim to the band name. By unceremoniously replacing those three other faces on the group's Siamese Dream-era posters—by demonstrating that his band mates were and probably always had been dispensable—he has trampled on fans' powerful memories of not only a favorite band, but also of their very youth.

Corgan knows this. He takes a kind of pride in it.

“I did an interview with Greg Kot a while back,” Corgan recalls, “And he said, 'Why are you still using the band name? Why not tour under a new name?' And I said, 'Greg, you've known me for 20 years. I'm playing under the name precisely because people don't want me to play under the name.' People's annoyance at the continuance of the band name just hands me another hand grenade.”

Reinvention, Corgan reasons, has always been intrinsic to the band—“We were never about just one thing,” he insists. “There was never a Smashing Pumpkins record that sounded like the others”—and this new lineup is, by that logic, just another reinvention.

“Look, I'm in the same position as a lot of fans,” Corgan says. “All the time people ask me if I want to see some old band, and I'll say, 'Well, who's still in the band?' I think that way, too. I'm that shallow. But I want to challenge that train of thought. The Smashing Pumpkins is all about poking a hole in that construct, and, if we do this next album right, that's what we'll have done."

Corgan is referring to Oceania, the upcoming Smashing Pumpkins album that as of our conversation late last month he had just finished recording. If the album is good, he reasons, it will put to rest questions of the group's legitimacy.

“If we can turn the corner with Oceania, and get people to say, 'Oh, there's still gas in this tank,' it will blow up all that falsity,” he explains. “What would people have left to complain about? 'Oh, he looks old?'”

It's hard to argue with that logic: A good album goes a long way toward winning people over. And, no doubt, part of the reason the resurrected Smashing Pumpkins have been written off by so many fans is that their comeback record, 2007's Zeitgeist, was not a good album. Its brutal, ugly guitar assault captured none of the majesty of the band's most beloved work, nor any of the sweetness that ran through even the band's heaviest work. Corgan concedes it wasn't the album he had wanted to make.

“I really wanted to return to psychedelic music, but I was surprised that I just couldn't find it in me,” he says. “I tried, and eventually I gave in and said, 'Well, this is what's coming out of me.' I didn't want to keep playing dark proto-metal that whole time.” Corgan doesn't outright disown the album, at least not in our conversation, but the disapproving tone in his voice when he uses the phrase “dark proto-metal” suggests that he probably feels the same way about it as everybody else.

Fans already uneasy with the idea of a partially reunited Smashing Pumpkins can be forgiven for not giving Corgan a second chance after an album so unlovable, but his subsequent work has, if nothing else, been truer to the band name. The mostly (and, following Zeitgeist, mercifully) acoustic 2008 American Gothic EP showed Corgan could still write songs with heart, and with the band's ongoing, 44-song project Teargarden by Kaleidyscope, Corgan has reclaimed the psychedelic muse that proved so elusive during the Zeitgeist sessions.

Oceania will be part of that Teargarden project, “an album within an album,” and to hear Corgan describe it, it should sound a whole lot closer to the Smashing Pumpkins full-length that fans were probably hoping for the last time around. “It's got an epic quality to it,” he says. “It's probably one of the prettiest records I've made, but it's still very loud. There's some shoegazey elements in there.”

He's proud of the work, and excited about it, and not just in the way that every musician is excited about his latest album. This is going to be the record that proves everybody wrong, the record that vindicates him as the lone heir to the Smashing Pumpkins.

“Enough arty games of perception—at the end of the day, it's about the music,” Corgan says. Since drummer Jimmy Chamberlin left the band in 2009, he says, “I've had enough time to recalibrate the lineup, to make the album that I want to make. Enough talk. Let's see what I've got.”

That kind of chest-beating strikes me as a pretty reckless way to set expectations for an album. I tell Corgan that it seems like he's positioning Oceania as a do-or-die, make-or-break record.

“It is,” he says.

Smashing Pumpkins headline the Riverside Theater on Thursday, Oct. 13, with openers Fancy Space People and Light FM. Doors open at 6 p.m.