Taylor Swift fans have been hoping that Disney/Pixar will “just say yes” when it comes to confirming longstanding rumors that the pop superstar is involved in some way with “Toy Story 5.” That’s not happening… yet. But anticipation over the possibility was further piqued Friday, with the unveiling of billboards that any reasonable person would suspect either (a) point toward a coming announcement of Swift being a part of the movie or (b) will get the company crucified by Swifties if it should all turn out to be a faux tease.

The billboards feature the giant letters “TS,” which happens to be an acronym for both Swift’s name and the film franchise, obviously. Although “Toy Story” movies have never been boiled down to two letters before, there’s a first time for everything, so there is plausible deniability in a connection there.

But then there are 13 cartoon clouds on the billboards… which holds true both for horizontal and vertical variants of the advertising. With that employment of the singer’s favorite number in the new ad campaign, any deniability would no longer be very plausible.

Of course, no one is denying anything right now. Reps for both Disney and Swift had no comment when asked about the billboards Friday.

What her involvement might be is still open to rampant speculation. It could be a speaking voice role in the cast; it could be a song embedded in the body of the film that is written or co-written and/or sung by Swift. But thinking outside the toybox may be advised. For all that anyone outside the cone of silence knows, it could be a live, picture-in-picture simulcast of Swift and Travis Kelce’s wedding embedded into opening-night screenings.

There is only one thing that it’s certain it won’t be: Swift doing an end-titles theme. Producers strictly ruled that out during an oft-cited interview this past week, although they were peculiarly specific about exactly what it was they were denying.

In a video interview published Wednesday, the filmmakers were cagey when asked about rumors Swift had done a song for the film. The chatter “surprised us. We’d be frickin’ honored,” director Andrew Stanton said. Then he clarified: “The sad truth is, we watched the movie being mixed last week, done, and the song on the end of that was not Taylor Swift’s song.” Which was little clarification for anyone wanting to know if the artist has a song anywhere in the film.

The rumors got underway months ago when a mysterious countdown clock briefly popped up on Swift’s website with a cloud pattern that eagle-eyed fans recognized as looking just like the wallpaper in the “Toy Story” series. The clock disappeared nearly as quickly as it appeared, and nothing seemed to happen at the time to which the ticker had been pointing. But there are few accidents in Swift-land, least of all the accident of seeming to randomly evoke Disney visual IP.

Fans further noted that the release date for “Toy Story 5,” June 19, coincides with the anniversary date for Swift’s first single release, “Tim McGraw.” And the singer has said that she has a “Taylor’s Version” edition of her debut album in the can that she planned to still release someday. So some theories have those being tied in somehow… but how? Will she put out “Taylor Swift (TV)” that day? Will she have recorded a new version of “Tim McGraw” with Buzz- and Woody-themed lyrics? Will the movie turn out to be a period piece set in 2006, with all the human and inanimate characters obsessed with the debut album by a 16-year-old country singer from Tennessee? Will she and franchise music-meister Randy Newman have hooked up to recut “Short People” as a tribute to the ultimate short people — action figures? (Or a duet of “Jessie,” set to the tune of “Marie”?)

Any of these theories may be outlandish, but possibly not as crazy as whatever the reality may turn out to be, assuming the tease is real. Unless it just turns out to be a product tie-in, but Swift’s Easter eggs rarely crack open to reveal anything that’s not fit for the griddle.

Barring any leaks, the likeliest date for fans finding out whether any of this faith is rewarded is June 9, when “Toy Story 5” has its premiere. Assuming that the gala unveiling does not still leave a “TBA” blank spot for where a Swift contribution would come on the June 19 release date — an unlikely scenario, but stranger things have happened. And if a cigar is just a cigar, an acronym is just an acronym and clouds just look better in sets of a baker’s dozen, we can all wipe the Easter egg off our faces.