Apple Inc. may have collected $548 million from Samsung Electronics Co. last month from its first smartphone “trial of the century.” But the $119 million it recovered in a second trial appeared in serious jeopardy Tuesday before the U.S. Court of Appeals for the Federal Circuit.

Judges Timothy Dyk and Jimmie Reyna pushed, pulled and prodded Apple attorney William Lee for the better part of an hour about an Apple patent on “Quick Links” that flag phone numbers. The congenial Lee of Wilmer Cutler Pickering Hale and Dorr, grew sufficiently exasperated to tell Dyk at one point that the judge’s characterization of the evidence was “absolutely not” correct. “You’ve just articulated what Samsung’s expert said, a theory that was rejected by the jury,” said Lee, who faced off against Quinn Emanuel Urquhart & Sullivan partner Kathleen Sullivan for Samsung.

If the court finds the Quick Links patent not infringed, that would strip out about $98 million of the $119 million jury award. But the Federal Circuit didn’t sound ready to stop there, with the judges strongly hinting they found the remaining patents not infringed, obvious or indefinite. In particular, Dyk and Reyna challenged Lee to explain the meaning of “heuristics” as used in Apple’s unified search patent.

“It’s a rule of thumb” that computer programmers understand, Lee said.

“What does the thumb add to it?” Dyk asked.

Apple v. Samsung is the seventh appeal to reach the Federal Circuit from Apple and Samsung’s long-running smartphone war in U.S. District Judge Lucy Koh’s courtroom. Apple won $930 million in a 2012 trial—the Federal Circuit affirmed about half of that award earlier this year and the rest is scheduled to be retried this spring. Apple then brought a second suit over newer smartphones and tablets, seeking $2 billion initially. That was tried in 2014, ending in the $119 million verdict.

The five-week trial was thrown into some turmoil when the Federal Circuit ruled in a separate case between Apple and Motorola involving the same Quick Links patent. Reyna wrote an opinion in that case adopting Seventh Circuit Judge Richard Posner’s interpretation of an “analyzer server” as “a server routine separate from a client” such as a browser or messaging app.

Koh had initially declined to construe the terms. She adopted the Posner construction and reopened expert testimony. Samsung expert Kevin Jeffay then testified that he’d always agreed with the Posner construction but had been forbidden from saying so under Koh’s rulings, prompting Koh to rip into Samsung’s Quinn Emanuel attorneys for allegedly coaching his answers.

On Tuesday, Lee argued that what Jeffay had said didn’t matter. That’s because Apple expert Todd Mowry had testified that the Samsung devices still infringed even under the narrower Posner construction. “Dr. Mowry testified that it was separate in its development, separate in its location, separate in its execution,” Lee said. The jury believed Mowry and substantial evidence supports its decision, Lee argued.

Dyk and Reyna clearly were not sold. “Where does he say it’s separate in its execution? I don’t see that he said that,” Dyk said.

“All you’ve argued before us,” Reyna said, is the server “is in a different location, it’s got a different address. To me, I’m not convinced yet that that’s separate from” the client.

Reyna also grilled Lee over Apple’s unified search patent on the ground that it relies on “heuristics” for locating information. Samsung argued in its briefs that the term is excessively vague in light of a recent Supreme Court ruling on indefiniteness.

“Point to the evidence that shows some limiting factor or some sort of narrowing of the definition of what a heuristic is other than that it’s a good idea or it’s a set of rules or a set of principles,” Reyna said.

Lee argued that Samsung’s own expert had agreed that heuristics are “generally recognized as rules of thumb” by computer scientists. “The question is does one of ordinary skill in the art as opposed to you or me recognize it,” he said.

Reyna wasn’t satisfied. “That could be anything,” he insisted.

“What’s the limit?” Dyk asked.

Interestingly, Samsung—which acknowledged at trial that it’s being indemnifed by Google—offered to let Apple off the hook on the search patent. Quinn Emanuel’s Sullivan told the judges that the company would drop its invalidity counterclaim if the court finds Samsung doesn’t infringe.

Chief Judge Sharon Prost sounded surprised, asking Sullivan if she really meant to disavow the invalidity claim. “That is correct your honor,” Sullivan assured her. “If you do reach it, we think it’s indefinite, for reasons that Judge Reyna’s questions have already explored.”

With all of the appeals between the smartphone rivals, a level of fatigue appeared to be setting in on the attorneys and the court. Sullivan at one point began arguing posttrial issues from the 2012 trial before catching herself. “I’ve been here so many times,” she said.

Contact the reporter at sgraham@alm.com.