As Apple shares surge to make the company the most profitable firm ever at $621 billion, the stage is set for a jury to deliberate in the lawsuit between Apple and Samsung. Both sides are preparing to present their closing arguments Tuesday.

As the Wall Street Journal reported, the jury will have to decide whether Samsung infringed on Apple patents, if Apple infringed on Samsung patents, and what — if any — damages and royalties will have to be paid.

It’s been a long and contentious trial. Apple has made its case to the jury that Samsung has blatantly copied Apple’s tablets and smartphones and diluted the Cupertino, Calif.-based company’s brand in the process. Meanwhile, Samsung has argued that Apple’s products were not as innovative as the company has made them out to be, showing prior art that it hopes makes the case that the iPhone and iPad were the next step in an evolutionary process.

Meanwhile, the judge in the case has made her own argument — that Apple and Samsung should come to an agreement on their own.

According to a report from Bloomberg, Samsung Chief Executive Kwon Oh Hyun and Apple Chief Executive Tim Cook are said to be speaking via phone to find a mutually agreeable solution before leaving the case’s outcome to a jury. Citing an unnamed person “familiar with the matter,” the report said that the companies’ lawyers will report on the call’s outcome to Judge Lucy Koh. The two men have met before, but could not come to a settlement agreement.

If the case does go to the jury, the nine men and women will have to make a complicated decision that could have wider implications for the smartphone and tablet markets. Not only is Apple asking for a permanent ban on all infringing products, it’s also probably looking for ammunition with which to fight further patent disputes with Android handset makers. Samsung is the company’s fiercest, but far from sole, competitor.

Pulling of a win in the federal court case would put Apple on solid footing, and could lead to serious design changes across the industry to give Apple’s design patents a wide berth, the New York Times reported. A loss for Apple, on the other hand, could produce years of similarly designed products, analyst Michael Gartenberg told the Times.

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