Apple and Samsung are taking up arms again Thursday, continuing discussion of their $1 billion case. The two companies head back to the courtroom of Judge Lucy Koh in San Jose, Calif. to talk about damages and further details in their patent battle.

A jury decided in August that Samsung should pay Apple $1.05 billion in damages, but Koh could enhance or soften those damages. She could also add supplementary damages. Finally, based on an argument from Samsung, she will also hear arguments on whether or not to award a new trial based on claims of jury misconduct.

In the run-up to the hearing, Samsung released documents about Apple’s settlement with another Android phone maker, HTC. According to the filing, posted by All Things Digital, the companies appear to be cross-licensing some patents. The agreement does not include any products defined as a copy of an Apple product — Apple can request an arbitration process if it feels HTC has released such a product.

The filing did not include information on what, if any, licensing fees HTC may be paying to Apple.

All Things Digital’s Ina Fried wrote that she suspects Samsung entered the document into the public record to demonstrate that Apple may not need an injunction to resolve patent infringement disputes.

The hearing is a continuation of a drawn-out, worldwide battle between the world’s top two smartphone makers. It’s not clear whether Apple and Samsung could reach a mutual agreement that could stop the legal jousting.

In an interview with Bloomberg Businessweek Thursday, Apple chief executive said the rift has strained the relationship between the companies.

“It is awkward,” Cook said. “I hate litigation. I absolutely hate it. For us, this is about values. What we would like, in a perfect world, is for everyone to invent their own stuff. We love competition. But we want people to have their own ideas and invent their own stuff. So after lots of trying, we felt we had no other choice. We tried every other avenue, and so we’ll see what happens in the future.”

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