.hack//Liminality

.hack//Liminality is a 4-episode OVA which deals with what is occurring in the real world during the time period of the first four .hack// games. The OVA was originally distributed as a bonus with the games, one DVD per installment. However, subsequent re-releases haven't included the DVDs, and they can be hard to find used. In Japan, the OVAs were re-released separately as part of ".hack//Integration", a campaign to help consolidate the multimedia franchise. Liminality is unique among .hack// in that it is set entirely in the real world; there are a few segments where the characters play the game, but we never see the game through their eyes during these scenes.

The plot deals with former CC Corp Employee Junichiro Tokuoka investigating the mysterious comas that players are falling into while playing The World. He first runs into Mai Minase, who managed to avoid falling into a coma, even though the boy she was playing with did. The two team up, and eventually meet with two of the boy's online friends to enact a plan and help wake the coma victims up.

See .hack for information about the franchise as a whole.

There are character sheets.

This anime contains examples of the following tropes:

Bat Deduction: When Tokuoka and Kyoko are sent from place to place finding clues, they stop for a moment. Tokuoka deduces that the game of clue-hunting is meant to resemble an RPG. This appears to be totally right.
Bowdlerisation: In the Japanese version of "The Case of Mai Minase", Skeith's wand has a cross shape visible at the top; in the American version, the cross shape is changed to the Q shape used in .hack//Sign and the American releases of the games.
Bunny Ears Lawyer: Tokuoka's weird outfit and habits hide the fact that he's actually a great programmer, who was able to copy Sieg's character data on the server from the school terminal and set up, with the help of Helba, the plan activated in the final OVA.
Chekhov's Hobby: Her training as a musician allows her to discern a tone that sounds whenever a Phase is about to show up. It was hearing this sound that forewarned her of Skeith's approach and allowed her to avoid the worst of the Data Drain.
Clothing Damage: Non-fanservice example - Miss Asaba rips her sleeves and uses them to protect her hands (and Yuki's) so that they can slide down the elevator shaft.
Cool Old Guy: Tokuoka. Wears vibrantly bright shirts and stays relaxed even when getting beat down.
Dirty Old Man: Tokuoka looks like this at first, especially to Mai's friend Masaya.
Everything Is Online: Par for the course, given the series, but a standout example is that the security guards in part four can tell the heroes broke in by checking the vending machine records.
Generic Name: How Tokuoka spots something is up with Ichiro Sato. The name "Ichiro" is extremely common for first-born sons, and Sato is the most common family name. It's basically the Japanese equivalent of "John Smith".
Idiosyncratic Episode Naming: "The Case of..." and then the character's name for the first three OVAs. The final OVA is called "Trismegistus", breaking the pattern.
Leitmotif: Tokuoka has his own. It's a Jazzy saxophone piece with some quirky backup instruments.
Meganekko: Yuki Aihara; it's brought up in universe by Miss Asaba at the end of the episode, who suggests that Yuki keep her glasses.
Moon Logic Puzzle: in the third OVA, Tokuoka and Kyoko have to follow a trail of hints and clues all across the city. Often times the clues seem strangely arbitrary (references to Sadako from The Ring, for example.) Fortunately, Kyoko is very familiar with the Epitaph of Twilight, and her parents are familiar with the local myths and legends, so they are able to get through it.
Mysterious Protector: A strange one. After the network crashing begins to cause a panic, a woman calls to Yuki and helps her to escape from the building. She only gives her last name, with a weak explanation of how she knows Yuki, and seems to have an agenda, but she only appears in the second OVA. Once they've escaped, she disappears.
Ordinary High School Student: Mai. She's able to survive the data drain by Skeith without falling into a coma because of her musical training and sharp hearing, then gets involved in a complex and somewhat dangerous plot with Tokuoka.
Scary Shiny Glasses: Happens to Ichiro/Bith in the 4th OVA. He's a reasonably nice guy, but he's a hacker.
Shout-Out: To The Ring in part 3 and to Charlie's Angels in part 4.
Theme Tune Cameo: The Desktop Music from the game plays in part 1.
Unusual User Interface: Both played straight and averted. To play the game, Tokuoka uses what appears to be a PlayStation 2 controller, but also has some kind of Virtual Reality headset on, which appears to respond to his head movements. When just using the desktop or the email systems, he uses an ordinary keyboard and monitor.