Insolubilia (Fargo)

Gator (Joe Keery) and his gang prepare to ambush Dot (Juno Temple) inside her house. Despite Dot heavily guarding the house with traps, Gator and the gang easily anticipate and avoid them. As they wander through the house, Dot attacks them and is shocked to see that Gator is one of the invaders. While locking her family in the bedroom, Wayne (David Rysdahl) accidentally shocks himself and falls unconscious, also causing a fire in the house. Dot and Scotty (Sienna King) take Wayne out of the house, while Gator and his gang are forced to flee as the fire department arrives.

While Roy (Jon Hamm) is inside the barn, Munch (Sam Spruell) enters the Tillman house. Roy grabs a shotgun when he sees Munch's footprints. He enters his children's bedroom, finding that Munch has carved a bloodied symbol on the wall. At the police station, Indira (Richa Moorjani) and Witt (Lamorne Morris) find surveillance footage from the gas station, with Indira identifying Dot. As she prepares to talk to her, she is informed that her husband's activities got their family indebted with Lorraine's (Jennifer Jason Leigh) debt collection company. Lorraine goes to the hospital to check on her son, blaming Dot for his condition. As Indira and Witt arrive to question Dot, she decides to visit Wayne at his bed, finding that he has been given morphine. In his state, she tells him that the assailants were trick-or-treaters looking for candy.

FBI agents Meyer (Jessica Pohly) and Joaquin (Nick Gomez) report to their superior about Roy's strange tactics, as many informants have disappeared while investigating him. Their superior compares the events to the Great Chinese Famine, telling them they cannot go to war against Roy and his militia as it would lead to chaos. While annoyed, they are delighted when they find that Dot, whose real name is actually Nadine, has been tracked down in Minnesota. The elderly woman (Clare Coulter) confronts Munch as he rests inside her house, asking what he wants from her; he replies "pancakes".

Gator and his gang return to the Tillman ranch, learning that Munch visited during the previous night. Roy visits a couple, whom he had previously talked to about a prior domestic violence incident. The husband pulls out a gun, but Roy continues insulting him. When the husband decides to shoot, Roy is faster and kills him. Gator arrives and is disturbed by the scene. Noticing that Dot was not caught, Roy plans to frame the dead husband for Munch's crimes at the gas station to close the case, bribing the wife to corroborate the story. As Gator leaves to report the shooting, Roy rides off on horseback into the sunset.

In November 2023, it was reported that the fourth episode of the season would be titled "Insolubilia", and was to be written by series creator Noah Hawley, and directed by Donald Murphy.^[1] This was Hawley's 38th writing credit, and Murphy's second directing credit.^[2]

For the home invasion scene, Noah Hawley drew comparisons to Home Alone and No Country for Old Men. For the former, he wanted the audience to "feel" the threat; and for the latter, he wanted the "level of suspense even if it has a rusticness to it." To achieve the effect, the series used "I Got You Babe" covered by Tiny Tim as it would be "unsettling." He also wanted the scene to show Dot as a fighter, but also in a humanistic way, saying "She's been so good for so long, but the house is literally destroyed. The life she was trying to protect has ended on some level."^[3]

Gator uses a nail-spiked baseball bat as a weapon, and many considered it as a reference to Joe Keery's role as Steve Harrington in Stranger Things, who similarly uses a bat as a weapon. However, Hawley said that this was not an intended nod, explaining "the joke, of course, was that the 12-year-old girl is making a Zombie Killer, and their home defense system is a sledgehammer over the front door. And then, once you created and use that joke, now the Zombie Killer is in play and so of course he's gonna break into the house."^[4] The scene required Gator and his gang to wear masks from characters from The Nightmare Before Christmas. Executive producer Steve Stark contacted Tim Burton, who allowed them in using the iconography of the film. Hawley felt the series and the film shared similar concepts, saying "it pretends to be this dark and disturbing thing, but at the center of it is just this guy with a heart of gold, who wants to understand this holiday. It's disturbing, it's comedic, it's sort of more graphic than a children's movie should be, in some places — but never cynically. And I think that echoes what we're trying to do."^[5]

David Rysdahl explained that he researched for Wayne's hospital scene, particularly the effects of electrocution. He said, "His brain is not only fried, but the reality that he had been living with has also been shaken. The idea of who he is in relation to his wife and who his wife actually is has all been shaken. So he's awakening from two dreams: The fog of his brain and also the fog of his life. And so I told Noah that I thought it was so fun to play."^[6]