Milieu, Idea, Character, Event
There is no "Inquiry" thread, the I stands for "Idea".
For all readers: Each of the M.I.C.E. are types of stories, or main focus of a story, as detailed by Orson Scott Card originally, and expanded upon by others. As Orson wrote, all stories contain all four pieces, but they tend to focus on one:
Milieu focuses on the world where the story takes place; "stranger in a strange world" stories. These begin with a character entering a strange new world, and end when they leave the no longer strange world. (Alice in Wonderland, The Wizard of Oz).
Idea stories are about a central question: They begin when the question is presented, and end when the question is answered. (The DaVinci Code, Sherlock Holmes).
Character stories are about the nature and development of one or more characters. They begin with a character dissatisfied with their life or circumstances, and end when through the character's efforts those circumstances change, or the character learns to accept them. (A Christmas Carol, The Catcher in the Rye.)
Event stories are about an event or situation, including the story of its causes and consequences. They begin when the status quo is disrupted. They end when the status quo is either restored, or replaced with a better one, or entirely destroyed. (Macbeth, or many disaster films).
The additional idea of "threads" is that some or all of these stories can be either nested or woven together, we can begin with a Milieu story, and at the same time have a character story. Star Wars basically begins this way, we have both a new setting for the audience to learn (the scroll at the start is introducing the setting), and at first Luke Skywalker is the Stranger in a Strange Land. But Luke does not stay the same and just learn about this new setting (like Gulliver's Travels), we also have a Character story: Luke must transform from a "moisture farmer" and basically a teen having fun into a Jedi Knight; an Interstellar civilization depends on this raw kid to literally knock down the greatest army ever known.
In your story receiving equipment is not a thread in itself. It is not an "Idea" thread. At best it is part of the Character thread, the growth of character through training, and how using the weapon changes him. Like learning to use the Force for Luke, and in the end having the faith to turn off all his targeting equipment and rely on the Force (his weapon).
I think you are trying to get too microscopic with your threads. An Idea thread would exist throughout a large part of the story, and would require several clues and discoveries to count as a thread. It cannot be "Oh, he got an interesting weapon... and three weeks later... He used the interesting weapon; cool."
That's not a thread; in the Da Vinci Code, there are clues, misinterpretations, setbacks, and through it all the mystery of what are we trying to discover that is so well hidden?
A thread needs all the basics, even if abbreviated, of the Three Act Structure. An inciting incident; leaving the normal the world; complications, failures, and finally success.
In other words, to qualify as a thread, it must be in brief a story in itself. In most recent incarnations of the "Sherlock Holmes" series, you can see this in the developing relationship between Sherlock and Dr. Watson, typically portrayed as a platonic love story. Strangers meet, at first Sherlock is using Dr. Watson (or in Elementary even rejecting her), but the long story of the series is actually a Character love story! The episodes are nearly all straight-up Idea stories, but the Character story is woven throughout, with a slow development over the course of seasons. In fact the long thread of the Relationship threads, between Sherlock and Watson, them and Detectives or Inspectors, is much of the draw for the audience. (Compare to an Idea-Only series like Columbo.)
I hope that helps.
