SPOILER FOR FUTURE ARC, so if that worries you, read later. If not, read on.
Box theory (as given by Lal Mirch) is in manga chapter 147 and anime episode 79.
The basics of the weapon boxes are these:
– Have a power ring (Vongola, Mare, or others)
– Have a weapon box fit to the power ring
– Have a person with a life force (wave energy) much like the dying will system
– Have the person’s wave energy pulse through a power ring…
– which will energize the power ring to create a ring flame…
– which is pressed into a hole in the weapon box…
– which will then activate and open the weapon box…
– releasing the specific weapon inside (a fighter animal or components of a weapon).
The rings you will most often hear about are the:
– Vongola rings (highest purity)
– Mare (pronounce mah-reh) rings (highest purity)
– Hell rings (lesser purity, rare)
– various rings of lesser purity, with specific dying-will flame types
The boxes you will most often hear about are the:
– Vongola boxes
– various weapon boxes used by others
– Millefiore transcendent boxes
A few more specifics and details:
– The ring flames do NOT work at all times. The person must have enough determination, will, or focus (whichever works for the person) to generate enough life force, and thus enough wave energy to create ring flames. It’s like a smaller version of Tsuna’s Dying Will system.
– The power rings may sometimes be used independent from the boxes, but more can be done when they are used to activate weapon boxes.
– “Think of the box as a tool that can transform the flames of the rings into other functions and motions. If you think of the flames as electrical energy, then the boxes are like electrical appliances.” (Lal Mirch, as translated by Kirimi) From that, there are many variations on the principle.
– Majority of the weapon boxes are custom-made for their users. Thus, Yamamoto’s boxes are tailored to the rain wave energy and ring, and to the fact that he primarily uses a sword. Gokudera developed this insanely complicated system for his storm wave energy and ring (Sistema CAI).
– One ring emits one ring flame through one wave energy. However, some people can emit more than one wave energy, and are thus capable of using more than one type of ring and ring flame. Gokudera is one of them. He uses a primary storm ring and secondary rain, cloud, sun, and lightning rings.
– The Sky Ring flame is a special case. It can activate ANY box from any wave energy to a certain degree. “The Sky Flame can open boxes of all the attributes, but it cannot draw out all the power of the boxes of the other attributes.” (Hibari, as translated by Kirimi)
– The Rings that various fighters have contain varying degrees of purity. The levels are not too important to know, but these generalizations are:
— The rings with highest purity, and thus with greatest power, are the Vongola and Mare rings.
— The ring flame with the highest purity is the Sky flame (orange). The ring flames for the guardians have varying levels of purity after that.
– The weapon boxes were developed and constructed by Innocenti, Koenig, and (the Arcobaleno) Verde, based on plans drafted by a scientist in the Middle Ages. 343 boxes are based on living things (thus, the box animals), and others were developed to house weapons. Many of these boxes were sold to members of the Mafia.