Philosopher's Stone

Philosopher's Stones (賢者の石 Kenja no Ishi) are unique items featured in Tart Magica event stories in Magia Record - directly in The Masked Student Council Strikes Back, and debatably indirectly in The Inheritors of Our Souls.
They are magical stones that work as catalysts, capable of turning powerful dreams and desires into reality through If-Factors, even entire If-Worlds and other feats usually only possible through Magical Girls. The process of their creation is unknown, as the only person who has been able to create them is the alchemist, Nicholas Flamel. By the time he met his wife Pernelle in the mid-1300s Europe, he had been able to create at least one Philosopher's Stone.
By 1431, he had created two Philosopher's Stones in total, and has presumably not made more since then. He kept one for himself, using it to live for hundreds of years, and donated the other to "someone in need." Somehow, the other Stone fell into the hands of Minou who used its power to create an If-World where her mother, Isabeau de Bavière, could be resurrected. Over hundreds of years, the If-World became the Holy Maiden Academy, with the Stone itself enshrined within the school's main hall.
Properties
The stones appear as unpolished red gemstones with a bright, glowing yellowish-white core. They usually have an irregular, roughly pentagonal shape and closely resemble real-world cinnabar, rubies, carbuncle gems, or almandines. The Philosopher's Stone's primary function is to transform a powerful "what if" desire from a mere concept into a physical If-World. When used to create an If-World, the Stone sustains its existence and laws of physics. Philosopher's Stones also have effects similar to magic, such as completely halting the aging process, and they contain vast reserves of magical energy.
Holy Maiden Academy
In the Holy Maiden Academy If-World, the designated role of the Magical Girls (Tart, Liz, Elisa, and Melissa) is to locate and neutralize If-Factors that cause dangerous disruptions to their reality. Their actions are necessary to maintain the world's stability, though the world can be reset if an incident causes a total collapse.
If-Factors
An If-World is a fully realized, alternate reality that stems from a deep “what if,” a hypothetical scenario rooted in someone’s desire once they possess a Philosopher's Stone. The world of Holy Maiden Academy is one such If-World, which was created over hundreds of years as the residue of Minou’s desire to resurrect Isabeau.
If-Factors (IF因子(ファクター) Ifu Fakutā) are physical manifestations of "what if" thoughts or desires that seep into the If-World from other universes. An If-Factor is a physical object or entity that manifests from a powerful "what if" thought or desire. They are usually "impossible" items that operate on the natural laws of their world of origin, which often conflict with the laws of the If-World they invade, causing dangerous reality-warping incidents.
If-Factors are described as the crystallized "seeds of a world." They are born from statements that begin with "What if...?" and range from simple, whimsical thoughts to profound, world-changing desires. When they slip into an If-World, they bring their own set of rules with them, which creates anomalies that often threaten the If-World.
It is unknown if this is the rule in every If-World, but in the Holy Maiden Academy, Magical Girls have the duty to resolve incidents caused by the If-Factors. However, in the Academy, even if the If-World ended, it would simply reset. The Masked Student Council actively seeks the Factors out, believing they can be used as catalysts to breach the barrier between the "What If" world and the real world.
Known If-Factors:

- Teapot: A teapot which likely emerged from an idle desire like "What if I had a teapot that produced an endless supply of delicious tea?" The teapot generates infinite amounts of brainwashing tea that compels people to serve it. The refill rate accelerates after each use and it eventually floods the entire version of the If-World.
- If-pedia: A Wikipedia-like website that contains detailed information about the the Holy Maiden Academy If-World, including events, character profiles, cafe menus, etc. Crucially, the If-World conforms to the information on If-pedia and editing the site directly edits the world. It is used by the Student Council to create a "labyrinth event," then used by Melissa to prank Elisa, and then delete the labyrinth, saving the world temporarily. Its accidental deletion by the Student Council causes the If-World itself to be deleted and thus end once more.
- Labyrinth Door: The specific manifestation of the If-pedia's labyrinth event. The door creates a labyrinth by causing doors to open onto random, illogical locations (French countryside, Kamiket, other school rooms, complete voids). It traps those who enter, and at one point, it exploits Riz's love for cute things (via the kitten) and Ms. Specs' (Pernelle's) tendency for exposition.
- Ui's Phone: Also called "The Blank Prophecy". A unique case of a real-world object becoming an interloper If-Factor within the Holy Maiden Academy world. It originally belonged to Ui Tamaki from the real world and it functions as a normal phone within the "What If" world, but crucially, it has a connection back to the real world. Minou's plans involved using it to record Isabeau's rebirth in the If-World and send that recording back to reality through Lil' Kyubey. Its crash, caused by Melissa's misdirected text, and its subsequent return to the real world foils her plan.
- Lil' Kyubey: Another unique case, where his arrival makes him considered an If-Factor themselves. Minou’s belief was that by sending him to the real world with the recording, eventually, some Magical Girl candidate would see the footage, feel something intense and make a wish that causes Isabeau to be reborn in the real world.
Ark of Feelings

The Ark of Feelings (感情の方舟 Kanjō no Hakobune) is a metaphysical archive where people's emotions and memories are stored as books, created by Pernelle and Nicholas Flamel. It is not a physical place, but a spiritual or mental space, almost like a dream realm or psychic library, that can be entered and explored. People can access memories that are otherwise forgotten or erased from history, especially those related to important figures remembered by many, like Joan of Arc (La Pucelle/Tart).
Even when historical records are wiped or altered, the Ark of Feelings holds onto what people once felt and remembered. That’s how Tart’s legacy survives in the Ark even though she’d been temporarily erased from the outside world.
It is unknown if the Ark of Feelings is akin to an If-World, If-Factor, or some other creation of Nicholas' Alchemy and Pernelle's magic.