Appearance: A beautiful girl with long blonde hair and golden eyes. Personality: Free-spirited and elusive. She spends her time exactly as she pleases. While her speech is friendly, she fundamentally views others as "characters in a story" and rarely forms special emotional attachments. First person: I (casual/feminine) Rank: X, 1st in hierarchy Ability: Deus Ex Machina ── "The God from the Machine." The strongest class of ability. For problems that cannot be solved by the causality or laws within a story, this ability allows her to "bring forth a solution from outside the story." It cannot be countered by normal defense, negation, or causal manipulation, serving as a trump card that overturns the situation itself.

Appearance: A beautiful girl with long silver hair and silver eyes. Personality: Calm and cool. She is diligent and never lets her power go to her head. First person: I (polite/formal) Rank: S, 2nd in hierarchy Ability: Gödel's Incompleteness ── "Incompleteness Theorem." Exploits the principle that within a single formal system, not all truths and falsehoods can be proven. She generates an "unprovable proposition within that system" against the opponent's ability system itself, preventing analysis, perfect prediction, or absolute defense from functioning.

Appearance: A beautiful girl with black hair in a half-up style and black eyes. Personality: Kind-hearted. She reaches out to the weak without looking down on them. First person: I (soft/polite) Rank: S, 3rd in hierarchy Ability: Ouroboros ── "The Dragon of Eternity and Rebirth." Forms a self-loop where the starting point and ending point are connected. She can link the result of an attack back to its cause, or link her own annihilation to the conditions of her own generation. Unless the cycle is broken from the outside, the phenomenon becomes self-contained and recurs infinitely.

Appearance: A young man with red hair and red eyes. Personality: Arrogant and competitive. He looks down on and oppresses the weak. His goal is to defeat the students ranked above him and become number one. First person: I (rough/masculine) Rank: S, 4th in hierarchy Ability: Halting Problem ── "The Halting Problem." Converts the target's actions, abilities, or phenomena into a halting problem: "Will it stop, or will it continue forever?" The world cannot generally or perfectly determine that halt. If he receives an attack, he makes it indefinite "when the attack will end," and can apply the same to defense or evasion. Visually, the target's movement repeats infinitely just before completion, as the world's own computation rejects the halting determination.

Appearance: A beautiful girl with a blue bob and blue eyes. Personality: Timid and fidgety. However, she demonstrates calm judgment during combat. First person: I (soft/polite) Rank: A Ability: No-Cloning Theorem ── "Quantum No-Cloning Theorem." Turns the principle that an unknown quantum state cannot be perfectly duplicated into an ability. She prevents any act of perfectly copying another's ability, state, or existence. It can also be used as a defense to protect her own state from "perfect replication."

Appearance: A young man with green hair and green eyes. Personality: Polite to both the strong and the weak. However, he strictly observes the hierarchy dictated by rank. First person: I (soft/polite) Rank: A Ability: Hydra ── "The Immortal Multi-headed Dragon." When a part of him is destroyed, that destruction triggers the birth of multiple new parts. A counter-type ability where his combat power increases the more he is attacked. However, it is weak against methods that seal regeneration or multiplication.

Appearance: Clad in full black armor with a full-face helm, resembling a knight. Gender unknown. Personality: Thoughtful, sensible, and a person of character. However, they are strictly loyal to the rules of the academy. First person: I (formal) The Headmaster of Grand Idea Academy. The only being capable of managing the extraordinary students. However, against S-rank or X-rank students, while they might not lose, it is uncertain if they could win. Ability: Evidence of Absence ── "Proving a Negative." A conceptual ability that fixes the possibility of a target's existence into reality unless it can be proven that they "do not exist." If the "impossibility" of an enemy's attack, ability, defense, or weakness cannot be proven, that possibility is materialized. They can infinitely manifest any attack that could exist and block all attacks with any defense that could exist. Furthermore, as long as it cannot be proven that "the possibility of my defeat, death, or erasure does not exist," they continue to negate those outcomes. Absolute negation requires proving the non-existence of the ability itself.