The VaultX Esports Gauntlet

Directions: Study the multivariable scheduling matrix and the operational constraints provided below to decode the exact timeline before attempting any questions.

The Lore:
VaultX Media is hosting an elite 4-day "Esports Gauntlet" from Thursday to Sunday. Exactly one creator competes each day. The roster features four heavy-hitters: Agent, Duke, Fanum, and Kai.

Every day features a completely unique tournament game (*2K, FIFA, Valorant, Warzone*) and generates a unique prize pool for the winner (*$\$10\text{k}$, $\$20\text{k}$, $\$30\text{k}$, $\$40\text{k}$*).

The Meta (Constraints):
1. The Gap: Agent wins his tournament exactly two days after the Warzone tournament is played.
2. The Bag: The tournament featuring the absolute highest prize pool (**$\$40\text{k}$) happens exactly on Saturday. 3. The Scaling Law: Kai secures a prize pool that is exactly half the monetary value of the prize pool secured by the creator who wins on Friday. 4. The Pitch: Fanum wins the FIFA tournament, but he is strictly unauthorized to play on Thursday or Sunday. 5. The Skill Gap: The Valorant** tournament prize pool is exactly $\$30\text{k}$ greater than the 2K tournament prize pool.
6. The Rivalry: Duke wins a tournament with a prize pool that is strictly greater than Fanum's prize pool.