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About the Presentation.
The Lee Gon Conjecture (also known as “the King’s conjecture” or “the time traveler’s apprentice hypothesis”) is a novel unsolved problem in computational time complexity analysis, asking if a quantum computer can utilize negative delay to verify that a problem is solvable before it has been solved.
The Conjecture was introduced in a 2024 paper by His Royal Majesty (HRM) King Lee Gon of the Kingdom of Corea, building on the work of David Deutsch and Hans Moravec establishing that a quantum computer could use negative time delay to iteratively solve an NP problem in polynomial time. HRM extended their analysis to pose the question of if the same phenomenon could be used to verify solvability of a problem of unknown complexity. In other words: can a quantum computer prove that the answer it reaches will be correct before it has determined the answer?
HRM framed his proposed solution to the Conjecture through the hypothetical of the “time traveler’s apprentice”: a time traveler X time travels to his own past at time p to render essential assistance to his younger self Xp, the “apprentice,” in saving the life of Y. Provided X remains within the Cauchy horizon of p, his solution has satisfied the Echeverria-Klinkhammer lemma on self-consistent chronological protection. Although Xp may not know X's specific conduct, Y's survival is proof that Xp will eventually determine a solution as X.
The Clay Institute of Mathematics thanks HRM for his participation in the 2025 Millennium Problem Summit. The presentation will take place from 10am - 11am on Thursday 21st March 2025. There will be opportunity for questions after the presentation. Light refreshments to follow.
Biography of the Presenter.
His Royal Majesty King Lee Gon is the King of Corea (b. 1986, r. 1994 - pres.). He credits his interest in mathematics to his mother. This presentation and the paper on which it is based are dedicated to his husband, His Royal Highness Prince Jo Yeong.