This short idea suggests that LHC can be used as an information storage based on the holographic property of mini black hole produced while controllable amount of collisions happen.

This paper aims to introduce new method for forcing logical thinking to AI by delicate instruction prompting with multiple executions. exhaustive prompting uses general reasoning formation to force the way of thinking to the AI by accomodating of essential factors in prompting. With this new methodology, accuracy in well-known benchmarks has been boosted up at 1.0%p to 9.7%p.

Bunyakovsky conjecture is proved to be true.

This paper is about understanding Poincaré theorem in the view of observation. And suggests counterexample of the proved theorem.

There are infinitely many primes which are of the form in near-square.

Hodge conjecture is turned out to be false in extension of graph theory based on its algebraic attribute.

Legendre's conjecture is proved to be true.

Beal conjecture can be proved extending the understanding of Goldbach's discussion.

β function in continued fractions forms reality of Fermion-Dirac and Bose-Einstein statistics everytime stochastic distribution event happens. And entropy is decided everytime uniquely.

Birch and Swinnerton-Dyer Conjecture can be understood with uniqueness provided by continued fractions.

In this paper, a direct general specification for simulating an entire universe would be given. The simulation would be targeted as same as maximally having physical considerations in reality. Background: By identifying the universal attributes of basic attributes in an universe, scientific proposition of creating simulated universe could be derived. Methods: By extending the Monty Hall Problem derived from the result of P vs NP Problem and Game Theory to the understanding of a single observation, the continuum of total observation events creates a distribution of probability which could be translated into distribution of possibility. And using from what has been defined in this universe, methods of utilizing simulation of reality could be described. Results: Technical specification for creating axiomatic universe in existing universe could be described. Conclusions: In generalized terms, simulated universe could exist with a customized reality.

Investigating the base ground of economic growth as a mathematical model is an essential economic issue. Every economic entity does economic behaviors to maximize its goal, total utility, in a given time. By bringing out the premises of the game theory, market participants, transactions, and market entities-related agents are defined. Next, concerning the general regional economy, the transaction model in the market participants could be set. And finally, a law and economics notion to set a model of economic growth would be drawn.