The Jump Maximum Function and the Subordination of Formalism

The Jump Maximum Function and the Subordination of Formalism — A Record of Unprovability in the Collatz Mapping — This project presents a structural record concerning the so-called Collatz conjecture. It focuses on the behavior of the jump maximum function M(N), defined on a class of odd numbers N = (1/2)·(a·3ⁿ − 1), where a is odd and n is a natural number. The project consists of: - A Japanese-language manuscript that explores the structural limitations of formal systems (ZFC) in capturing the unpredictable behavior of M(N), and proposes a philosophical framework in which formalism is subordinated to the integrity of record. - An English-language version of the manuscript, preserving the structure and tone of the original, for international accessibility and citation. - An Excel record table that documents the behavior of M(N) across various values of a and n, including mod 8 and mod 16 classifications, jump positions, and unpredictability markers. This record does not claim to complete a proof. Rather, it seals structural traces that formalism has not yet reached. If a formal proof is ever constructed, it must be subordinated to this record as its source. May this project serve as a lantern, quietly illuminating the limits of formalism.