This paper presents the one-dimensional framework of Multidimensional Descriptive Mathematics (MdM), a mathematical system derived from first principles to describe relations between interconnected properties. Beginning from three axioms—parameter representation, ordered elements, and reference definition—the framework derives the binumber: a relational structure distinct from a numerical value. The central theorem establishes the forced fold direction, from which binumber range, decomposition, fold reversal, cross-origin impossibility, and reciprocal rules follow as direct consequences. Key results include: named spaces preserving relational precision through whole-number arithmetic; the space gate mechanism for cross-unit measurement; seven comparison operators forming a closed commutative algebra; gate operators, regulators, and logical chains; and the discovery that Boolean logic is the point-rendered special case of a richer zone-based algebra—providing the mathematical foundation for analog logic. Formal content: 3 axioms, 52 definitions, 13 theorems, 23 propositions, 4 lemmas, 15 corollaries. This record contains two companion documents:- Framework Presentation — full exposition with motivation, proofs, examples, and applications- Formal Reference — formal objects only with identical numbering The one-dimensional framework is the first layer of a multidimensional structure. The plane framework (trinumber mathematics) constitutes subsequent work.
Pavel Ovcharov (Sat,) studied this question.