Numerometry, Volume I: Fusion Operators, Numeric Chains, and Structural Arithmetic

his volume introduces Numerometry, a formal framework for studying numerical structure at the level of digit composition.

Instead of treating numbers solely as abstract magnitudes, the theory focuses on the internal mechanisms by which numerals are formed in positional systems. A primitive binary operation, called fusion and denoted by ⋄, is introduced to represent the ordered concatenation of digits into structured numeric chains.

The book develops the axiomatic basis of fusion, establishes the algebra of numeric chains, and defines the numerometric absolute value (NAV), which separates structural information from quantitative magnitude. This allows arithmetic operations to be reformulated in purely structural terms while remaining consistent with classical positional arithmetic.

As a central result, the volume derives and proves a previously undocumented invariant property of Pascal’s triangle obtained through numerometric interpretation.

This work constitutes the foundational stage of a broader research program. Subsequent volumes extend the framework to higher-order numerometric operations, including numeric abbreviation, structural dissolution, and fusional invariants.