In the heart of representable metric jets

TL;DR

This paper explores the core concepts of representable metric jets, clarifies previous ideas, introduces new examples like the bifractal wave function, and enhances understanding of metric Differential Calculus.

Contribution

It provides a deeper analysis of representable metric jets, simplifies previous proofs, and introduces new illustrative examples to advance metric Differential Calculus.

Findings

Clarification of key concepts in metric jets

Introduction of the bifractal wave function as an example

Enhanced understanding of metric Differential Calculus

Abstract

Here, I aim to immerse myself in the heart of the metric jets, more precisely of those which are representable, restricting myself to the main basic concepts, while going deeper into some notions already mentionned in our previous papers; this will give me the opportunity of lightening the previous texts (including some proofs), while precising some ideas and giving new examples (as the bifractal wave function) with a proof at the end of this paper. Concerning the concrete examples found all along this paper: they play the "starring role" in the understanding of our metric Differential Calculus!