Graph of Life, Borders of Life, and Global Life Network

In this work, we pose and aim to answer the following questions, among others: Which quantitative characteristics, being satisfied, led to the phase transition from "primordial soup" to living organisms? How to measure the negentropy of a certain organic matter that underpinned the appearance of a certain species? To what extent do the biosequences of living organisms differ from random sequences? How do we quantitatively distinguish primitive from higher-level organisms? How can we compare the complexity of two living things? Is there an adequate mathematical structure that naturally and appropriately represents each organism biosequence and all of them as a whole? What are the properties of that structure? How does that structure evolve, and what are the theoretical limits of any further evolution? Is it likely that these bounds will be reached, and what are the "limits of life?" How to estimate the effect on the mechanism of evolution of natural selection vs. the one of chance and mutations? To this end, we introduce relevant mathematical structures and use them for modeling purposes. Finally, we also speculate on possible scenarios of the origin of life, evolution, and related issues.