Power-laws and the Conservation of Information in discrete token systems: Part 2 The role of defect

TL;DR

This paper explores how defects influence power-law distributions in discrete token systems, extending previous work on conservation principles and providing a functional model supported by experimental data.

Contribution

It introduces a functional model for defects in token systems consistent with power-law behaviors, building on prior conservation principles and empirical evidence.

Findings

Defects significantly affect power-law distributions in token systems.

A functional behavior for defects is derived and validated.

Implications for understanding discrete systems and information conservation.

Abstract

In a matching paper (arXiv:1207.5027), I proved that Conservation of Size and Information in a discrete token based system is overwhelmingly likely to lead to a power-law component size distribution with respect to the size of its unique alphabet. This was substantiated to a very high level of significance using some 55 million lines of source code of mixed provenance. The principle was also applied to show that average gene length should be constant in an animal kingdom where the same constraints appear to hold, the implication being that Conservation of Information plays a similar role in discrete token-based systems as the Conservation of Energy does in physical systems. In this part 2, the role of defect will be explored and a functional behaviour for defect derived to be consistent with the power-law behaviour substantiated above. This will be supported by further experimental data and the implications explored.