PAPER TITLE: Introducing The Anagram Distance Statistic, Ã, A Quantifier of Lexical Proximity For Base-10 o-SSI And Any Arbitrary Length Ordered Sequences, Its Relevance And Proposed Applications in Computer Science, Engineering And Mathematical Statistics

ABSTRACT:
While studying various permutations of the base-10 natural symbol set identity (n-SSI)-technically the root of base-10 orthogonal symbol set identities (o-SSI), we have come to realize that there is a simple statistical measure that could be used to quantitatively express how different any two base-10 o-SSI are from the n-SSI. By extending this analysis we have found that we can likewise quantify how different or far apart-in terms of positional order, any two o-SSI expressions are from each other. This idea has then been generalized so that we can use it to statistically test how much disorder (or entropy) a string of a given length has relative to some other reference ordered sequence of similar symbols with finite length, via the Anagram Distance, Ã(•) measure and associated test. New definitions and some new theorems were likewise developed and have been rigorously presented. We conclude by using this measure and the presented o-SSI analysis method to demonstrate several practically relevant problems and their potential solutions, across disciplines such as computer science (in cryptography and information security), the engineering of intelligent systems (in cybernetics and aircraft flight control systems) and in mathematical statistics (in statistical distance measures and goodness-of-fit tests). But this is not the only way this useful statistical measure and associated theory might be applied. Interesting research problems relating to this newly developed entropy measure have been proposed or hinted at, and all this work meant to offer a fundamental theoretical basis for new solutions (or solution methods) to old and new mathematical science problems across many disciplines, domains and fields.

KEYWORDS: Foundations, Entropy Sources, Ordered Sequences, Chaos, Statistical Measures, Intelligent Systems

ABOUT PAPER: This research further advances earlier work concerning information expressions and number sequence transformations as part of random number generator research by Joseph W. Lutalo at his private Nuchwezi Research laboratory. It introduces a new theory, ADT, Anagram Distance Theory, with general applications not only in computer science - his original focus area, but also in mathematical statistics and the mathematical sciences in general, especially those dealing with matters around entropy, ordered sequences and statistic distance measures.

TAGS: #Research #Physics #InformationTheory #RandomNumbers #InformationGenerators #Entropy #Cybernetics #Statistics #OrderedSequences #ComputerScience #ProfJWL #Nuchwezi

TO CITE:

Lutalo, Joseph Willrich. “Introducing The Anagram Distance Statistic, Ã, A Quantifier of Lexical Proximity For Base-10 o-SSI And Any Arbitrary Length Ordered Sequences, Its Relevance And Proposed Applications in Computer Science, Engineering And Mathematical Statistics.” Academia, FigShare, 2025. https://doi.org/10.6084/m9.figshare.29402363

Introducing ADT: Anagram Distance Theory #research & necessary #activism

IN BRIEF: https://doi.org/10.6084/m9.figshare.29424710

"We are formally proposing to offer to your school a robust, time-tested Software Platform for operating and managing the school at all levels: the PSMP: Primary School Management Platform, specifically and originally designed and tailor-made to suit the special needs of operating and managing a fast-paced, highly performant primary school utilizing the Standard Uganda National Curriculum for Primary Schools."

---[THE CALL]:

Dear Community,

Please find the proposal here attached, and kindly respond directly to me if you have a customer or yourself can use the presented solution. Terms and Conditions included.

God Bless you as you extend a helping hand.

Thanks. Regards

Joseph W.L.
Nuchwezi Research

### From GTNC to Anagram Distance Theory... The On-going Work in Mathematics by Joseph at NUCHWEZI:

What He Said Concerning his recent work:

Mathematics isn't like Art or Programming. A mathematical theory is timeless and can never expire even for 1 million years. I have decided to invest in building new, better mathematics for the future of humanity. GTNC, theory of Number Cardinality and Anagram Distance Theory are my first contributions thus far. Only a fool or the blind can say we are wasting time.

Further research has just revealed that ADT can be applied to any two sequences of symbols or information even though they aren't of the same length. 

This shall have applications in biology (like genetic engineering), in physics, statistics, computer science, economics and more...

---[Many People and Government Institutions Are Instead Investing in Short-term Science and Knowledge that Shall Undoubtedly Eventually Expire!]

Joseph is also currently continuing to build this Mathematical Theory and more measures and other ways to quantify Entropy are being developed at his lab at NUCHWEZI as we speak, as entirely independent and mostly voluntary work.

GO FOLLOW & SUPPORT Building A Better FUTURE: https://bit.ly/profjwl

GO READ First ADT PAPER: https://bit.ly/anagrampaper

#future #mathematics #informationprocessing #foundationaltheories #entropy #measures #intelligent #systems