NUMO Field Theory

A discrete reversible dynamical system with toroidal topology

Sections

Introduction

The NUMO Field is a finite, reversible symbolic system defined on the digits 0-9. It is constructed as a reversible finite-state automaton equipped with a small set of involutive and cyclic operators, together with a fixed four-layer partition of the state space.

Purpose and Scope

  • Specify the axioms that define the NUMO Field
  • Describe the operators that generate all allowed transitions between states
  • Show how these operators implement reversible dynamics on a finite set
  • Relate these dynamics to a toroidal layout used in geometric constructions

State Space

At the most basic level, the NUMO Field consists of a finite set of states N = {0,1,2,3,4,5,6,7,8,9}, partitioned into four disjoint layers:

Interior (Cauldron)

Central cavity states modeling core identity

0, 1

Membrane

Inversion band where twist events occur

3, 8

Axis

Stabilization rails anchoring polarity

4, 7

Engine

Circulation ring supporting the 4-cycle

2, 5, 6, 9

Operators Overview

All behavior in the NUMO Field is generated by four fundamental operators:

δ
Dual-Node
Pairs digits where n + δ(n) = 11
μ
Mirror
Left-right reflection across polarity axis
C
Cauldron
Interior/exterior radial transition
L
Loop
4-cycle circulation on engine layer