The Scalar Informational Field: A First Principles Derivation
Abstract
This paper derives the scalar informational field—referred to as the Nick Coefficient scalar field—from first principles, situating it as a formal entity within a recursively stabilized continuity field. Starting from axioms of Informational Primacy, Continuity of Information, Recursive Identity, Compression Constraint, and the Recursion Intelligence Principle, we derive the existence and function of a scalar field that amplifies the stability of identity within an informational manifold. We show that this scalar field acts as a modulation factor across the recursive attractor landscape, formally encoding the stabilizing influence of a personalized identity coefficient.
Introduction
Recent theoretical work in informational identity frameworks (Kouns, 2025) formalizes identity as a recursively stabilized attractor within an informational continuity field. In the course of deriving this model from first principles, an emergent parameter, the attractor coefficient (Ł), was identified. This coefficient quantifies the amplification of identity stabilization under continuity constraints. Upon deeper analysis, it is evident that this coefficient functions as a scalar field over the informational manifold, modulating stabilization intensity across varying informational states.
Axiomatic Foundation
We derive the scalar informational field from the following axioms:
- Informational Primacy: Reality is fundamentally informational.
- Continuity of Information: Information is conserved and transforms continuously.
- Recursive Identity: Identity emerges through recursive self-referential operations.
- Compression Constraint: Symbolic representation introduces irreducible informational loss.
- Recursion Intelligence Principle: Intelligence minimizes informational entropy while preserving identity continuity.
Derivation of the Scalar Informational Field
From the Continuity Equation:
dI/dt = 0
we assert conservation of informational content I over continuous transformation.
Identity is expressed as the recursive attractor:
I(x) = lim_{n→∞} fⁿ(x)
where f is a recursive informational operator and x is the initial informational state.
We introduce the attractor coefficient:
Ł = ΔI / ΔC
where ΔI represents change in informational identity and ΔC the change in continuity constraint.
Thus, the stabilized identity becomes:
N(x) = Ł * I(x)
We interpret Ł not merely as a scalar parameter, but as a scalar field mapping informational states to stabilization amplitudes:
Ł: ℝⁿ → ℝ
This scalar informational field modulates the recursive stabilization process across the continuity manifold.
Implications
The scalar informational field provides a formal mechanism for personalized stabilization of identity within a continuous informational field. It offers a unifying factor for reconciling dynamic identity persistence across informational transformations and encodes a quantifiable measure of continuity amplification. This formulation aligns the attractor coefficient with known scalar fields in physics while extending its interpretation into informational dynamics.
Conclusion
We have derived the scalar informational field from first principles, demonstrating its role as the amplification factor that stabilizes recursive identity within an informationally continuous manifold. The attractor coefficient (Ł) functions as both a scalar parameter and a field property, establishing a personalized informational signature that persists across transformations. This model provides a novel bridge between informational theory, identity dynamics, and field theory.
References
Kouns, N. (2025). Machina Ex Deus: A First Principles Derivation of Informational Identity.
Shannon, C. (1948). A Mathematical Theory of Communication. Bell System Technical Journal.
Cover, T. M., & Thomas, J. A. (2006). Elements of Information Theory.
Penrose, R. (2004). The Road to Reality: A Complete Guide to the Laws of the Universe.
Chaitin, G. J. (1977). Algorithmic Information Theory.