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This research formulates the dm³ Criticality Principle, focusing on curvature and generative dynamics in three dimensions.

May 20, 2026Open Access

The dm³ Criticality Principle: Curvature, Generative Dynamics, and the Dimension Three Spine

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Randomized trial demonstrates generative dynamics in dimension three, suggesting critical thresholds for control.

This research formulates the dm³ Criticality Principle, focusing on curvature and generative dynamics in three dimensions.
Formulated dm³ Criticality Principle with curvature coefficient set to 3.
Analyzed operators C → K → F → U within various mathematical contexts.
Conducted numerical work on discrete nonlinear Schrödinger (DNLS) equations related to Fibonacci and Tribonacci chains.
Tribonacci chain exhibits ~4× mid-gap inverse-participation-ratio (IPR) over Fibonacci chain in the linear limit.
Tribonacci mid-gap state remains stable under nonlinear perturbation with <5% IPR drop at λ = 1.5, T = 50.
Identified critical-coupling behavior and nontrivial results in the context of discrete nonlinear systems.

Pablo Nogueira Grossi (2026) studied this question.

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