What question did this study set out to answer?

To establish the first invariant equation relating coupling geometry to structural limits in physical systems.

March 23, 2026Open Access

The Floor That Never Reaches Zero: IE-001 and the Structural Minimum of Coupling Geometry

Key Points

To establish the first invariant equation relating coupling geometry to structural limits in physical systems.
Developed the invariant equation IE-001: alpha(d,beta) = 1 + d/(d+beta)
Analyzed the bounds of coupling for positive values of d and beta
Explored the implications of structural and geometric limitations in systems.
Demonstrated that coupling is always bounded between 1 and 2
Proved that the 'floor' at alpha=1 is structural, not emergent
Established that the asymptote at alpha=2 is unattainable, indicating systems can never be fully decoupled from geometry.

Abstract

Establishes IE-001: the first invariant equation proving that alpha(d,beta) = 1 + d/(d+beta) bounds coupling to 1 < alpha < 2 for all positive d and beta. The floor at alpha=1 is structural not emergent; the asymptote at alpha=2 is unattainable. No system is ever fully decoupled from its geometric context. Mathematical foundations with five-domain physical interpretation. GCT Letters series.

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James E. Dunn

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Directorate-General for Interpretation

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The Floor That Never Reaches Zero: IE-001 and the Structural Minimum of Coupling Geometry

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Abstract

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