What question did this study set out to answer?

The research aims to redefine habitability through a geometric coupling theory framework.

March 23, 2026Open Access

The Goldilocks Geometry: Planetary Habitability as a Coupling Regime Boundary

Key Points

The research aims to redefine habitability through a geometric coupling theory framework.
Used geometric coupling theory (GCT) to analyze planetary habitability.
Identified convergence invariant and sign-flip threshold conditions.
Examined Earth's ozone layer as a selective permeability membrane.
Classified Venus and Mars based on their positions relative to the coupling thresholds.
Established that Earth's ozone layer plays a crucial role in UV protection and planetary habitability.
Found that Venus exists beyond the sign-flip boundary, suggesting inhospitable conditions.
Confirmed Mars is situated below the habitability coupling threshold, indicating a lack of suitable conditions.

Abstract

Reframes the habitable zone concept through GCT. Habitability is determined by a system's position on the coupling surface relative to the convergence invariant (alpha=1.920) and sign-flip threshold (alpha=2.000). Four geometric channels — information, surface area, proximity, permeability — must simultaneously satisfy convergence conditions. Earth's ozone layer is identified as a zona pellucida: selective permeability membrane gating UV coupling. Venus represents a system past the sign-flip boundary; Mars lies below the coupling threshold. Extends GCT from nuclear physics through geophysics to planetary science.

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