What question did this study set out to answer?

The aim is to establish a theoretical and computational framework for understanding negative phantom geometry in cosmology.

February 25, 2026Open Access

ψ-Phantom Geometry: Negative Retentional Echoes and the Keys of Furious Geometry

Key Points

The aim is to establish a theoretical and computational framework for understanding negative phantom geometry in cosmology.
Introduced subtractive retentional operators
Developed five Retentional Keys and a full taxonomy of phantoms
Established multi-epoch weak-lensing criteria
Formulated mathematical lemmas
Presented experimental protocol for detecting structural negativity in kappa maps
Defined both positive and negative phantoms
Demonstrated criteria for identifying structural negativity
Validated the Structural Skeleton Theorem
Laid groundwork for future experiments in cosmological observations

Abstract

A formal theoretical and computational framework for negative phantom geometry in ψ-Retention Cosmology, introducing subtractive retentional operators, the five Retentional Keys, a full taxonomy of positive and negative phantoms, multi-epoch weak-lensing criteria, mathematical lemmas, the Structural Skeleton Theorem, and the first experimental protocol for detecting structural negativity in cosmological kappa maps.

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