What question did this study set out to answer?

The aim is to create a framework that separates two limits of observability in reduced inverse geometry.

June 3, 2026Open Access

Structural Walls and Observable Horizons in Reduced Inverse Geometry

Key Points

The aim is to create a framework that separates two limits of observability in reduced inverse geometry.
Formulates a reduced inverse-geometric framework to define structural walls and observable horizons.
Proves covariance whitening deforms operational Fisher geometry while keeping structural rank intact.
Builds a two-domain dictionary linking reduced dynamical-decoupling spectroscopy and reheating reconstruction.
Introduces the concept of structural walls defined by rank loss of the reduced Jacobian.
Establishes that the rank of the covariance-adjusted Jacobian equals that of the original Jacobian.
Creates a connection between different methodologies in cosmology, aiding in the understanding of observability.

Abstract

This initial draft formulates a reduced inverse-geometric framework separating two distinct limits of observability: structural walls, defined by rank loss of the reduced Jacobian, and observable horizons, defined by covariance-dependent Fisher-threshold suppression. The paper proves that covariance whitening deforms the operational Fisher geometry while preserving the structural rank stratification, rank (Σ^-1/2J) =rank (J). It then uses this distinction to build a two-domain dictionary connecting reduced dynamical-decoupling spectroscopy and reheating reconstruction in cosmology. The work is intended as a bridge/framework paper rather than a comprehensive review of the model-specific results in the separate ratio-map, DD, reheating, formulation-switching, and cusp/swallowtail precursor papers.

Structural Walls and Observable Horizons in Reduced Inverse Geometry

Key Points

Abstract

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