Fixed Points V: Curvature Coupling, Multi-Structure Dynamics, and Admissibility Barriers

Corrected sixth edition. This paper formulates multi-structure covariance and admissibility diagnostics on the corrected Fixed Points I-IV spine. For a frozen stable linearization it derives the stationary covariance and Sylvester equations, an operator-normalized canonical-correlation bound, finite-grid and continuous-time Gaussian exit estimates for affine margin observables, and an exact deficit score for declared admissibility constraints. Scope boundary. Equal-time covariance and correlation do not determine causal propagation, localization, an exit-causing force, dynamics after exit, or selection of a post-exit basin.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-28
DOI
https://doi.org/10.5281/zenodo.21650468
Primary Topic
Control Systems and Identification
Type
preprint
Controls
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preprint

Fixed Points V: Curvature Coupling, Multi-Structure Dynamics, and Admissibility Barriers

Peter Nero
Zenodo (CERN European Organization for Nuclear Research)
Control Systems and Identification
preprint

Fixed Points V: Curvature Coupling, Multi-Structure Dynamics, and Admissibility Barriers

Peter Nero
preprint en

Abstract

Corrected sixth edition. This paper formulates multi-structure covariance and admissibility diagnostics on the corrected Fixed Points I-IV spine. For a frozen stable linearization it derives the stationary covariance and Sylvester equations, an operator-normalized canonical-correlation bound, finite-grid and continuous-time Gaussian exit estimates for affine margin observables, and an exact deficit score for declared admissibility constraints. Scope boundary. Equal-time covariance and correlation do not determine causal propagation, localization, an exit-causing force, dynamics after exit, or selection of a post-exit basin.

Zenodo (CERN European Organization for Nuclear Research)
Control Systems and Identification
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