⚠️ Status Notice

Psi–Continuum Cosmology v5 represents the archived background-level formulation of the macroscopic state–space framework.

The results and diagnostics presented in v5 remain fully reproducible and internally consistent within the adopted fixed reference background.

Version v5 does not include nuisance-parameter marginalization or extended statistical inference procedures. Its purpose is strictly diagnostic: to organize late-time expansion data within a macroscopic state–space description relative to a chosen ΛCDM baseline.

Subsequent developments will address extended statistical treatments and broader parameter handling as standalone methodological studies.

Psi–Continuum State-Space Diagnostics (v5)

A lightweight, reproducible diagnostic package for macroscopic state–space analysis of late–time cosmic expansion.

📦 Software package

• PyPI: psi-continuum-statespace
• Source code: github.com/dmitrylife/psi-continuum-statespace

📄 Scientific reference

This page documents the diagnostic software companion to the article:

Psi–Continuum Cosmology v5
A Macroscopic State–Space Response Framework for Late–Time Cosmic Expansion

• Preprint (Zenodo DOI):
  https://doi.org/10.5281/zenodo.18088720

Purpose

The psi-continuum-statespace package provides a purely diagnostic, background–level implementation of the macroscopic state–space framework introduced in Psi–Continuum Cosmology v5.

Install directly from PyPI:

pip install psi-continuum-statespace

Example usage (interactive shell):

psi-statespace interactive

The software is designed to:

• construct the macroscopic state–space coordinate Ψ(z),
• visualize state–space trajectories derived from background expansion histories,
• assess the internal consistency of independent late–time observational datasets.

The package does not introduce new cosmological models, does not modify gravitational dynamics, and does not perform parameter estimation.

Conceptual scope

The state–space framework implemented here is:

• macroscopic — formulated at the background level,
• diagnostic — descriptive rather than predictive,
• model–independent — defined via ratios of expansion histories,
• reproducible — fully determined by frozen background APIs.

Within this formulation:

• ΛCDM appears as the instantaneous–response limit in state space,
• late–time acceleration corresponds to small, smooth deformations organized as trajectories in Ψ(z).

Clarifications

Technical clarifications:
Additional explanations regarding reference background, parameter fixing, and normalization conventions are available
here.

Relation to Psi–Continuum v2

This package relies on the frozen background–level API of Psi–Continuum Cosmology v2 for computing reference expansion histories.

No modifications to the v2 implementation are introduced.

The v5 framework should be understood as a macroscopic reinterpretation of late–time background information, not as an extension of the underlying cosmological model.

Reproducibility

All figures and diagnostics presented in the v5 article are reproducible using the public release of this package.

The figures included in the publication are provided separately in the publication/ directory of the repository for reference.

Intended audience

This software is intended for:

• researchers in observational and phenomenological cosmology,
• readers of Psi–Continuum Cosmology v5,
• users interested in alternative organizational languages for late–time expansion data.

It is not intended as a general–purpose cosmological analysis pipeline.

Citation

If you use this diagnostic framework or reproduce results from the article, please cite:

Dmitry V. Klimov (2025).
Psi–Continuum Cosmology v5:
A Macroscopic State–Space Response Framework for Late–Time Cosmic Expansion.
Zenodo. https://doi.org/10.5281/zenodo.18088720