| _version_ | 1866901616108503040 |
|---|---|
| author | Okada, Masaki |
| author_facet | Okada, Masaki |
| contents | <p>Version v1.0 — Zenodo fixed release</p> <p>This work establishes a structural compression principle for linear cosmological growth observables derived from the second-order growth ODE. We show that, under growing-mode dominance and smooth parameter deformations, the observable data matrix formed from a smooth map O[D] is approximately rank-1, with variance concentration</p> <p>λ1 / Σ λi ≥ 1 − O(ε),</p> <p>where ε ≡ sup |Dd/Dg| quantifies the decaying-mode suppression.</p> <p>Using eigenvector perturbation theory, we derive a transport equation for the principal direction in observable space and demonstrate that its drift is background-locked to Ωm(zc). Numerically, sliding-window SVD confirms:</p> <p>- Global PC1 ≈ 99.9%<br>- Local PC1 > 99.96% in all windows<br>- Cumulative drift ≈ 12°<br>- Spearman ρ = 1.00 with Ωm(zc)</p> <p>These results indicate that low effective dimensionality in linear growth observables is not accidental but a structural consequence of the two-mode hierarchy of the growth ODE. The observable manifold is dynamically transported: locally rank-1, globally deformed, and geometrically constrained by cosmological background evolution.</p> <p>This record includes the manuscript PDF, input datasets, reproduction scripts, figure bundle, and SHA-256 checksums for full reproducibility.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18752081 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Structural Compression and Transport in Linear Growth Dynamics Okada, Masaki • cosmology • large-scale structure • linear growth • growth equation • dynamical systems • principal component analysis • singular value decomposition • spectral gap • transport equation • low-dimensional manifold • eigenvector perturbation • structural compression <p>Version v1.0 — Zenodo fixed release</p> <p>This work establishes a structural compression principle for linear cosmological growth observables derived from the second-order growth ODE. We show that, under growing-mode dominance and smooth parameter deformations, the observable data matrix formed from a smooth map O[D] is approximately rank-1, with variance concentration</p> <p>λ1 / Σ λi ≥ 1 − O(ε),</p> <p>where ε ≡ sup |Dd/Dg| quantifies the decaying-mode suppression.</p> <p>Using eigenvector perturbation theory, we derive a transport equation for the principal direction in observable space and demonstrate that its drift is background-locked to Ωm(zc). Numerically, sliding-window SVD confirms:</p> <p>- Global PC1 ≈ 99.9%<br>- Local PC1 > 99.96% in all windows<br>- Cumulative drift ≈ 12°<br>- Spearman ρ = 1.00 with Ωm(zc)</p> <p>These results indicate that low effective dimensionality in linear growth observables is not accidental but a structural consequence of the two-mode hierarchy of the growth ODE. The observable manifold is dynamically transported: locally rank-1, globally deformed, and geometrically constrained by cosmological background evolution.</p> <p>This record includes the manuscript PDF, input datasets, reproduction scripts, figure bundle, and SHA-256 checksums for full reproducibility.</p> |
| title | Structural Compression and Transport in Linear Growth Dynamics |
| topic | • cosmology • large-scale structure • linear growth • growth equation • dynamical systems • principal component analysis • singular value decomposition • spectral gap • transport equation • low-dimensional manifold • eigenvector perturbation • structural compression |
| url | https://doi.org/10.5281/zenodo.18752081 |