| _version_ | 1866901826277736448 |
|---|---|
| author | Schutza, Aaron Moore |
| author_facet | Schutza, Aaron Moore |
| contents | <p>The Feigenbaum constant δ ≈ 4.6692016, representing the universal scaling of period-<br>doubling bifurcations, has traditionally been viewed as a purely numerical property of one-<br>dimensional maps. We present a rigorous physical derivation of this constant within the<br>Axiomatic Physical Homeostasis (APH) framework. We demonstrate that δ repre-<br>sents the Dimensional Compression Ratio of the vacuum geometry as it undergoes a<br>phase transition from the non-associative bulk (G2) to the stable associative cycle (S3).<br>By accounting for the topological leakage of information mediated by the fine structure<br>constant α and the Euler characteristic of the manifold (χ = 24), we derive an exact closed-<br>form expression for δ. This geometric prediction matches the standard numerical value to<br>eight decimal places, suggesting that chaos is a signature of the topological decay of the G2<br>vacuum.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18243896 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | An Exact Analytic Derivation of the Feigenbaum Constant δ via the Octonionic G2 Manifold Schutza, Aaron Moore <p>The Feigenbaum constant δ ≈ 4.6692016, representing the universal scaling of period-<br>doubling bifurcations, has traditionally been viewed as a purely numerical property of one-<br>dimensional maps. We present a rigorous physical derivation of this constant within the<br>Axiomatic Physical Homeostasis (APH) framework. We demonstrate that δ repre-<br>sents the Dimensional Compression Ratio of the vacuum geometry as it undergoes a<br>phase transition from the non-associative bulk (G2) to the stable associative cycle (S3).<br>By accounting for the topological leakage of information mediated by the fine structure<br>constant α and the Euler characteristic of the manifold (χ = 24), we derive an exact closed-<br>form expression for δ. This geometric prediction matches the standard numerical value to<br>eight decimal places, suggesting that chaos is a signature of the topological decay of the G2<br>vacuum.</p> |
| title | An Exact Analytic Derivation of the Feigenbaum Constant δ via the Octonionic G2 Manifold |
| url | https://doi.org/10.5281/zenodo.18243896 |