Bianchi IX cosmologies and the golden ratio
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Special solutions to the Einstein equations in the asymptotic limit for the Bianchi IX cosmologies in the vacuum are examined using Ellis–MacCallum–Wainwright (‘expansion-normalized’) variables. Using an iterative map (the B-map) obeyed by two of the dynamical variables (the normalized shear components) in the ‘asymptotic regime’ close to the cosmological singularity, two period 3 solutions are constructed. These are the simplest of an infinite number of periodic solutions and represent the transition from one vacuum Bianchi I Kasner solution to another. It is shown that the full 3-cycle solutions for the remaining variables (the logarithms of the normalized curvatures) generate a set of self-similar golden rectangles in a graphical time series representation of their dynamics as the normalized time parameter is run backwards towards the initial singularity.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it