Constrained growth of complex scale-independent systems
Bibliographic record
Abstract
Scale independence is a ubiquitous feature of complex systems that implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution, and stock actions all feature scale independence. Assuming that they simply do, we focus here on describing how this behavior emerges, in contrast to more idealized models usually considered. We arrive at the conjecture that a minimal model to explain the growth toward scale independence involves only two coupled dynamical features: the first is the well-known preferential attachment principle, and the second is a general form of delayed temporal scaling. While the first is sufficient, the second is present in all studied data and appears to maximize the speed of convergence to true scale independence. The delay in this temporal scaling acts as a coupling between population growth and individual activity. Together, these two dynamical properties appear to pave a precise evolution path, such that even an instantaneous snapshot of a distribution is enough to reconstruct the past of the system and predict its future. We validate our approach and confirm its usefulness in diverse spheres of human activities, ranging from scientific and artistic productivity to sexual relations and online traffic.
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How this classification was reachedexpand
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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".