Bibliographic record
Abstract
In 1956, Shell Oil Company geologist M. King Hubbert published a model for the growth and decline over time of the production rates of oil extracted from the land mass of the continental US. Employing an estimate for the amount of ultimately recoverable oil and a logistic curve for the oil production rate, he accurately predicted a peak in US oil production for 1970. His arguments and the success of his prediction have been much celebrated, and the original paper has 1400 publication citations to date. The theory of “peak oil” (and subsequently, of natural resource scarcity in general) has consequently become associated with Hubbert and “Hubbert” curves and models. However, his prediction for the timing of a world peak oil production rate and the subsequent predictions of many others have proven inaccurate. We revisit the Hubbert model for oil extraction and provide an analysis of it and several variants in the language of (time) autonomous differential equations.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.005 | 0.005 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".