A Generalized Hyperbolic Decline Equation with Rate-Time Dependent Function
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract Nearly all the decline curve equations used today are based on the Arps hyperbolic equation1, given as: Using this equation, the production rate ‘Q’ at anytime ‘t’ can be calculated from the hyperbolic exponent ‘b’, the initial production rate ‘Q0’ and its corresponding decline rate ‘D0’ at time zero. Although Equation (1) is easy to use, the variation of the decline rate with time (except b = 0) limits the applicability of the equation. For a hyperbolic decline curve (b>0), if a different production rate ‘Qi’ on the curve is used an initial rate, a different corresponding decline rate ‘Di’ needs to be identified for the equation to represent the same decline curve. Moreover, if there is a rate or reference time change in the production forecast period, the identified hyperbolic equation from the production history is no longer applicable. (1) Q(t)=Q 0 × (1+b × D 0 × t) − 1 / b In this paper, a generalized hyperbolic equation is derived to overcome the above limitations. Once a set of ‘Q0’, ‘D0’ and ‘b’ is identified from the production history, the equation can be used to predict the future rate regardless of the initial rate or time change.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.000 |
| 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