The Use of the Partitioning Theorem to Prove Further Results Regarding the Distribution of IRRs: And an Open Question
Bibliographic record
Abstract
In 2018, Cuthbert proved that any transaction vector can be uniquely partitioned into a sequence of pure investments with strictly decreasing internal rates of return (IRRs). In a subsequent paper, Cuthbert used the partitioning theorem to derive a new sufficient condition for a transaction to have a unique IRR and proved some results regarding how the IRRs of a transaction must be distributed. This paper proves some further results on the distribution of IRRs. It also poses an open question regarding the possible relationship between the number of IRRs of a transaction and the relative sizes of the smallest and largest IRRs of the terms in the unique partition of that transaction.
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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 | 0.009 | 0.055 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.005 | 0.020 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.010 | 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".