A Study on the Minimum and Maximum Sum of C2 Problem in IMO2014
Bibliographic record
Abstract
The focus of this paper is primarily on a problem: the principle of the extreme value under some special operations. After enumerating from the maximum sum to minimum and solving these cases, I found that the use of the two mathematical models enabled the derivation of the general form of the use of the two mathematical models enabled the derivation of the general form of the maximum and the minimum sum. This program looks into the principles of minimum and maximum sum, and the various patterns that come along with it. In order to further discuss this kind of problems, we set up other different conditions, solving them with two mathematical models and principle of sequence recursive relationship, induction proof, etc. We also extend all these problems to explore the generating functions of the maximum and the minimum sum with operating number m based on the parity of the number of papers. Finally, using computer generated software, we demonstrate the various sums of a particular state, along with coming up with a general rule for all states that can predict the maximum and the minimum sum through the usage of induction.
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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 | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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 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".