Bibliographic record
Abstract
<div class="abstract" data-abstract-type="normal"> In Hungarian Problem Book III, we covered a large number of theorems in basic mathematics. Not much else is needed to tackle the problems in the current volume. We list them again without further discussion, and add two sections on theorems not covered in the earlier volume. <span class='bold'>Theorems in Combinatorics</span> <span class='bold'>Principle of Mathematical Induction</span><span class='italic'>If S is a set of positive integers such that</span> 1 ∈ <span class='italic'>S, and n</span> + 1 ∈ <span class='italic'>S whenever n</span> ∈ <span class='italic'>S, then S is the set of all positive integers.</span> <span class='bold'>Well Ordering Principle</span><span class='italic'>Any non-empty set of positive integers has a minimum.</span> <span class='bold'>Extremal Value Principle</span><span class='italic'>Every non-empty finite set of real numbers has a maximum and a minimum.</span> <span class='bold'>Mean Value Principle</span><span class='italic'>In every non-empty finite set of real numbers, there is at least one which is not less than the arithmetic mean of the set, and at least one not greater.</span> <span class='bold'>Pigeonhole Principle</span><span class='italic'>Several pigeons are stuffed into several holes. If there are more pigeons than holes, then at least one hole contains at least two pigeons. If there are more holes than pigeons, then there is at least one empty hole.</span> <span class='bold'>Finite Union Principle</span><span class='italic'>The union of finitely many finite sets is also finite.</span> <span class='bold'>Parity Principle</span><span class='italic'>The sum of two even integers is even, the sum of two odd integers is also even, while the sum of an odd and an even integer is odd. Moreover, an odd integer can never be equal to an even integer.</span> <span class='bold'>Multiplication Principle</span> |<span class='italic'>A</span> × <span class='italic'>B</span>| = |<span class='italic'>A</span>| · |<span class='italic'>B</span>|. </div>
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.
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) | 0.000 | 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) | 0.009 | 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".