Bibliographic record
Abstract
Alice said to the twins, “Instead of passing the day rattling each other's bones, why don't you get some gainful employment? I have just imported some apples and bananas into Wonderland. Each kind of fruit comes in boxes each of which holds exactly the same number, apples or bananas. I do not remember how many there are in each box, but it is more than 1. I do know that there are 289 apples and 221 bananas in the boxes.” “We will give it a try,” said Tweedledum doubtfully. “I will sell apples and my twin brother will sell bananas.” “We need to know how many fruit there are in each box,” said Tweedledee. “Well, see if you can figure that out before I come back,” said Alice. “Perhaps until you do, you should just sell whole boxes of fruit.” “That is a good idea,” said the twins together. The Duchess's Cook came in shortly after Alice took off, went to Tweedledum and said, “I see that you have more boxes of apples than Tweedledee has boxes of bananas. I want to buy as many boxes of apples as he has boxes of bananas.” Tweedledum made the sale, and recorded that now he had 289 − 221 = 68 apples left. The next three to come were the Dormouse, the March Hare and the Mad Hatter. Each of them bought as many boxes of bananas from Tweedledee as Tweedledum had boxes of apples. Tweedledee recorded that now he had 221 − 68 − 68 − 68 = 17 bananas left. The next four customers were the Two, the Five, the Seven and the Knave of Hearts. Each bought as many boxes of apples from Tweedledum as Tweedledee had boxes of bananas. Now Tweedledum had no apples left. Tweedledee said, “I still have 17 bananas left.” “They are still inside unopened boxes because neither of us had opened one at any time. This means that the number of bananas in each box is a divisor of 17.” “The only divisors of 17 are 1 and 17,” said Tweedledee. “Since Alice told us the number of bananas in each box is not 1, it must be 17.” “Let me check,” said Tweedledum. “We have 221 ÷ 17 = 13 and we have 289 ÷ 17 = 17. So 17 indeed divides both 221 and 289.”
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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 | 0.004 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.005 | 0.011 |
| Scholarly communication | 0.006 | 0.013 |
| Open science | 0.001 | 0.006 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.033 | 0.005 |
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".