FACTORING FOR THE PLUGBOARD – WAS REJEWSKI'S PROPOSED SOLUTION FOR BREAKING THE ENIGMA FEASIBLE?
Why this work is in the frame
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Bibliographic record
Abstract
We prove a generalization of a theorem of Rejewski. This theorem shows how one can solve an equation of the form XY=α in a symmetric group, where α is a given permutation and X and Y are each of order two with a specified number of disjoint transpositions. The number of solutions is also part of the theorem. Using this theorem we outline what we believe was the Polish solution (or very close to it) to the Enigma assuming that one had no data from daily keys. With some assumptions on independence of events, we show that the Polish Cipher Bureau would probably have broken the Enigma in just over four years.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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