AN ALTERNATIVE PROOF OF MODIFIED-BOOTH RECODING ALGORITHM BASED ON NUMBER-DOMAIN TRANSFORMATIONS
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Bibliographic record
Abstract
In this letter, the nonredundant radix-4 representation of two's complement numbers is exploited to develop an alternative proof for the modified-Booth recoding algorithm. This proof is established by showing that the modified-Booth recoding algorithm essentially amounts to successive transformations of the number from its two's complement to its nonredundant radix-4 representation and from its nonredundant radix-4 to its modified radix-4 signed-digit representation. The salient feature of these transformations is that the digits in the resulting modified radix-4 signed-digit number take on values from the same balanced digit-set, placing in evidence the main principle and motivation behind the modified-Booth recoding algorithm.
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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 | 0.000 |
| 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 | 0.001 |
| 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