Minimality and other properties of the width-𝑤 nonadjacent form
Bibliographic record
Abstract
Let w ≥ 2 w \geq 2 be an integer and let D w D_w be the set of integers that includes zero and the odd integers with absolute value less than 2 w − 1 2^{w-1} . Every integer n n can be represented as a finite sum of the form n = ∑ a i 2 i n = \sum a_i 2^i , with a i ∈ D w a_i \in D_w , such that of any w w consecutive a i a_i ’s at most one is nonzero. Such representations are called width- w w nonadjacent forms ( w w -NAFs). When w = 2 w=2 these representations use the digits { 0 , ± 1 } \{0,\pm 1\} and coincide with the well-known nonadjacent forms . Width- w w nonadjacent forms are useful in efficiently implementing elliptic curve arithmetic for cryptographic applications. We provide some new results on the
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.017 | 0.004 |
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".