Why this work is in the frame
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Bibliographic record
Abstract
Consider the integer sequences () and , letting [x] denote the integer part of a nonnegative value x, and where Fn denotes the nth Fibonacci number for a nonnegative integer n. We apply an Abel-type summation lemma to prove explicit evaluations for and for a natural number m. We then apply this summation lemma to determine an analytical formula for , letting s denote a natural number parameter, and we demonstrate how our method may be applied to evaluate sums of the form for integers r ≥ 2 and s ≥ 1. We also consider the problem of evaluating finite sums of expressions of the form for a natural number s. Much of our work is closely connected with evaluations for Fibonacci sums of the form , where t is a nonnegative integer.
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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 | 0.000 | 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) | 0.001 | 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