Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The final step of some algebraic algorithms is to reconstruct the common denominator d of a collection of rational numbers (ni/d)1≤ i≤ n from their images (ai)1≤ i≤ n mod M, subject to a condition such as 0 < d ≤ N and Ni}≤ N for a given magnitude bound N. Applying elementwise rational number reconstruction requires that M ∈ Ω(N2). Using the gradual sublattice reduction algorithm of van Hoeij and Novocin, we show how to perform the reconstruction efficiently even when the modulus satisfies a considerably smaller magnitude bound M ∈ Ω(N1+1/c) for c a small constant, for example 2 ≤ c ≤ 5. Assuming c ∈ O(1) the cost of the approach is O(n(log M)3) bit operations using the original LLL lattice reduction algorithm, but is reduced to O(n(log M)2) bit operations by incorporating the L2 variant of Nguyen and Stehle. As an application, we give a robust method for reconstructing the rational solution vector of a linear system from its image, such as obtained by a solver using p-adic lifting.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
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