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
A k -uniform, d -regular instance of EXACT COVER is a family of m sets F_{n,d,k} = \{ S_j \subseteq \{1,\ldots,n\} \} , where each subset has size k and each 1 \le i \le n is contained in d of the S_j . It is satisfiable if there is a subset T \subseteq \{1,\ldots,n\} such that |T \cap S_j|=1 for all j . Alternately, we can consider it a d -regular instance of POSITIVE 1-IN- k SAT, i.e., a Boolean formula with m clauses and n variables where each clause contains k variables and demands that exactly one of them is true. We determine the satisfiability threshold for random instances of this type with k > 2 . Letting d^\star = \frac{\ln k}{(k-1)(- \ln (1-1/k))} + 1 \, , we show that F_{n,d,k} is satisfiable with high probability if d < d^\star and unsatisfiable with high probability if d > d^\star . We do this with a simple application of the first and second moment methods, boosting the probability of satisfiability below d^\star to 1-o(1) using the small subgraph conditioning method.
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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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