Correlation Bounds and #SAT Algorithms for Small Linear-Size Circuits.
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
We revisit the gate elimination method, generalize it to prove correlation bounds of boolean circuits with Parity, and also derive deterministic satisfiability counting algorithms for small linear-size circuits. Let B2 be the full binary basis, and let U2=B2{,}. We prove that, for circuits over U2 of size 3nn for any constant >0.5, the correlation with Parity is at most 2n(1), and there is a #SAT algorithm (which counts the number of satisfying assignments) running in time 2nn(1); for circuit size 3nn for >0, the correlation with Parity is at most 2(n), and there is a #SAT algorithm running in time 2n(n). Similar correlation bounds and algorithms are also proved for circuits over B2 of size almost 2.5n.
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 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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