Why this work is in the frame
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Bibliographic record
Abstract
The main goal of this paper is to prove the Hanna Neumann Conjecture; in fact, we prove a strengthened form of the conjecture. We study these conjectures using what we have called “sheaves on graphs” in [Fri]. We show that both conjectures are implied by the vanishing of a certain invariant, the “maximum excess,” of certain sheaves that we call ρ-kernels. Our approach involves “graph Galois theory,” an analogue of classical Galois theory in the graph setting. We use it to construct the ρ-kernels. We use the symmetry in Galois theory to argue that if the Strengthened Hanna Neumann Conjecture is false, then the maximum excess of “most of” these ρ-kernels must be large. We then give an inductive argument to show that this is impossible.
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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 | 0.001 |
| Science and technology studies | 0.000 | 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