Geometric local systems on the projective line minus four points
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Let J ( m ) be an $m\times m$ Jordan block with eigenvalue 1. For $\lambda\in\mathbb{C}\setminus\{0,1\}$ , we explicitly construct all rank 2 local systems of geometric origin on $\mathbb{P}^1\setminus\{0,1,\lambda,\infty\}$ , with local monodromy conjugate to J (2) at $0,1,\lambda$ and conjugate to $-J(2)$ at $\infty$ . The construction relies crucially on Katz’s middle convolution operation. We use our construction to prove two conjectures of Sun, Yang and Zuo (one of which was proven earlier by Lin, Sheng and Wang; the other was proven independently of us by Yang and Zuo) coming from the theory of Higgs–de Rham flows, as well as a special case of the periodic Higgs conjecture of Krishnamoorthy and Sheng.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.000 | 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