End-to-end distance from the Green’s function for a hierarchical self-avoiding walk in four dimensions
Why this work is in the frame
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Bibliographic record
Abstract
In [BEI92] we introduced a Levy process on a hierarchical lattice which is four 1 dimensional, in the sense that the Green’s function for the process equals |x | 2. If the process is modified so as to be weakly self-repelling, it was shown that at the critical killing rate (mass-squared) βc, the Green’s function behaves like the free one. Now we analyze the end-to-end distance of the model and show that its expected value grows as a constant times √ T log 1 8 T 1 + O, which is log log T log T the same law as has been conjectured for self-avoiding walks on the simple cubic lattice Z 4. The proof uses inverse Laplace transforms to obtain the end-to-end distance from the Green’s function, and requires detailed properties of the Green’s function throughout a sector of the complex β plane. These estimates are derived in a companion paper [BI02]. Research supported by NSF Grant DMS-9706166Contents
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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 | 0.002 |
| 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) | 0.000 | 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