Topological Iwasawa invariants and arithmetic statistics
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
Given a prime number p , we study topological analogues of Iwasawa invariants associated to \mathbb{Z}_p -covers of the 3 -sphere that are branched along a link. We prove explicit criteria to detect these Iwasawa invariants, and apply them to the study of links consisting of 2 component knots. Fixing the prime p , we prove statistical results for the average behaviour of p -primary Iwasawa invariants for 2 -bridge links that are in Schubert normal form. Our main result, which is entirely unconditional, shows that the density of 2 -bridge links for which the \mu -invariant vanishes, and the \lambda -invariant is equal to 1 , is (1-\frac{1}{p}) . We also conjecture that the density of 2 -bridge links for which the \mu -invariant vanishes is 1 , and this is significantly backed by computational evidence. Our results are proven in a topological setting, yet have arithmetic significance, as we set out new directions in arithmetic statistics and arithmetic topology.
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 | 0.000 | 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 | 0.002 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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