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
Throughout this paper, the word “circle” means a circle or a straight line. We are always assuming that the space R is equipped with a fixed “standard” Euclidean inner product. A collection of curves in R passing through 0 is said to be a simple bundle of curves if no two of them are tangent at 0. A simple bundle of curves is called rectifiable if there exists a germ of diffeomorphism in a neighborhood of the origin that sends all curves from this bundle to straight lines. Rectifiable bundles of curves appear, for example, in Riemannian geometry — the set of geodesics passing through a given point is rectifiable. A. G. Khovanskii proved in [1] that a rectifiable simple bundle of more than 6 circles on plane necessarily pass through some point different from the origin. F. A. Izadi [2] generalized Khovanskii’s arguments to dimension 3. A rectifiable simple bundle of circles in R containing sufficiently many circles in general position must pass through some other common point. In dimension 4, this is not true. The simplest counterexample is a family of circles that are obtained from straight lines by some complex projective transformation (with respect to some identification R = C such that the multiplication by i is an orthogonal operator). It turns out that in dimension 4 there is a large family of transformations that round lines (i.e., take them to circles). To construct such a family, fix a quaternionic structure on R compatible with the Euclidean structure. If A and B are some affine maps, then the map x 7→ A(x)−1B(x) rounds lines (the multiplication and the inverse are in the sense of quaternions). Such transformations will be called (left) quaternionic fractional transformations. Right quaternionic fractional transformations AB−1 also round ∗Partially supported by RFBR 99-01-00245 and CRDF RM1-2086
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 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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