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
Venn diagrams are a graphical way to represent a set system. Each of the n sets is represented by a simple closed curve. The n curves subdivide the plane into 2^n open connected regions, each of which represents the intersection of its containing curves' sets. For example, two overlapping circles can divide the plane into 4 regions representing {}, A, B, and A intersect B. Three overlapping circles can also be used to represent the 2^3 ways in which 3 sets can intersect. One of the primary questions related to Venn diagrams concerns which shapes can be used for the curves. The previous examples used 2 and 3 circles, but a 4-set Venn diagram cannot be represented by 4 circles; instead, ellipses must be used. In this paper, we consider Venn diagrams whose curves are the outlines of polyominoes. In particular, we give examples of Venn diagrams where the curves are rotations and translations of a single polyomino, so-called congruent polyVenn diagrams. We also consider the problem of area-minimization (relative to a scaling factor) and present examples of Venn polyominoes which minimize area according to various constraints. At present, these examples do not generalize and so we develop an algorithm that comes close to minimizing the area. The algorithm is simple and utilizes symmetric chain decompositions of the Boolean lattice. We also provide asymptotic results that relate the area required by the algorithm's diagrams to the theoretical minimum area. We conclude by presenting some open problems related to Venn polyominoes and other shape-constrained Venn diagrams.
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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.000 | 0.001 |
| 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