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
We consider crossbar switching networks with base b (that is, constructed from $b\times b$ crossbar switches), scale k (that is, with $b^k$ inputs, $b^k$ outputs, and $b^k$ links between each consecutive pair of stages), and depth l (that is, with l stages). We assume that the crossbars are interconnected according to the spider-web pattern, whereby two diverging paths reconverge only after at least k stages. We assume that each vertex is independently idle with probability q, the vacancy probability. We assume that $b\ge2$ and the vacancy probability q are fixed, and that k and $l=ck$ tend to infinity with ratio a fixed constant $c > 1$. We consider the linking probability Q (the probability that there exists at least one idle path between a given idle input and a given idle output). In a previous paper [Discrete Appl. Math., 37/38 (1992), pp. 437-450] it was shown that if $c\le2$, then the linking probability Q tends to 0 if $0 < q < q_c$ (where $q_c=1/b^{(c-1)/c}$ is the critical vacancy probability) and tends to $(1-\xi)^2$ (where $\xi$ is the unique solution of the equation $\bigl(1-q(1-x)\bigr)^b=x$ in the range $0 < x < 1$) if $q_c < q < 1$. In this paper we extend this result to all rational $c > 1$. This is done by using generating functions and complex-variable techniques to estimate the second moments of various random variables involved in the analysis of the networks.
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 | 0.002 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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