MAGIC MOORE-PENROSE INVERSES AND PHILATELIC MAGIC SQUARES WITH SPECIAL EMPHASIS ON THE DANIELS–ZLOBEC MAGIC SQUARE
Bibliographic record
Abstract
We study singular magic matrices in which the numbers in the rows and columns and in the two main diagonals all add up to the same sum.Our interest focuses on such magic matrices for which the Moore-Penrose inverse is also magic.Special attention is given to the "Daniels-Zlobec magic square'' introduced by the British magician and television performer Paul Daniels (b.1938) and considered by Zlobec (2001); see also Murray (1989, pp.30-32).We introduce the concept of a "philatelic magic square" as a square arrangement of images of postage stamps so that the associated nominal values form a magic square.Three philatelic magic squares with stamps especially chosen for Sanjo Zlobec are presented in celebration of his 70 th birthday; most helpful in identifying these stamps was an Excel checklist by Mnnikk (2009).
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How this classification was reachedexpand
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 | 0.001 | 0.002 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.011 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".