Prologue: the ancient protagonists
Bibliographic record
Abstract
This introductory chapter provides a first glimpse at the principal characters of the book: Albert algebras and octonions, but also at other members of the families of Freudenthal and composition algebras. They are presented here in the familiar surroundings of the field of real numbers and over the integers. This has the advantage of following rather closely the historical development of the subject (stretching back into the nineteenth century), and of providing a first motivation for the study of quadratic Jordan algebras. Following Zorn (1933), we define the algebra of Graves–Cayley octonions, allowing us to view the Hamiltonian quaternions as an appropriate subalgebra. We describe in detail the Z-algebras of Hurwitz quaternions (1896) and of Dickson–Coxeter octonions (1923, 1946), which in turn give rise to our first encounter with Albert algebras over the integers.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.005 | 0.005 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.021 | 0.006 |
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 source (direct Gemma or distilled Codex), 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".