Bibliographic record
Abstract
This paper introduces a novel theoretical framework for representing the internal structure of numeral systems. This framework is based on labels and reading conventions for the entries and columns of an abacus, which suffice to describe numeral systems in a systematic way (including ones that have sub-bases or are irregular). The abacus represents, for example, a decimal place-value numeral with columns of equal height (labelled from 0 (empty) to 9) by reading the label of the greatest filled entry in each column; and a Roman numeral with columns of different heights (1 and 4), repeating the label of each column as many times as it is filled. Owing to its uniform and abstract character, this abacus representation allows for the structural comparison of numeral systems across different representational formats (such as notational, verbal and body-based formats) and for the discussion of various irregularities of such systems.This article is part of the theme issue 'A solid base for scaling up: the structure of numeration systems'.
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.
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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.006 | 0.008 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.020 | 0.005 |
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".