Bibliographic record
Abstract
The object of this chapter is to describe the structure of maximal bifix codes. This family of codes has quite remarkable properties and can be described in a rather satisfactory manner. As in the rest of this book, we will work here within the family of thin codes. As we will see, this family contains all the usual examples, and most of the fundamental properties extend to this family when they hold in the simple (that is, finite or recognizable) case. To each thin maximal bifix code, two basic parameters will be associated: its degree and its kernel . The degree is a positive integer which is, as we will see in Chapter 9, the degree of a permutation group associated with the code. The kernel is the set of codewords which are proper factors of some codeword. We shall prove that these two parameters characterize a thin maximal bifix code. In the first section, we introduce the notion of a parse of a word with respect to a bifix code. It allows us to define an integer-valued function called the indicator of a bifix code. This function will be quite useful in this and later chapters. In the second section, we give a series of equivalent conditions for a thin code to be maximal bifix. The fact that thin maximal bifix codes are extremal objects is reflected in the observation that a subset of their properties suffices to characterize them completely. We also give a transformation (called internal transformation ) which preserves the family of maximal bifix codes.
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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 | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.015 | 0.004 |
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".