Randomness Measurements and <i>m</i>-Sequences
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
Randomness of a sequence refers to the unpredictablity of the sequence. Any deterministically generated sequence used in practical applications is not truly random. The best that can be done here is to single out certain properties as being associated with randomness and to accept any sequence that has these properties as random or more properly, a pseudorandom sequence. In this chapter, we will discuss the randomness of sequences whose elements are taken from a finite field. In Section 5.1, we present Golomb's three randomness postulates for binary sequences, namely the balance property, the run property, and the (ideal) two-level autocorrelation property, and the extension of these randomness postulates to nonbinary sequences. M-sequences over a finite field possess many extraordinary randomness properties except for having the lowest possible linear span, which has stimulated researchers to seek nonlinear sequences with similarly such favorable properties for years. In Section 5.2, we show that m-sequences satisfy Golomb's three randomness postulates. In Section 5.3, we introduce the interleaved structures of m-sequences and the subfield decomposition of m-sequences. In Sections 5.4–5.6, we present the shift-and-add property, constant-on-cosets property, and 2-tuple balance property of m-sequences, respectively. The last section is devoted to the classification of binary sequences of period 2n − 1.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.002 |
| 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