Bibliographic record
Abstract
Algebraic simplification is the task of reducing an algebraic expression to a simpler form without changing the meaning of the expression. Simplification is generally a difficult task and may have different meanings according to what the subject considers as "simple" . This thesis starts off by reverse-engineering the concept of algebraic processors in the IMPS interactive mathematical proof system - which is responsible for handling all the algebraic simplification tasks - and discusses its algorithm and usage in detail. Then it explores the idea of algebraic processors as generic programs that can be configured for any type of algebraic structure to simplify expressions of that type by first formalizing the theory of algebraic processors of IMPS and then extending it to provide solutions for related topics. Algebraic processors can be defined for any user-defined algebra, as long as it conforms to the structure defined in this paper. The processors are defined as external units that can communicate with other mechanized mathematics systems in a trustable fashion and provide a program and a proof of correctness for any requests of simplification. Finally, some related processors such as one for simplification in partial orders and equivalence classes are outlined with some discussion of possible future expansions.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.007 | 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".