Proving arithmetic functions over gaussian integer rings with applications to Saskatchewan prairie wheat yields
Bibliographic record
Abstract
Arithmetic functions defined on the Gaussian integers Z[i] encode structural information that standard integer arithmetic misses entirely. This research proved a set of extension theorems for multiplicative and additive arithmetic functions over Gaussian integer rings, then applied the resulting algebraic framework to model wheat yield variability across Saskatchewan’s prairie crop districts. Daily weather data, soil moisture readings, and harvest records from five crop districts covering the 2018-2023 growing seasons were mapped onto Gaussian integer norms, with the real part encoding thermal accumulation and the imaginary part encoding precipitation deficit. A Gibbs sampling scheme estimated posterior distributions for the norm-yield regression coefficients, and a variogram analysis quantified spatial correlation among district-level residuals. The Gaussian-integer model explained 86.7% of yield variance, compared with 78.4% for a conventional real-valued regression. Prediction errors were distributed symmetrically around zero in all five districts, with median absolute errors between 0.09 and 0.17 tonnes per hectare. Zero-sum game theory was used to allocate limited crop insurance resources across districts under worst-case yield scenarios. The results show that embedding agronomic data into Gaussian integer rings captures interaction effects between heat and moisture that real-valued models treat as separable.
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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 | 0.004 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".