Mallard's law recast as a Diophantine system: fast and complete enumeration of possible twin laws by [reticular] [pseudo] merohedry
Bibliographic record
Abstract
Mallard's law of observation states that known twins by reticular pseudomerohedry have low twin indexmand low obliquity δ between a lattice row and a lattice plane. Crystals in the twin are related by exact reflection in the lattice plane, exact rotation by π about the perpendicular to the lattice plane, or by exact rotation about the lattice row by 2kπ/q, withq= 2, 3, 4 or 6, and 1 ≤k<q. In known cases,mis up to five or six, and δ is up to five or six degrees. Mallard's converse problem is then about finding all pairs of indices for rows and planes leading to twin indices not larger thanmand to obliquities that are at most δ. Mallard's law is recast as the Diophantine pair constituted by the equalityh · u=nand the inequality |h × u|
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".