Bibliographic record
Abstract
Abstract I consider the conditions for defining a mineral by its dominant end-member formula. One can calculate the end-member proportions of the end-members of a mineral provided that the end-members are linearly independent (i.e. they are phase components of the mineral); the result includes the dominant end-member of the mineral. If the end-members used in this calculation are not linearly independent, the corresponding set of simultaneous equations is indeterminate. One may remove an end-member from the system, removing the linear dependence; however, any end-member formula may be removed, leaving various sets of end-members that function as phase components. Each set of end-members produces a different solution for the end-member proportions. Each set of positive end-member proportions may (or may not) result in a different dominant end-member; however, within the compositional limits of the species, the same end-member is dominant over all others calculated with different combinations of component end-members. Problems previously encountered in attempting to calculate the dominant end-member formula were due to (1) using mineral formulae that do not accord with the requirements of stoichiometry, and (2) using end-members that are not components of the system. Where the set of end-members chosen to relate mineral composition to end-member proportions contains an end-member that is a linear combination of the other end-members, one must calculate the end-member proportions for all distinct subsets of linearly independent end-members. The dominant end-member over all sets of end-member proportions with all proportions positive is the dominant end-member. Thus for any mineral formula, the dominant end-member formula may be identified and serves to uniquely characterize and identify the mineral. The arguments used here are illustrated by reference to the minerals of the garnet supergroup.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.010 | 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".