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Record W4412882236 · doi:10.1180/mgm.2025.10109

Components, end-members and mineral species

2025· article· en· W4412882236 on OpenAlex
F. C. Hawthorne

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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueMineralogical Magazine · 2025
Typearticle
Languageen
FieldMaterials Science
TopicX-ray Diffraction in Crystallography
Canadian institutionsUniversity of Manitoba
FundersUniversity of Cambridge
KeywordsMineralGeologyGeochemistryEnvironmental scienceChemistryBiologyEcology

Abstract

fetched live from OpenAlex

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Bench or experimental · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.943
Threshold uncertainty score0.996

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0050.000

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.

Opus teacher head0.020
GPT teacher head0.252
Teacher spread0.232 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it