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Extrinsic Quaternion Spin

2023· preprint· en· W4362482834 on OpenAlex

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

VenuePreprints.org · 2023
Typepreprint
Languageen
FieldMathematics
TopicAlgebraic and Geometric Analysis
Canadian institutionsMcGill University
FundersÉcole Polytechnique Fédérale de Lausanne
KeywordsQuaternionHelicitySpin (aerodynamics)Dirac equationCoherence (philosophical gambling strategy)Symmetry (geometry)Mathematical physicsPhysicsClifford algebraMathematicsAlgebra over a fieldQuantum mechanicsPure mathematicsGeometry

Abstract

fetched live from OpenAlex

We present an analysis of the Dirac equation when the spin symmetry is changed from SU(2) to the quaternion group, $Q_8$, afforded by multiplying one of the $\gamma$-matrices by the imaginary number $i$. The reason for doing this is to introduce a bivector into the spin algebra. The resulting spin equation separates into distinct and complementary spaces, one describing polarization and the other coherence. The former describes a 2D structured spin and the latter its helicity, generated by a unit quaternion. We discuss some consequences.

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)0.002
metaresearch head score (Gemma)0.003
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Observational · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.628
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.003
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0010.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.004
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0030.019

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 head0.340
GPT teacher head0.422
Teacher spread0.082 · 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