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Record W2594898845 · doi:10.1145/3055282.3055289

The bohemian eigenvalue project

2017· article· en· W2594898845 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

VenueACM communications in computer algebra · 2017
Typearticle
Languageen
FieldMathematics
TopicRandom Matrices and Applications
Canadian institutionsWestern University
Fundersnot available
KeywordsEigenvalues and eigenvectorsBounded functionCardinality (data modeling)MathematicsUniversality (dynamical systems)CombinatoricsDimension (graph theory)Integer (computer science)Computer scienceMathematical analysisPhysics

Abstract

fetched live from OpenAlex

Bohemian eigenvalues are the eigenvalues of matrices with entries of bounded height, typically drawn from a discrete set. We will call this set F with cardinality #F . The name "Bohemian" is intended as a mnemonic and is derived from "bounded height integer matrices." These objects are surprisingly interesting to study, with many unsolved problems related to them, and with many applications. See the works of Tao and Vu [10] for universality results for larger dimension in the generic structured case, for instance. This project concentrates on explicit construction of high resolution pictures of the eigenvalues for modest dimensions and sizes of the entries; for instance, Figure 1a is a picture of the eigenvalues of all 5 × 5 matrices with entries in {−1, 0, 1} colored by density and plotted on the complex plane.

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)0.001
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesScience and technology studies, Open science
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.205
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0020.000
Scholarly communication0.0000.000
Open science0.0070.002
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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 head0.138
GPT teacher head0.414
Teacher spread0.277 · 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