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Record W2019396321 · doi:10.1112/s0024609399006426

Non-Linear Spectrum-Preserving Maps

2000· article· en· W2019396321 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

VenueBulletin of the London Mathematical Society · 2000
Typearticle
Languageen
FieldMathematics
TopicHolomorphic and Operator Theory
Canadian institutionsUniversité Laval
Fundersnot available
KeywordsMathematicsHolomorphic functionAutomorphismEigenvalues and eigenvectorsMathematics Subject ClassificationSpectrum (functional analysis)Unit spherePure mathematicsCombinatoricsUnit (ring theory)

Abstract

fetched live from OpenAlex

Let Mn denote the space of complex n×n matrices, and let Ωn denote the spectral unit ball of Mn, namely the set of matrices in Mn whose eigenvalues lie within the open unit disc. As a step towards the eventual classification of the holomorphic automorphisms of Ωn, we prove that every such automorphism F satisfying F(0) = 0 and F′(0) = I has the property that F(x) is conjugate to x for each x∈Ωn. This result is obtained by combining earlier work of Ransford and White with a general theorem about spectrum-preserving maps proved in this paper. 1991 Mathematics Subject Classification 15A18.

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)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.622
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0270.001

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 head0.021
GPT teacher head0.262
Teacher spread0.241 · 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