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Record W4245323049 · doi:10.1215/ijm/1355927037

Ultrametric dynamics

2011· article· en· W4245323049 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

VenueIllinois Journal of Mathematics · 2011
Typearticle
Languageen
FieldMathematics
TopicFixed Point Theorems Analysis
Canadian institutionsQueen's University
Fundersnot available
KeywordsUltrametric spaceMathematicsSurjective functionFixed-point theoremBrouwer fixed-point theoremCompleteness (order theory)Fixed pointPure mathematicsPicard–Lindelöf theoremProperty (philosophy)Discrete mathematicsMathematical analysisMetric space

Abstract

fetched live from OpenAlex

This paper is concerned with dynamics in general ultrametric spaces. We prove the Fixed Point theorem, the Stability theorem, the Common Point theorem, the Local Fixed Point theorem, the Attractor theorem and we derive conditions for a mapping to be surjective. We also discuss tightly continuous mappings and prove a theorem about the transfer of the property of principal completeness by a mapping between ultrametric spaces.

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)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
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 score0.143
Threshold uncertainty score0.756

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0010.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.000

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 head0.062
GPT teacher head0.281
Teacher spread0.219 · 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