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Record W2514502459 · doi:10.4153/cmb-2016-061-9

Isometry on Linear <i>n</i>-G-quasi Normed Spaces

2016· article· en· W2514502459 on OpenAlex
Yumei Ma

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.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueCanadian Mathematical Bulletin · 2016
Typearticle
Languageen
FieldMathematics
TopicFunctional Equations Stability Results
Canadian institutionsnot available
Fundersnot available
KeywordsMathematicsIsometry (Riemannian geometry)Normed vector spaceDimension (graph theory)Pure mathematicsSpace (punctuation)Discrete mathematicsCombinatorics

Abstract

fetched live from OpenAlex

Abstract This paper generalizes the Aleksandrov problem: the Mazur-Ulam theoremon n -G-quasi normed spaces. It proves that a one- n -distance preserving mapping is an n -isometry if and only if it has the zero- n -G-quasi preserving property, and two kinds of n -isometries on n -G-quasi normed space are equivalent; we generalize the Benz theorem to n-normed spaces with no restrictions on the dimension of 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)0.001
metaresearch head score (Gemma)0.012
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMetaresearch, Insufficient 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: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.553
Threshold uncertainty score0.997

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.012
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)0.0280.048

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 head0.040
GPT teacher head0.279
Teacher spread0.238 · 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