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Record W2107854391 · doi:10.1287/moor.25.4.539.12117

A Further Extension of the KKMS Theorem

2000· article· en· W2107854391 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

VenueMathematics of Operations Research · 2000
Typearticle
Languageen
FieldMathematics
TopicAdvanced Topology and Set Theory
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsMathematicsIntersection (aeronautics)GeneralizationExtension (predicate logic)Countable setIntersection theoremPoint (geometry)Property (philosophy)Fixed-point theoremDiscrete mathematicsCombinatoricsBrouwer fixed-point theoremDanskin's theoremComputer scienceMathematical analysisGeometry

Abstract

fetched live from OpenAlex

Reny and Wooders (1998) showed that there is some point in the intersection of sets in Shapley's (1973) generalization of the Knaster-Kuratowski-Mazurkiwicz Theorem with the property that the collection of all sets containing that point is partnered as well as balanced. We provide a further extension by showing that the collection of all such sets can be chosen to be strictly balanced, implying the Reny-Wooders result. Our proof is topological, based on the Eilenberg-Montgomery Fixed Point Theorem. Reny and Wooders (1998) also show that if the collection of partnered points in the intersection is countable, then at least one of them is minimally partnered. Applying degree theory for correspondences, we show that if this collection is assumed to be zero-dimensional, then there is at least one strictly balanced and minimally partnered point in the intersection. Our approach sheds a new geometric-topological light on the Reny-Wooders results.

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)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
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 score0.027
Threshold uncertainty score0.998

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0030.000

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 head0.130
GPT teacher head0.440
Teacher spread0.310 · 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