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Record W2753058904 · doi:10.1287/moor.2017.0871

Ideal Clutters That Do Not Pack

2017· article· en· W2753058904 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.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueMathematics of Operations Research · 2017
Typearticle
Languageen
FieldEngineering
Topicgraph theory and CDMA systems
Canadian institutionsUniversity of Waterloo
FundersOffice of Naval ResearchNatural Sciences and Engineering Research Council of CanadaHausdorff Center for MathematicsNational Science Foundation
KeywordsIdeal (ethics)ClutterMathematicsCombinatoricsCharacterization (materials science)Set (abstract data type)Class (philosophy)Identification (biology)Discrete mathematicsComputer scienceArtificial intelligencePhysics

Abstract

fetched live from OpenAlex

For a clutter 𝒞 over ground set E, a pair of distinct elements e, f ∈ E are coexclusive if every minimal cover contains at most one of them. An identification of 𝒞 is another clutter obtained after identifying coexclusive elements of 𝒞. If a clutter is nonpacking, then so is any identification of it. Inspired by this observation, and impelled by the lack of a qualitative characterization for ideal minimally nonpacking (mnp) clutters, we reduce ideal mnp clutters even further by taking their identifications. In doing so, we reveal chains of ideal mnp clutters, demonstrate the centrality of mnp clutters with covering number two, as well as provide a qualitative characterization of irreducible ideal mnp clutters with covering number two. At the core of this characterization lies a class of objects, called marginal cuboids, that naturally give rise to ideal nonpacking clutters with covering number two. We present an explicit class of marginal cuboids, and show that the corresponding clutters have one of Q 6 , Q 2, 1 , Q 10 as a minor, where Q 6 , Q 2, 1 are known ideal mnp clutters, and Q 10 is a new ideal mnp clutter.

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 categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.781
Threshold uncertainty score0.381

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
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 science0.0010.000
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 head0.133
GPT teacher head0.375
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