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Record W4403201646 · doi:10.1002/jcd.21957

Nestings of BIBDs with block size four

2024· article· en· W4403201646 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

VenueJournal of Combinatorial Designs · 2024
Typearticle
Languageen
FieldEngineering
Topicgraph theory and CDMA systems
Canadian institutionsUniversity of Waterloo
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsMathematicsBlock (permutation group theory)Block sizeCombinatoricsBiologyEcologyKey (lock)

Abstract

fetched live from OpenAlex

Abstract In a nesting of a balanced incomplete block design (or BIBD), we wish to add a point (the nested point ) to every block of a ‐BIBD in such a way that we end up with a partial ‐BIBD. In the case where the partial ‐BIBD is in fact a ‐BIBD, we have a perfect nesting . We show that a nesting is perfect if and only if . Perfect nestings were previously known to exist in the case of Steiner triple systems (i.e., ‐BIBDs) when , as well as for some symmetric BIBDs. Here we study nestings of ‐BIBDs, which are not perfect nestings. We prove that there is a nested ‐BIBD if and only if , . This is accomplished by a variety of direct and recursive constructions.

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 score0.170
Threshold uncertainty score0.393

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 science0.0000.000
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 head0.014
GPT teacher head0.207
Teacher spread0.194 · 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