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Record W2724743195 · doi:10.20382/jocg.v9i1a10

Placing your Coins on a Shelf

2017· preprint· en· W2724743195 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

VenueResearch Publications (Maastricht University) · 2017
Typepreprint
Languageen
FieldEngineering
TopicOptimization and Packing Problems
Canadian institutionsUniversity of Waterloo
Fundersnot available
KeywordsRADIUSPoint (geometry)CombinatoricsBinary logarithmMathematicsComputer scienceGeometry

Abstract

fetched live from OpenAlex

We consider the problem of packing a family of disks ``on a shelf,'' that is, such that each disk touches the x-axis from above and such that no two disks overlap. We study the problem of minimizing the distance between the leftmost point and the rightmost point of any disk in such a packing. We show how to approximate this problem within a factor of 4/3 in O(n log n) time. We further provide an O(n log n)-time exact algorithm for a special case which includes inputs where the ratio between the largest radius and the smallest radius is less than four. On the negative side, we prove that the problem is NP-hard even when the ratio between the largest radius and the smallest radius is at most 36.

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 categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: none
Teacher disagreement score0.814
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0030.001
Science and technology studies0.0010.000
Scholarly communication0.0010.000
Open science0.0020.001
Research integrity0.0000.002
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 head0.149
GPT teacher head0.337
Teacher spread0.188 · 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