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Record W2170751889 · doi:10.1093/imrn/rnp052

Counting Open Nodal Lines of Random Waves on Planar Domains

2009· article· en· W2170751889 on OpenAlex
Juraj Tóth, Igor Wigman

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

VenueInternational Mathematics Research Notices · 2009
Typearticle
Languageen
FieldEarth and Planetary Sciences
TopicGeology and Paleoclimatology Research
Canadian institutionsUniversité de MontréalMcGill University
Fundersnot available
KeywordsLibrary scienceArt historyMathematicsManagementHistorySociologyComputer science

Abstract

fetched live from OpenAlex

We compute the asymptotic expectation of the number of open nodal lines for random waves on smooth planar domains. We find that for both the long energy window [0, λ], and the short one [λ, λ +1], the expected number of open nodal lines is proportional to λ, asymptotically as λ → ∞. Our results are consistent with the predictions of Blum, Gnutzmann, and Smilansky [4] in the physics literature.

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)0.003
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: Observational · Consensus signal: Observational
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.355
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.001
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)0.0020.000

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 head0.100
GPT teacher head0.395
Teacher spread0.295 · 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