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Record W3189397579 · doi:10.1002/rsa.21117

Self‐avoiding walk on the hypercube

2022· article· en· W3189397579 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

VenueRandom Structures and Algorithms · 2022
Typearticle
Languageen
FieldMathematics
TopicStochastic processes and statistical mechanics
Canadian institutionsUniversity of British Columbia
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsConstant (computer programming)HypercubeInteger (computer science)Mathematical proofMathematicsFunction (biology)Dimension (graph theory)CombinatoricsComputer scienceGeometry

Abstract

fetched live from OpenAlex

Abstract We study the number of ‐step self‐avoiding walks on the ‐dimensional hypercube, and identify an ‐dependent connective constant and amplitude such that is for all and , and is asymptotically as long as for any fixed . We refer to the regime as the dilute phase . We discuss conjectures concerning different behaviors of when reaches and exceeds , corresponding to a critical window and a dense phase. In addition, we prove that the connective constant has an asymptotic expansion to all orders in , with integer coefficients, and we compute the first five coefficients . The proofs are based on generating function and Tauberian methods implemented via the lace expansion, for which an introductory account is provided.

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)0.000
metaresearch head score (Gemma)0.001
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: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.771
Threshold uncertainty score0.665

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0010.000
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 head0.032
GPT teacher head0.280
Teacher spread0.249 · 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