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Record W2004887104 · doi:10.1017/s0963548305006772

Self-Avoiding Walks on Hyperbolic Graphs

2005· article· en· W2004887104 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

VenueCombinatorics Probability Computing · 2005
Typearticle
Languageen
FieldMathematics
TopicStochastic processes and statistical mechanics
Canadian institutionsYork University
Fundersnot available
KeywordsEuclidean geometryHyperbolic geometryMathematicsHyperbolic triangleReversingPlane (geometry)CombinatoricsDiscrete mathematicsPure mathematicsGeometry

Abstract

fetched live from OpenAlex

We study self-avoiding walks (SAWs) on non-Euclidean lattices that correspond to regular tilings of the hyperbolic plane (‘hyperbolic graphs’). We prove that on all but at most eight such graphs, (i) there are exponentially fewer $N$ -step self-avoiding polygons than there are $N$ -step SAWs, (ii) the number of $N$ -step SAWs grows as $\mu_w^N$ within a constant factor, and (iii) the average end-to-end distance of an $N$ -step SAW is approximately proportional to $N$ . In terms of critical exponents from statistical physics, (ii) says that $\gamma=1$ and (iii) says that $\nu=1$ . We also prove that $\gamma$ is finite on all hyperbolic graphs, and we prove a general identity about non-reversing walks that had previously been discovered for certain special cases.

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)0.004
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.331
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.004
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.001
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 head0.048
GPT teacher head0.305
Teacher spread0.257 · 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