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Record W2130357412 · doi:10.1112/s0010437x09004667

A gap principle for dynamics

2010· article· en· W2130357412 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

VenueCompositio Mathematica · 2010
Typearticle
Languageen
FieldMathematics
TopicMathematical Dynamics and Fractals
Canadian institutionsUniversity of Lethbridge
FundersNatural Sciences and Engineering Research Council of CanadaNational Science FoundationVetenskapsrådetKnut och Alice Wallenbergs StiftelseGöran Gustafssons StiftelserRoyal Swedish Academy of Sciences
KeywordsSubvarietyMathematicsDimension (graph theory)CombinatoricsVariety (cybernetics)

Abstract

fetched live from OpenAlex

Abstract Let f 1 ,…, f g ∈ℂ( z ) be rational functions, let Φ=( f 1 ,…, f g ) denote their coordinate-wise action on (ℙ 1 ) g , let V ⊂(ℙ 1 ) g be a proper subvariety, and let P be a point in (ℙ 1 ) g (ℂ). We show that if 𝒮={ n ≥0:Φ n ( P )∈ V (ℂ)} does not contain any infinite arithmetic progressions, then 𝒮 must be a very sparse set of integers. In particular, for any k and any sufficiently large N , the number of n ≤ N such that Φ n ( P )∈ V (ℂ) is less than log k N , where log k denotes the k th iterate of the log function. This result can be interpreted as an analogue of the gap principle of Davenport–Roth and Mumford.

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)0.001
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: Methods · Consensus signal: Methods
Teacher disagreement score0.280
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
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)0.0010.000

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 head0.045
GPT teacher head0.353
Teacher spread0.308 · 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