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Record W4405309012 · doi:10.2140/agt.2024.24.4007

Lattices, injective metrics and the K(π,1)conjecture

2024· article· en· W4405309012 on OpenAlex
Thomas Haettel

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

VenueAlgebraic & Geometric Topology · 2024
Typearticle
Languageen
FieldMathematics
TopicGeometric and Algebraic Topology
Canadian institutionsUniversité de Montréal
FundersAgence Nationale de la Recherche
KeywordsMathematicsInjective functionCombinatoricsConjectureMetric spacePure mathematicsDiscrete mathematics

Abstract

fetched live from OpenAlex

Starting with a lattice with an action of Z or R, we build a Helly graph or an injective metric space.We deduce that the `1 orthoscheme complex of any bounded graded lattice is injective.We also prove a Cartan-Hadamard result for locally injective metric spaces.We apply this to show that any Garside group or any FC-type Artin group acts on an injective metric space and on a Helly graph.We also deduce that the natural piecewise `1 metric on any Euclidean building of type QA n extended, z B n , z C n or z D n is injective, and its thickening is a Helly graph. Concerning Artin groups of Euclidean types QA n and z C n , we show that the natural piecewise `1 metric on the Deligne complex is injective, the thickening is a Helly graph, and it admits a convex bicombing.This gives a metric proof of the K. ; 1/ conjecture, as well as several other consequences usually known when the Deligne complex has a CAT(0) metric.20E42, 05B35, 52A35, 06A12 6.The thickening of a semilattice 4047 7. Application to Euclidean buildings and the Deligne complex of other Euclidean types 4051 8. Bicombings on Deligne complexes in types Q A n and z C

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)0.002
metaresearch head score (Gemma)0.007
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
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 score0.269
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.007
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0030.010
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.001
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 head0.022
GPT teacher head0.294
Teacher spread0.272 · 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