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Record W4414112189 · doi:10.1007/s00233-025-10571-w

Thin MC left regular bands

2025· article· en· W4414112189 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.

fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueSemigroup Forum · 2025
Typearticle
Languageen
FieldComputer Science
TopicCellular Automata and Applications
Canadian institutionsnot available
FundersNatural Sciences and Engineering Research Council of CanadaUniversidad de Sevilla
KeywordsAdjacency listAdjacency matrixPartially ordered setRegular semigroupRegular graphTwo-graphGraph energyGraph

Abstract

fetched live from OpenAlex

Abstract We study left regular bands using the adjacency graph of chambers, labeled by facets. In particular, we define a particular family of left regular bands which we call thin MC left regular bands whose face poset is a meet-semilattice and whose adjacency graph is connected. We provide a criterion for when the face poset is a meet-semilattice using the multiplication of the semigroup and its associated support lattice. It turns out that the thin MC left regular bands have a particularly nice adjacency graph. In particular we prove that the adjacency graph of an arbitrary thin MC left regular band is such that each label appears precisely once and every simple cycle has an even number of edges whose associated facets have equal support, implying every simple cycle is of even length. Conversely, we define a set of graphs which we call thin LRB graphs which encode rank two thin MC left regular bands.

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)0.000
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: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.948
Threshold uncertainty score0.386

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
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)0.0000.000

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 head0.004
GPT teacher head0.225
Teacher spread0.221 · 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