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Record W4413965834 · doi:10.70930/tac/ugrides5

Categorical aspects of congruence distributivity

2024· article· en· W4413965834 on OpenAlex
Michael Hoefnagel, Diana Rodelo

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.

venuePublished in a venue whose home country is Canada.
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

VenueTheory and applications of categories · 2024
Typearticle
Languageen
FieldComputer Science
TopicAdvanced Algebra and Logic
Canadian institutionsnot available
FundersCentro de Matemática, Universidade de CoimbraFundação para a Ciência e a TecnologiaMinistério da Ciência, Tecnologia e Ensino SuperiorUniversidade de Coimbra
KeywordsDistributivityCongruence (geometry)Categorical variableMathematicsPure mathematicsStatisticsDistributive propertyGeometry

Abstract

fetched live from OpenAlex

We study a categorical condition on relations, which is a categorical formulation of Jnsson's characterisation of congruence distributive varieties.Categories satisfying these conditions need not be varieties; for instance, the dual of the categories of topological spaces, ordered sets, G-sets, and the dual of any (pre)topos all provide us with examples.However, this notion has several drawbacks.For one thing, its denition relies on the existence of suprema of equivalence relations a condition not guaranteed by familiar categorical contexts such as nite completeness, regularity [1], or even Barr-exactness [1].

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: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.989
Threshold uncertainty score0.233

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 science0.0000.000
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 head0.008
GPT teacher head0.255
Teacher spread0.247 · 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