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Record W2329919292 · doi:10.1515/advgeom-2013-0035

Cubic tessellations of the didicosm

2014· article· en· W2329919292 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

VenueAdvances in Geometry · 2014
Typearticle
Languageen
FieldMathematics
TopicGeometric and Algebraic Topology
Canadian institutionsYork University
Fundersnot available
KeywordsMathematicsTessellation (computer graphics)QuotientGroup (periodic table)Isomorphism (crystallography)AutomorphismHomogeneous spaceCombinatoricsAutomorphism groupManifold (fluid mechanics)GeometryPure mathematicsCrystallographyCrystal structurePhysics

Abstract

fetched live from OpenAlex

Abstract Up to isomorphism, there is a unique fixed-point-free crystallographic group generated by two (2-fold) twists whose non-intersecting axes have perpendicular directions. Identifying points in E 3 which are in the same orbit under the action of this group yields the flat, closed 3-manifold known as the didicosm (also as the Hantzsche-Wendt manifold). When this group is realized as a group of symmetries of the standard cubical tessellation in E 3 , the resulting quotient gives a cubical tessellation on the didicosm. This paper describes a complete classification of these cubical tessellations on the didicosm into ten classes, according to their automorphism groups.

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)0.002
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: Empirical
Teacher disagreement score0.157
Threshold uncertainty score0.229

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.002
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 integrity0.0000.000
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 head0.013
GPT teacher head0.297
Teacher spread0.284 · 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