Bibliographic record
Abstract
We obtain a detailed classification for a class of non-simply connected Calabi-Yau 3-folds which are of potential interest for a wide range of problems in string phenomenology.These 3-folds arise as quotients of Schoen's Calabi-Yau 3-folds, which are fiber products over P 1 of two rational elliptic surfaces.The quotient is by a freely acting finite abelian group preserving the fibrations.Our work involves a classification of restricted finite automorphism groups of rational elliptic surfaces.group of automorphisms G X ∼ = G.Moreover, by pulling back the Calabi-Yau metric of X we see that the universal cover X is also Calabi-Yau.Conversely, let X be a smooth simply connected Calabi-Yau 3-fold, with a freely acting finite abelian group of automorphisms G X .It turns out that G X automatically preserves the volume form, 2 so the quotient manifoldIn this paper we use the second point of view to construct a large class of non-simply connected Calabi-Yau 3-folds.Namely, we classify all Calabi-Yau 3-folds X constructed as a smooth fiber product of two rational elliptic surfaces and admitting a freely acting finite abelian group of automorphisms G X .Since we will eventually also need to use the spectral construction to build Standard Model bundles on X, we require that G X preserves the elliptic fibration of X, so that the quotient 3-fold X is torus-fibered.3 Let us now describe in more details the family of Calabi-Yau 3-folds we are interested in.Let B and B be rational elliptic surfaces.Consider the fiber product X := B × P 1 B .That is, construct the 3-foldwhere β : B → P 1 and β : B → P 1 are the elliptic fibrations of the rational elliptic surfaces B and B .X can also be described by the commutative diagram shown next.(1.2) X π ~~~~~~~~π
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".