Bibliographic record
Abstract
We develop notions of "almost complex analytic subsets" of almost complex manifolds, modelled after complex analytic subsets of complex manifolds. Basic analytic-geometric results are presented, including an identity principle for almost complex maps, and a proof that the singular locus of an almost complex analytic set is itself an "equational" almost complex analytic set, under certain conditions.This work is partly motivated by geometric model theory. B. Zilber observed that a compact complex manifold, equipped with the logico-topological structure given by its complex analytic subsets, satisfies the axioms for a so-called "Zariski geometry", kick-starting a fruitful model-theoretic study of complex manifolds. Our results point towards a natural generalization of Zilberâs theorem to almost complex manifolds, using our notions of almost complex analytic subset. We include a discussion of progress towards this goal.Our development draws inspiration from Y. Peterzil and S. Starchenkoâs theory of nonstandard complex analytic geometry. We work primarily in the real analytic setting.
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.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 teacher head, 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".