SIblings of an aleph_zero categorical relational structure
Why is this work in the frame?
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Full frame distilled prediction
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.
- Candidate categories
- Meta-epidemiology (narrow), Insufficient payload (model declined to judge)
- Consensus categories
- none
- Domain
- Candidate signal: noneConsensus signal: none
- Study design
- Candidate signal: Theoretical or conceptualConsensus signal: Theoretical or conceptual
- Genre
- Candidate signal: EmpiricalConsensus signal: Empirical
- Teacher disagreement score
- 0.202
- Threshold uncertainty score
- 1.000
- Validation status
machine_predicted_unvalidated·codex-gemma-dda1882f352a
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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.
- Teacher spread
- 0.247 · how far apart the two teachers sit on this one work
- Validation status
score_only:v0-immature-baseline· verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it
Abstract
A \emph{sibling} of a relational structure $R$ is any structure $S$ which can be embedded into $R$ and, vice versa, in which $R$ can be embedded. Let $\sib(R)$ be the number of siblings of $R$, these siblings being counted up to isomorphism. Thomass\'e conjectured that for countable relational structures made of at most countably many relations, $\sib(R)$ is either $1$, countably infinite, or the size of the continuum; but even showing the special case $\sib(R)=1$ or infinite is unsettled when $R$ is a countable tree. We prove that if $R$ is countable and $\aleph_{0}$-categorical, then indeed $\sib(R)$ is one or infinite. Furthermore, $\sib(R)$ is one if and only if $R$ is finitely partitionable in the sense of Hodkinson and Macpherson. The key tools in our proof are the notion of monomorphic decomposition of a relational structure introduced in Pouzet-Thiery and studied further in Oudrar-Pouzet, and a result of Frasnay 1984.
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.
The record
- Venue
- HAL (Le Centre pour la Communication Scientifique Directe)
- Topic
- Advanced Topology and Set Theory
- Field
- Mathematics
- Canadian institutions
- University of Calgary
- Funders
- not available
- Keywords
- Countable setAlephMathematicsIsomorphism (crystallography)Categorical variableZero (linguistics)Pure mathematicsDiscrete mathematicsCombinatoricsPhilosophy
- Has abstract in OpenAlex
- yes