Jordan degree type for codimension three Gorenstein algebras of small Sperner number
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.
Bibliographic record
Abstract
The Jordan type P A , ℓ of a linear form ℓ acting on a graded Artinian algebra A over a field k is the partition describing the Jordan block decomposition of the multiplication map m ℓ , which is nilpotent. The Jordan degree type S A , ℓ is a finer invariant, describing also the initial degrees of the simple submodules of A in a decomposition of A as a direct sum of k [ ℓ ] -modules. The set of Jordan types of A or Jordan degree types (JDT) of A as ℓ varies, is an invariant of the algebra. This invariant has been studied for codimension two graded algebras. We here extend the previous results to certain codimension three graded Artinian Gorenstein (AG) algebras - those of small Sperner number. Given a Gorenstein sequence T - one possible for the Hilbert function of a codimension three graded AG algebra - the irreducible variety Gor ( T ) parametrizes all Gorenstein algebras of Hilbert function T . We here completely determine the JDT possible for all pairs ( A , ℓ ) , A ∈ Gor ( T ) , for Gorenstein sequences T of the form T = ( 1 , 3 , s k , 3 , 1 ) for Sperner number s = 3 , 4 , 5 and arbitrary multiplicity k . For s = 6 we delimit the prospective JDT, without verifying that each occurs.
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 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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it