Triple
T33761274
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jacobi ensemble |
E865110
|
entity |
| Predicate | hasJointEigenvalueDensityProportionalTo |
P128209
|
FINISHED |
| Object | ∏_{i<j} |λ_i-λ_j|^β ∏_{i} λ_i^{α} (1-λ_i)^{γ} |
—
|
LITERAL FINISHED |
How this triple was built (2 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: ∏_{i<j} |λ_i-λ_j|^β ∏_{i} λ_i^{α} (1-λ_i)^{γ} | Statement: [Jacobi ensemble, hasJointEigenvalueDensityProportionalTo, ∏_{i<j} |λ_i-λ_j|^β ∏_{i} λ_i^{α} (1-λ_i)^{γ}]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasJointEigenvalueDensityProportionalTo
Context triple: [Jacobi ensemble, hasJointEigenvalueDensityProportionalTo, ∏_{i<j} |λ_i-λ_j|^β ∏_{i} λ_i^{α} (1-λ_i)^{γ}]
-
A.
jointEigenvalueDensity
chosen
Indicates the relationship that assigns a probability density to each possible combination of eigenvalues considered jointly, rather than individually.
-
B.
areEigenfunctionsOf
Indicates that certain functions serve as eigenfunctions corresponding to a specified operator or transformation.
-
C.
hasEigenvalueEquation
Indicates that an operator or matrix is associated with an eigenvalue equation relating it to its eigenvalues and eigenvectors.
-
D.
hasEigenvalues
Indicates that a linear operator or matrix possesses one or more eigenvalues associated with its action on a vector space.
-
E.
hasJordanForm
Indicates that one mathematical object (typically a matrix or linear operator) possesses a specific Jordan normal form associated with it.
- F. None of above.
Provenance (3 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69f3498d3b748190aa3c4006c1f32f38 |
completed | April 30, 2026, 12:22 p.m. |
| NER | Named-entity recognition | batch_69f6ffbad8848190867c2988c0ceb84f |
completed | May 3, 2026, 7:56 a.m. |
| PD | Predicate disambiguation | batch_69f6fc5740fc81909774a4f65201a3ff |
completed | May 3, 2026, 7:42 a.m. |
Created at: May 1, 2026, 1:45 a.m.