Triple
T17798349
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Gaussian symplectic ensemble |
E444351
|
entity |
| Predicate | hasJointEigenvalueDensity |
P128209
|
FINISHED |
| Object | proportional to exp(- (β/2) Σ λ_i^2 ) ∏_{i<j} |λ_i - λ_j|^β with β = 4 |
—
|
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: proportional to exp(- (β/2) Σ λ_i^2 ) ∏_{i<j} |λ_i - λ_j|^β with β = 4 | Statement: [Gaussian symplectic ensemble, hasJointEigenvalueDensity, proportional to exp(- (β/2) Σ λ_i^2 ) ∏_{i<j} |λ_i - λ_j|^β with β = 4]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasJointEigenvalueDensity
Context triple: [Gaussian symplectic ensemble, hasJointEigenvalueDensity, proportional to exp(- (β/2) Σ λ_i^2 ) ∏_{i<j} |λ_i - λ_j|^β with β = 4]
-
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.
eigenvalueStatistics
Indicates that one entity characterizes or provides information about the distribution or behavior of the eigenvalues associated with another entity.
-
D.
isSelfAdjoint
Indicates that an operator is equal to its own adjoint (conjugate transpose), meaning it has the same effect as its Hermitian transpose in the given inner product space.
-
E.
hasCPApproximateEigenvalue
Indicates that one entity is an approximate eigenvalue of a completely positive (CP) map or operator associated with another entity.
- 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_69d8b9efe370819095cd219b143ae727 |
completed | April 10, 2026, 8:50 a.m. |
| NER | Named-entity recognition | batch_69e487fcfdc8819086f41152860dfe18 |
completed | April 19, 2026, 7:45 a.m. |
| PD | Predicate disambiguation | batch_69e3d8de28688190844b65acf6af54e6 |
completed | April 18, 2026, 7:17 p.m. |
Created at: April 10, 2026, 10:13 a.m.