Triple
T5212082
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Weyl law |
E117656
|
entity |
| Predicate | generalizedBy |
P2372
|
FINISHED |
| Object | Weyl law for pseudodifferential operators |
E117656
|
NE 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: Weyl law for pseudodifferential operators | Statement: [Weyl law, generalizedBy, Weyl law for pseudodifferential operators]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Weyl law for pseudodifferential operators Context triple: [Weyl law, generalizedBy, Weyl law for pseudodifferential operators]
-
A.
Weyl law
chosen
The Weyl law is a fundamental result in spectral theory that describes the asymptotic distribution of eigenvalues of the Laplacian (or similar operators) in terms of the volume of the underlying domain or manifold.
-
B.
Weyl quantization
Weyl quantization is a mathematical procedure in quantum mechanics that systematically associates classical observables with quantum operators in a symmetric and coordinate-independent way.
-
C.
Hilbert–Schmidt operators
Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
-
D.
Three regularity results in harmonic analysis
"Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
-
E.
Singular Integrals and Differentiability Properties of Functions
"Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
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_69bd4464ba3c8190bc16b2ebbe42ddb0 |
completed | March 20, 2026, 12:58 p.m. |
| NER | Named-entity recognition | batch_69bd7a7166848190805152142e184529 |
completed | March 20, 2026, 4:48 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69befe5aabbc8190bc09eaffb5ec9776 |
completed | March 21, 2026, 8:23 p.m. |
Created at: March 20, 2026, 1:47 p.m.