Triple
T18479412
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Tauberian theorems |
E451517
|
entity |
| Predicate | hasSubtype |
P1244
|
FINISHED |
| Object | Hardy–Littlewood Tauberian theorems |
—
|
NE NERFINISHED |
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: Hardy–Littlewood Tauberian theorems | Statement: [Tauberian theorems, hasSubtype, Hardy–Littlewood Tauberian theorems]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hardy–Littlewood Tauberian theorems Context triple: [Tauberian theorems, hasSubtype, Hardy–Littlewood Tauberian theorems]
-
A.
Tauberian theorems
chosen
Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
-
B.
Turán–Kubilius inequality
The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
-
C.
Harmonic Analysis and the Theory of Probability
Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
-
D.
Cartwright–Littlewood theory on nonlinear differential equations
Cartwright–Littlewood theory on nonlinear differential equations is a foundational body of work in dynamical systems that rigorously analyzed the complex, often chaotic behavior of solutions to nonlinear differential equations, particularly in the context of forced oscillations.
-
E.
Carleson theorem on almost-everywhere convergence
The Carleson theorem on almost-everywhere convergence is a fundamental result in harmonic analysis stating that the Fourier series of any square-integrable function on the circle converges almost everywhere to the function itself.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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_69d8d38465a0819099b9b42d2a662ac1 |
completed | April 10, 2026, 10:40 a.m. |
| NER | Named-entity recognition | batch_69e53065e8388190bb216dae89f8cf75 |
completed | April 19, 2026, 7:43 p.m. |
Created at: April 10, 2026, 11:35 a.m.