Triple
T5709652
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Elias Stein |
E125871
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object | Real Analysis: Measure Theory, Integration, and Hilbert Spaces |
E325281
|
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: Real Analysis: Measure Theory, Integration, and Hilbert Spaces | Statement: [Elias Stein, notableWork, Real Analysis: Measure Theory, Integration, and Hilbert Spaces]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Real Analysis: Measure Theory, Integration, and Hilbert Spaces Context triple: [Elias Stein, notableWork, Real Analysis: Measure Theory, Integration, and Hilbert Spaces]
-
A.
Lebesgue integration
Lebesgue integration is a foundational measure-theoretic framework for defining and analyzing integrals, particularly suited to handling limits, convergence, and more general functions than those allowed by Riemann integration.
-
B.
Lebesgue measure
Lebesgue measure is the standard way of assigning a consistent notion of "length," "area," or "volume" to subsets of Euclidean space, forming the foundation of modern measure theory and integration.
-
C.
Hilbert spaces
Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
-
D.
Singular Integrals and Differentiability Properties of Functions
chosen
"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.
-
E.
measure theory
Measure theory is a branch of mathematical analysis that rigorously formalizes the concepts of length, area, volume, and integration for very general sets and functions.
- 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_69c0082d6fe48190b777fb383769e5c8 |
completed | March 22, 2026, 3:18 p.m. |
| NER | Named-entity recognition | batch_69c0248c3dac8190824fca9ddde89665 |
completed | March 22, 2026, 5:19 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c05a6f5ac08190b5acbccea756d2de |
completed | March 22, 2026, 9:09 p.m. |
Created at: March 22, 2026, 3:46 p.m.