Triple
T3780919
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Ulam stability |
E85413
|
entity |
| Predicate | appliesTo |
P1129
|
FINISHED |
| Object | Jensen functional equation |
E87727
|
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: Jensen functional equation | Statement: [Ulam stability, appliesTo, Jensen functional equation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Jensen functional equation Context triple: [Ulam stability, appliesTo, Jensen functional equation]
-
A.
Jensen inequality
chosen
Jensen's inequality is a fundamental result in convex analysis and probability theory that relates the value of a convex (or concave) function of an expectation to the expectation of the function, providing bounds that underlie many other inequalities and convergence results.
-
B.
Ulam stability
Ulam stability is a concept in the theory of functional equations that studies when approximate solutions imply the existence of exact solutions nearby, forming the basis of what is now called Hyers–Ulam stability.
-
C.
Khinchin–Kahane type inequalities
Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
-
D.
Khinchin's representation theorem
Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
-
E.
Hadamard three-circle theorem
The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
- 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_69aed937fa8881908208ef3801060826 |
completed | March 9, 2026, 2:29 p.m. |
| NER | Named-entity recognition | batch_69aee3d98b38819094df9569b549124f |
completed | March 9, 2026, 3:14 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b4f04353a881908e612a10572eb8c5 |
completed | March 14, 2026, 5:21 a.m. |
Created at: March 9, 2026, 3:12 p.m.