Triple
T2852039
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Leonhard Euler |
E63113
|
entity |
| Predicate | notableFor |
P22
|
FINISHED |
| Object | Euler's identity |
E54268
|
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: Euler's identity | Statement: [Leonhard Euler, notableFor, Euler's identity]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Euler's identity Context triple: [Leonhard Euler, notableFor, Euler's identity]
-
A.
Euler’s theorem
Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
-
B.
Euler’s formula for complex exponentials
chosen
Euler’s formula for complex exponentials is the fundamental identity \(e^{i\theta} = \cos\theta + i\sin\theta\), which links complex exponentials with trigonometric functions and underpins much of complex analysis and engineering mathematics.
-
C.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
-
D.
Fermat's Last Theorem
Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
-
E.
E=MC²
E=MC² is Mariah Carey's eleventh studio album, a pop and R&B record known for hits like "Touch My Body" and its commercially successful, contemporary sound.
- 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_69ab4c407c408190857d25e027155ce9 |
completed | March 6, 2026, 9:50 p.m. |
| NER | Named-entity recognition | batch_69abdf5ca2648190bd32c6ec4b0dd3b6 |
completed | March 7, 2026, 8:18 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69afe8e4e0b881908de5c4927609725e |
completed | March 10, 2026, 9:48 a.m. |
Created at: March 6, 2026, 10:02 p.m.