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.