Triple

T2815347
Position Surface form Disambiguated ID Type / Status
Subject Euler’s formula for complex exponentials E54268 entity
Predicate geometricInterpretation P43784 FINISHED
Object e^{i\theta} represents a rotation by angle \theta in the complex plane — LITERAL 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: e^{i\theta} represents a rotation by angle \theta in the complex plane | Statement: [Euler’s formula for complex exponentials, geometricInterpretation, e^{i\theta} represents a rotation by angle \theta in the complex plane]
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: geometricInterpretation
Context triple: [Euler’s formula for complex exponentials, geometricInterpretation, e^{i\theta} represents a rotation by angle \theta in the complex plane]
  • A. geometricFunction
    Indicates a relationship where one entity serves as a geometric transformation or operation that, when applied, produces or modifies another geometric entity.
  • B. isGeometric
    Indicates that something has the properties or form of a geometric figure, pattern, or structure.
  • C. geodesicsAre
    Indicates that certain paths or curves in a space are geodesics, i.e., they locally minimize distance or follow the straightest possible trajectory according to the space’s geometry.
  • D. geodesicDefinition
    Indicates that one entity provides the formal definition or characterization of a geodesic (the shortest or extremal path between points in a given geometric or spacetime manifold).
  • E. hasGeodesics
    Indicates that the subject possesses or is characterized by geodesic paths, typically representing shortest or straightest possible routes within a given space or geometry.
  • F. None of above. chosen

Provenance (4 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_69ab49de0af08190b3da69683be1e728 completed March 6, 2026, 9:40 p.m.
NER Named-entity recognition batch_69abde4d29488190a32461906dd9ea7e completed March 7, 2026, 8:14 a.m.
PD Predicate disambiguation batch_69abdd0740208190911dc9c9546a79ae completed March 7, 2026, 8:08 a.m.
PDg Predicate description generation batch_69abde0f4c648190b9812e64f30c39da completed March 7, 2026, 8:13 a.m.
Created at: March 6, 2026, 9:59 p.m.