Triple

T998593
Position Surface form Disambiguated ID Type / Status
Subject Constantin Carathéodory E21550 entity
Predicate notableWork P4 FINISHED
Object Carathéodory’s theorem in complex analysis E118709 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: Carathéodory’s theorem in complex analysis | Statement: [Constantin Carathéodory, notableWork, Carathéodory’s theorem in complex analysis]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Carathéodory’s theorem in complex analysis
Context triple: [Constantin Carathéodory, notableWork, Carathéodory’s theorem in complex analysis]
  • A. Carathéodory’s theorem in convex geometry
    Carathéodory’s theorem in convex geometry is a fundamental result stating that any point in the convex hull of a set in ℝⁿ can be expressed as a convex combination of at most n+1 points from that set.
  • B. Riemann mapping theorem
    The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
  • C. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • D. Weierstrass preparation theorem
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • E. Carathéodory–Fejér interpolation chosen
    Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
  • 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_69a493c476b48190b41fc5e793171cc6 completed March 1, 2026, 7:30 p.m.
NER Named-entity recognition batch_69a4b4e2ad9c81908a0f488d3f261fc3 completed March 1, 2026, 9:51 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac3ba52ebc819084e3d003a3ec8417 completed March 7, 2026, 2:52 p.m.
Created at: March 1, 2026, 7:41 p.m.