Triple

T998594
Position Surface form Disambiguated ID Type / Status
Subject Constantin Carathéodory E21550 entity
Predicate notableWork P4 FINISHED
Object Carathéodory’s criterion for measurability E118705 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 criterion for measurability | Statement: [Constantin Carathéodory, notableWork, Carathéodory’s criterion for measurability]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Carathéodory’s criterion for measurability
Context triple: [Constantin Carathéodory, notableWork, Carathéodory’s criterion for measurability]
  • A. Carathéodory’s extension theorem chosen
    Carathéodory’s extension theorem is a fundamental result in measure theory that guarantees a unique extension of a pre-measure defined on an algebra of sets to a complete measure on the generated σ-algebra.
  • B. 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.
  • C. Lebesgue integration
    Lebesgue integration is a foundational measure-theoretic framework for defining and analyzing integrals, particularly suited to handling limits, convergence, and more general functions than those allowed by Riemann integration.
  • D. 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.
  • E. Cameron–Martin theorem
    The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
  • 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.