Triple

T20627132
Position Surface form Disambiguated ID Type / Status
Subject Radon’s theorem E506848 entity
Predicate implies P1661 FINISHED
Object Helly’s theorem E506847 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: Helly’s theorem | Statement: [Radon’s theorem, implies, Helly’s theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Helly’s theorem
Context triple: [Radon’s theorem, implies, Helly’s theorem]
  • A. Helly’s theorem chosen
    Helly’s theorem is a fundamental result in convex geometry that gives conditions under which a family of convex sets in Euclidean space has a nonempty common intersection.
  • B. colorful Helly theorem
    The colorful Helly theorem is a combinatorial geometric result that generalizes Helly’s theorem by asserting intersection properties for families of convex sets partitioned into color classes.
  • C. fractional Helly theorem
    The fractional Helly theorem is a result in combinatorial geometry that generalizes Helly’s theorem by asserting that if a sufficiently large fraction of small subfamilies of convex sets intersect, then a large subfamily of the whole collection has a common intersection.
  • D. Tverberg’s theorem
    Tverberg’s theorem is a fundamental result in combinatorial geometry that guarantees any sufficiently large set of points in Euclidean space can be partitioned into subsets whose convex hulls all intersect.
  • E. 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.
  • 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_69e0b4bd4a0081908d4e97a590a33fb2 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e6abe576c081909231dc0d7304b9a9 completed April 20, 2026, 10:42 p.m.
NED1 Entity disambiguation (via context triple) batch_6a08c583fb348190b5561a276f45bcf5 completed May 16, 2026, 7:29 p.m.
Created at: April 16, 2026, 11:42 a.m.