Triple

T8850260
Position Surface form Disambiguated ID Type / Status
Subject Hilbert’s seventeenth problem E210619 entity
Predicate relatedTo P37 FINISHED
Object Hilbert’s sixteenth problem
Hilbert’s sixteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the topology and arrangement of algebraic curves and surfaces, particularly the number and position of their ovals.
E761264 NE FINISHED

How this triple was built (4 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: Hilbert’s sixteenth problem | Statement: [Hilbert’s seventeenth problem, relatedTo, Hilbert’s sixteenth problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hilbert’s sixteenth problem
Context triple: [Hilbert’s seventeenth problem, relatedTo, Hilbert’s sixteenth problem]
  • A. Hilbert’s twenty-second problem
    Hilbert’s twenty-second problem is one of David Hilbert’s famous list of 23 problems, concerning the uniformization of analytic relations and the representation of multi-valued analytic functions by single-valued ones on suitable Riemann surfaces.
  • B. Hilbert’s seventeenth problem
    Hilbert’s seventeenth problem is a famous question in real algebraic geometry asking whether every nonnegative polynomial can be represented as a sum of squares of rational functions.
  • C. Smale’s 18 problems
    Smale’s 18 problems are a celebrated list of major open questions in mathematics proposed by Stephen Smale in 1998 as a successor in spirit to Hilbert’s famous problems.
  • D. Hilbert’s twenty-third problem
    Hilbert’s twenty-third problem is one of David Hilbert’s famous list of unsolved problems, focusing on the further development and systematic application of the calculus of variations.
  • E. Hilbert’s fourteenth problem
    Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Hilbert’s sixteenth problem
Triple: [Hilbert’s seventeenth problem, relatedTo, Hilbert’s sixteenth problem]
Generated description
Hilbert’s sixteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the topology and arrangement of algebraic curves and surfaces, particularly the number and position of their ovals.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hilbert’s sixteenth problem
Target entity description: Hilbert’s sixteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the topology and arrangement of algebraic curves and surfaces, particularly the number and position of their ovals.
  • A. Hilbert’s twenty-second problem
    Hilbert’s twenty-second problem is one of David Hilbert’s famous list of 23 problems, concerning the uniformization of analytic relations and the representation of multi-valued analytic functions by single-valued ones on suitable Riemann surfaces.
  • B. Hilbert’s seventeenth problem
    Hilbert’s seventeenth problem is a famous question in real algebraic geometry asking whether every nonnegative polynomial can be represented as a sum of squares of rational functions.
  • C. Smale’s 18 problems
    Smale’s 18 problems are a celebrated list of major open questions in mathematics proposed by Stephen Smale in 1998 as a successor in spirit to Hilbert’s famous problems.
  • D. Hilbert’s twenty-third problem
    Hilbert’s twenty-third problem is one of David Hilbert’s famous list of unsolved problems, focusing on the further development and systematic application of the calculus of variations.
  • E. Hilbert’s fourteenth problem
    Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
  • F. None of above. chosen

Provenance (5 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_69ca838a424c8190b1ecac115c2927e7 completed March 30, 2026, 2:07 p.m.
NER Named-entity recognition batch_69cc60abb0748190af41d4e1f419e39c completed April 1, 2026, 12:02 a.m.
NED1 Entity disambiguation (via context triple) batch_69cf89cb853c8190a7664f2e7de0de87 completed April 3, 2026, 9:35 a.m.
NEDg Description generation batch_69cf8ab7da348190b423f0768fe9dc1a completed April 3, 2026, 9:39 a.m.
NED2 Entity disambiguation (via description) batch_69cf8bd252a4819098891bbb67baf897 completed April 3, 2026, 9:43 a.m.
Created at: March 30, 2026, 6:49 p.m.