Triple

T1859189
Position Surface form Disambiguated ID Type / Status
Subject Hilbert problems E41774 entity
Predicate hasPart P35 FINISHED
Object Hilbert’s fifteenth problem
Hilbert’s fifteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the rigorous mathematical foundation and general theory of Schubert’s enumerative calculus in algebraic geometry.
E41774 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 fifteenth problem | Statement: [Hilbert problems, hasPart, Hilbert’s fifteenth problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hilbert’s fifteenth problem
Context triple: [Hilbert problems, hasPart, Hilbert’s fifteenth problem]
  • A. Hilbert problems
    The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
  • B. 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.
  • C. Hilbert’s tenth problem
    Hilbert’s tenth problem is a famous unsolved question in mathematics that asked for a general algorithm to determine whether any given Diophantine equation has an integer solution, and whose negative answer helped establish fundamental limits of computability.
  • D. Hilbert’s Nullstellensatz
    Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
  • E. Hilbert’s irreducibility theorem
    Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
  • 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 fifteenth problem
Triple: [Hilbert problems, hasPart, Hilbert’s fifteenth problem]
Generated description
Hilbert’s fifteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the rigorous mathematical foundation and general theory of Schubert’s enumerative calculus in algebraic geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hilbert’s fifteenth problem
Target entity description: Hilbert’s fifteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the rigorous mathematical foundation and general theory of Schubert’s enumerative calculus in algebraic geometry.
  • A. Hilbert problems chosen
    The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
  • B. 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.
  • C. Hilbert’s tenth problem
    Hilbert’s tenth problem is a famous unsolved question in mathematics that asked for a general algorithm to determine whether any given Diophantine equation has an integer solution, and whose negative answer helped establish fundamental limits of computability.
  • D. Hilbert’s Nullstellensatz
    Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
  • E. Hilbert’s irreducibility theorem
    Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
  • F. None of above.

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_69a8864a83848190a4ec02721306c511 completed March 4, 2026, 7:21 p.m.
NER Named-entity recognition batch_69abb0829f1481908d2b389d20827417 completed March 7, 2026, 4:58 a.m.
NED1 Entity disambiguation (via context triple) batch_69addf4ecdc08190a264b358d3883f70 completed March 8, 2026, 8:42 p.m.
NEDg Description generation batch_69ade0628a3881908443346eab47656e completed March 8, 2026, 8:47 p.m.
NED2 Entity disambiguation (via description) batch_69ade0c545e08190b4469e93922d9b4b completed March 8, 2026, 8:49 p.m.
Created at: March 4, 2026, 7:33 p.m.