Triple

T1859181
Position Surface form Disambiguated ID Type / Status
Subject Hilbert problems E41774 entity
Predicate hasPart P35 FINISHED
Object Hilbert’s seventh problem
Hilbert’s seventh problem is one of David Hilbert’s famous list of 23 problems, asking whether certain powers of algebraic numbers (notably exemplified by the Gelfond–Schneider theorem) are always transcendental.
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 seventh problem | Statement: [Hilbert problems, hasPart, Hilbert’s seventh problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hilbert’s seventh problem
Context triple: [Hilbert problems, hasPart, Hilbert’s seventh problem]
  • A. Lindemann–Weierstrass theorem precursor
    The Lindemann–Weierstrass theorem precursor is an early foundational result in transcendental number theory developed by Ferdinand von Lindemann that paved the way for the full Lindemann–Weierstrass theorem on the algebraic independence of exponentials of algebraic numbers.
  • B. 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.
  • C. 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.
  • D. Fermat's theorem on sums of two squares
    Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
  • E. Fermat's Last Theorem
    Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
  • 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 seventh problem
Triple: [Hilbert problems, hasPart, Hilbert’s seventh problem]
Generated description
Hilbert’s seventh problem is one of David Hilbert’s famous list of 23 problems, asking whether certain powers of algebraic numbers (notably exemplified by the Gelfond–Schneider theorem) are always transcendental.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hilbert’s seventh problem
Target entity description: Hilbert’s seventh problem is one of David Hilbert’s famous list of 23 problems, asking whether certain powers of algebraic numbers (notably exemplified by the Gelfond–Schneider theorem) are always transcendental.
  • A. Lindemann–Weierstrass theorem precursor
    The Lindemann–Weierstrass theorem precursor is an early foundational result in transcendental number theory developed by Ferdinand von Lindemann that paved the way for the full Lindemann–Weierstrass theorem on the algebraic independence of exponentials of algebraic numbers.
  • B. 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.
  • C. 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.
  • D. Fermat's theorem on sums of two squares
    Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
  • E. Fermat's Last Theorem
    Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
  • 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_69add1ce296c819093336cbaa257dfd2 completed March 8, 2026, 7:45 p.m.
NEDg Description generation batch_69add229de448190826bbb668c7611a0 completed March 8, 2026, 7:46 p.m.
NED2 Entity disambiguation (via description) batch_69add29e3c50819098ff87d254c25c45 completed March 8, 2026, 7:48 p.m.
Created at: March 4, 2026, 7:33 p.m.