Triple

T846896
Position Surface form Disambiguated ID Type / Status
Subject Leopold Kronecker E18296 entity
Predicate notableWork P4 FINISHED
Object Kronecker–Weber theorem
The Kronecker–Weber theorem is a fundamental result in algebraic number theory stating that every finite abelian extension of the rational numbers is contained in a cyclotomic field generated by roots of unity.
E100232 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: Kronecker–Weber theorem | Statement: [Leopold Kronecker, notableWork, Kronecker–Weber theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kronecker–Weber theorem
Context triple: [Leopold Kronecker, notableWork, Kronecker–Weber theorem]
  • A. Abel–Ruffini theorem
    The Abel–Ruffini theorem is a fundamental result in algebra proving that there is no general solution in radicals for polynomial equations of degree five or higher.
  • B. 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.
  • C. Noether's problem
    Noether's problem is a fundamental question in invariant theory and field theory that asks whether the fixed field of a finite group acting on a rational function field is itself a purely transcendental (rational) extension.
  • D. Gauss’s lemma in number theory
    Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
  • E. Levine-Fricke Field
    Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
  • 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: Kronecker–Weber theorem
Triple: [Leopold Kronecker, notableWork, Kronecker–Weber theorem]
Generated description
The Kronecker–Weber theorem is a fundamental result in algebraic number theory stating that every finite abelian extension of the rational numbers is contained in a cyclotomic field generated by roots of unity.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kronecker–Weber theorem
Target entity description: The Kronecker–Weber theorem is a fundamental result in algebraic number theory stating that every finite abelian extension of the rational numbers is contained in a cyclotomic field generated by roots of unity.
  • A. Abel–Ruffini theorem
    The Abel–Ruffini theorem is a fundamental result in algebra proving that there is no general solution in radicals for polynomial equations of degree five or higher.
  • B. 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.
  • C. Noether's problem
    Noether's problem is a fundamental question in invariant theory and field theory that asks whether the fixed field of a finite group acting on a rational function field is itself a purely transcendental (rational) extension.
  • D. Gauss’s lemma in number theory
    Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
  • E. Levine-Fricke Field
    Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
  • 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_69a4938b04208190b82e1df6b572c548 completed March 1, 2026, 7:29 p.m.
NER Named-entity recognition batch_69a4ac0ba6b4819089c15ed7e1765502 completed March 1, 2026, 9:13 p.m.
NED1 Entity disambiguation (via context triple) batch_69a7929e65d08190bcea03f581288cc4 completed March 4, 2026, 2:02 a.m.
NEDg Description generation batch_69a7937c2ce481908c04e08e2be02985 completed March 4, 2026, 2:05 a.m.
NED2 Entity disambiguation (via description) batch_69a79761ee34819094a0558ef195d8a0 completed March 4, 2026, 2:22 a.m.
Created at: March 1, 2026, 7:38 p.m.