Triple

T1994293
Position Surface form Disambiguated ID Type / Status
Subject Hilbert’s irreducibility theorem E43322 entity
Predicate hasVersion P455 FINISHED
Object arithmetic Hilbert irreducibility theorem E43322 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: arithmetic Hilbert irreducibility theorem | Statement: [Hilbert’s irreducibility theorem, hasVersion, arithmetic Hilbert irreducibility theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: arithmetic Hilbert irreducibility theorem
Context triple: [Hilbert’s irreducibility theorem, hasVersion, arithmetic Hilbert irreducibility theorem]
  • A. Hilbert’s irreducibility theorem chosen
    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.
  • B. Chebotarev density theorem
    The Chebotarev density theorem is a fundamental result in algebraic number theory that generalizes the prime number theorem to describe how often primes in a number field have a given Frobenius conjugacy class in its Galois group.
  • C. Hasse–Arf theorem
    The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
  • 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. Hasse norm theorem
    The Hasse norm theorem is a fundamental result in algebraic number theory that characterizes when an element of a global field is a norm from a cyclic extension by relating this property to its behavior in all completions of the field.
  • 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_69a88714cf2c819081644be450b8356e completed March 4, 2026, 7:25 p.m.
NER Named-entity recognition batch_69abb8640f30819080322bddb85881f1 completed March 7, 2026, 5:32 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae0ada17608190867681ee14aa217e completed March 8, 2026, 11:48 p.m.
Created at: March 4, 2026, 7:37 p.m.