Triple

T5570622
Position Surface form Disambiguated ID Type / Status
Subject Fermat's theorem on sums of two squares E146190 entity
Predicate relatedTo P37 FINISHED
Object Dirichlet's theorem on arithmetic progressions E466245 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: Dirichlet's theorem on arithmetic progressions | Statement: [Fermat's theorem on sums of two squares, relatedTo, Dirichlet's theorem on arithmetic progressions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dirichlet's theorem on arithmetic progressions
Context triple: [Fermat's theorem on sums of two squares, relatedTo, Dirichlet's theorem on arithmetic progressions]
  • A. Dirichlet's theorem on arithmetic progressions chosen
    Dirichlet's theorem on arithmetic progressions is a fundamental result in number theory stating that any arithmetic progression with first term and difference coprime contains infinitely many prime numbers.
  • B. Bateman–Horn conjecture
    The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
  • C. Vinogradov's three-primes theorem
    Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
  • D. Green–Tao theorem
    The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
  • E. Über die Anzahl der Primzahlen unter einer gegebenen Grösse
    Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
  • 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_69c008ffed108190a084602227af6157 completed March 22, 2026, 3:21 p.m.
NER Named-entity recognition batch_69c020502a288190af37f9ebb88fccae completed March 22, 2026, 5:01 p.m.
NED1 Entity disambiguation (via context triple) batch_69c0284bb71881908c0ac4ea2a302327 completed March 22, 2026, 5:35 p.m.
Created at: March 22, 2026, 3:37 p.m.