Triple

T12597203
Position Surface form Disambiguated ID Type / Status
Subject Mertens’ theorems E300762 entity
Predicate namedAfter P63 FINISHED
Object Austrian mathematician Franz Mertens
Franz Mertens was an Austrian mathematician best known for his contributions to number theory, including results related to the Möbius function and the distribution of prime numbers.
 E992322 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: Austrian mathematician Franz Mertens | Statement: [Mertens’ theorems, namedAfter, Austrian mathematician Franz Mertens]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Austrian mathematician Franz Mertens
Context triple: [Mertens’ theorems, namedAfter, Austrian mathematician Franz Mertens]
  • A. Charles-Jean de la Vallée Poussin
    Charles-Jean de la Vallée Poussin was a Belgian mathematician renowned for his foundational work in analysis and number theory, including an independent first proof of the prime number theorem.
  • B. Edmund Landau
    Edmund Landau was a prominent German mathematician known for his foundational work in analytic number theory and the rigorous development of mathematical analysis.
  • C. Kurt Mahler
    Kurt Mahler was a German-born British mathematician renowned for his contributions to number theory and transcendental number theory, including Mahler's classification and Mahler measure.
  • D. Kurt Hensel
    Kurt Hensel was a German mathematician best known for introducing p-adic numbers, which became fundamental in number theory and algebraic geometry.
  • E. Jacques Hadamard
    Jacques Hadamard was a prominent French mathematician known for his fundamental contributions to number theory, complex analysis, and partial differential equations, including the prime number theorem and the concept of well-posed problems.
  • 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: Austrian mathematician Franz Mertens
Triple: [Mertens’ theorems, namedAfter, Austrian mathematician Franz Mertens]
Generated description
Franz Mertens was an Austrian mathematician best known for his contributions to number theory, including results related to the Möbius function and the distribution of prime numbers.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Austrian mathematician Franz Mertens
Target entity description: Franz Mertens was an Austrian mathematician best known for his contributions to number theory, including results related to the Möbius function and the distribution of prime numbers.
  • A. Charles-Jean de la Vallée Poussin
    Charles-Jean de la Vallée Poussin was a Belgian mathematician renowned for his foundational work in analysis and number theory, including an independent first proof of the prime number theorem.
  • B. Edmund Landau
    Edmund Landau was a prominent German mathematician known for his foundational work in analytic number theory and the rigorous development of mathematical analysis.
  • C. Kurt Mahler
    Kurt Mahler was a German-born British mathematician renowned for his contributions to number theory and transcendental number theory, including Mahler's classification and Mahler measure.
  • D. Kurt Hensel
    Kurt Hensel was a German mathematician best known for introducing p-adic numbers, which became fundamental in number theory and algebraic geometry.
  • E. Jacques Hadamard
    Jacques Hadamard was a prominent French mathematician known for his fundamental contributions to number theory, complex analysis, and partial differential equations, including the prime number theorem and the concept of well-posed problems.
  • 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_69d7bdea2ca881908f379526c13b1145 completed April 9, 2026, 2:55 p.m.
NER Named-entity recognition batch_69d954cf33b88190bff339fcd3142cc8 completed April 10, 2026, 7:51 p.m.
NED1 Entity disambiguation (via context triple) batch_69f65ec75fc08190aa13cbb0161eb35c completed May 2, 2026, 8:29 p.m.
NEDg Description generation batch_69f6605bca10819086966e1574c31318 completed May 2, 2026, 8:36 p.m.
NED2 Entity disambiguation (via description) batch_69f6617997188190bfce14c54619af7f completed May 2, 2026, 8:41 p.m.
Created at: April 9, 2026, 5:08 p.m.