Triple

T373777
Position Surface form Disambiguated ID Type / Status
Subject Bernhard Riemann E8325 entity
Predicate knownFor P22 FINISHED
Object Riemann zeta function
The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
E47609 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: Riemann zeta function | Statement: [Bernhard Riemann, knownFor, Riemann zeta function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Riemann zeta function
Context triple: [Bernhard Riemann, knownFor, Riemann zeta function]
  • A. Riemann hypothesis
    The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
  • B. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • C. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • D. Riemann–Roch theorem
    The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
  • E. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • 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: Riemann zeta function
Triple: [Bernhard Riemann, knownFor, Riemann zeta function]
Generated description
The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Riemann zeta function
Target entity description: The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
  • A. Riemann hypothesis
    The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
  • B. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • C. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • D. Riemann–Roch theorem
    The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
  • E. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • 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_69a2e7f2ec648190b42bc7db424f8109 completed Feb. 28, 2026, 1:04 p.m.
NER Named-entity recognition batch_69a2ec13b9b48190b294d998c6720132 completed Feb. 28, 2026, 1:22 p.m.
NED1 Entity disambiguation (via context triple) batch_69a3f4da5b2881909f71546e714c7883 completed March 1, 2026, 8:12 a.m.
NEDg Description generation batch_69a3f544f4d48190ae1adb4b0f1fd438 completed March 1, 2026, 8:13 a.m.
NED2 Entity disambiguation (via description) batch_69a3f5932d888190bb1444d6372b1294 completed March 1, 2026, 8:15 a.m.
Created at: Feb. 28, 2026, 1:08 p.m.