Triple

T11534415
Position Surface form Disambiguated ID Type / Status
Subject Adolf Hurwitz E273508 entity
Predicate knownFor P22 FINISHED
Object Hurwitz zeta function
The Hurwitz zeta function is a complex analytic function that generalizes the Riemann zeta function by introducing a shift parameter, playing a key role in analytic number theory and special function theory.
E931273 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: Hurwitz zeta function | Statement: [Adolf Hurwitz, knownFor, Hurwitz zeta function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hurwitz zeta function
Context triple: [Adolf Hurwitz, knownFor, Hurwitz zeta function]
  • A. 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.
  • B. Riemann–Siegel theta function
    The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
  • C. Dirichlet eta function
    The Dirichlet eta function is an alternating Dirichlet series closely related to the Riemann zeta function and used in analytic number theory, particularly for studying series convergence and analytic continuation.
  • D. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • E. Riemann xi function
    The Riemann xi function is an entire, symmetrized version of the Riemann zeta function that encodes its nontrivial zeros and plays a central role in the study of the Riemann Hypothesis and related analytic number theory.
  • 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: Hurwitz zeta function
Triple: [Adolf Hurwitz, knownFor, Hurwitz zeta function]
Generated description
The Hurwitz zeta function is a complex analytic function that generalizes the Riemann zeta function by introducing a shift parameter, playing a key role in analytic number theory and special function theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hurwitz zeta function
Target entity description: The Hurwitz zeta function is a complex analytic function that generalizes the Riemann zeta function by introducing a shift parameter, playing a key role in analytic number theory and special function theory.
  • A. 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.
  • B. Riemann–Siegel theta function
    The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
  • C. Dirichlet eta function
    The Dirichlet eta function is an alternating Dirichlet series closely related to the Riemann zeta function and used in analytic number theory, particularly for studying series convergence and analytic continuation.
  • D. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • E. Riemann xi function
    The Riemann xi function is an entire, symmetrized version of the Riemann zeta function that encodes its nontrivial zeros and plays a central role in the study of the Riemann Hypothesis and related analytic number theory.
  • 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_69d6aae3fbec8190a14632a5df2538b6 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d8839b4bb48190b748ec4119f36c11 completed April 10, 2026, 4:59 a.m.
NED1 Entity disambiguation (via context triple) batch_69e6858af0d081909078d5862ec3d469 completed April 20, 2026, 7:59 p.m.
NEDg Description generation batch_69e68fd8210c8190a7b0bbd8a50ff6b1 completed April 20, 2026, 8:43 p.m.
NED2 Entity disambiguation (via description) batch_69e69f12cfcc8190a06e0922c9faa49e completed April 20, 2026, 9:48 p.m.
Created at: April 8, 2026, 9:37 p.m.