Triple

T2394171
Position Surface form Disambiguated ID Type / Status
Subject Riemann zeta function E47609 entity
Predicate universalityProperty P37894 FINISHED
Object Voronin universality theorem
The Voronin universality theorem is a result in analytic number theory stating that, in a precise sense, the Riemann zeta function can approximate any non-vanishing analytic function arbitrarily well on certain regions of the complex plane.
E262116 NE FINISHED

How this triple was built (5 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: Voronin universality theorem | Statement: [Riemann zeta function, universalityProperty, Voronin universality theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Voronin universality theorem
Context triple: [Riemann zeta function, universalityProperty, Voronin universality theorem]
  • A. 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.
  • B. Deuring–Heilbronn phenomenon
    The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
  • 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 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.
  • E. Euler product formula for the Riemann zeta function
    The Euler product formula for the Riemann zeta function is a fundamental identity in analytic number theory that expresses the zeta function as an infinite product over all prime numbers, revealing a deep connection between primes and the distribution of integers.
  • 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: Voronin universality theorem
Triple: [Riemann zeta function, universalityProperty, Voronin universality theorem]
Generated description
The Voronin universality theorem is a result in analytic number theory stating that, in a precise sense, the Riemann zeta function can approximate any non-vanishing analytic function arbitrarily well on certain regions of the complex plane.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Voronin universality theorem
Target entity description: The Voronin universality theorem is a result in analytic number theory stating that, in a precise sense, the Riemann zeta function can approximate any non-vanishing analytic function arbitrarily well on certain regions of the complex plane.
  • A. 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.
  • B. Deuring–Heilbronn phenomenon
    The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
  • 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 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.
  • E. Euler product formula for the Riemann zeta function
    The Euler product formula for the Riemann zeta function is a fundamental identity in analytic number theory that expresses the zeta function as an infinite product over all prime numbers, revealing a deep connection between primes and the distribution of integers.
  • F. None of above. chosen
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: universalityProperty
Context triple: [Riemann zeta function, universalityProperty, Voronin universality theorem]
  • A. generalizationProperty
    Indicates that one property is a more general, overarching version of another property, capturing a broader or more abstract relationship.
  • B. isUniversal
    Indicates that the relationship or property holds for all relevant entities or cases without exception.
  • C. convergenceProperty
    Indicates that one entity has a convergence-related characteristic or behavior with respect to another entity, such as approaching a limit or stabilizing under repeated application.
  • D. functorialityProperty
    Indicates that a mapping between categories preserves the structure of composition and identity morphisms, behaving consistently with the rules of a functor.
  • E. viewOnUniversals
    Indicates a philosophical stance or theory an entity holds regarding the nature and existence of universals (e.g., whether they are real, conceptual, or merely linguistic).
  • F. None of above. chosen

Provenance (7 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_69a88a1c450c81909f61abb8b6863885 completed March 4, 2026, 7:38 p.m.
NER Named-entity recognition batch_69abc87827d88190bb2351a688e6de32 completed March 7, 2026, 6:40 a.m.
NED1 Entity disambiguation (via context triple) batch_69aeb3da0978819094584cb23194fb3a completed March 9, 2026, 11:49 a.m.
NEDg Description generation batch_69aeb46f882881909294a3698ead865e completed March 9, 2026, 11:52 a.m.
NED2 Entity disambiguation (via description) batch_69aeb4c715a88190b1009a2cf1d95441 completed March 9, 2026, 11:53 a.m.
PD Predicate disambiguation batch_69abc5a3825c81909ec6111dfc165453 completed March 7, 2026, 6:28 a.m.
PDg Predicate description generation batch_69abc664317c8190a6bb5a5065c21bde completed March 7, 2026, 6:32 a.m.
Created at: March 4, 2026, 7:57 p.m.