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.