Triple
T2815452
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euler product formula for the Riemann zeta function |
E54270
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object |
Chebyshev functions
Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
|
E300761
|
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: Chebyshev functions | Statement: [Euler product formula for the Riemann zeta function, relatedConcept, Chebyshev functions]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Chebyshev functions Context triple: [Euler product formula for the Riemann zeta function, relatedConcept, Chebyshev functions]
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
Dirichlet L-functions
Dirichlet L-functions are complex analytic functions built from Dirichlet characters that generalize the Riemann zeta function and play a central role in number theory, particularly in the study of primes in arithmetic progressions.
-
E.
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.
- 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: Chebyshev functions Triple: [Euler product formula for the Riemann zeta function, relatedConcept, Chebyshev functions]
Generated description
Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Chebyshev functions Target entity description: Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
Dirichlet L-functions
Dirichlet L-functions are complex analytic functions built from Dirichlet characters that generalize the Riemann zeta function and play a central role in number theory, particularly in the study of primes in arithmetic progressions.
-
E.
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.
- 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_69ab49de0af08190b3da69683be1e728 |
completed | March 6, 2026, 9:40 p.m. |
| NER | Named-entity recognition | batch_69abde4d29488190a32461906dd9ea7e |
completed | March 7, 2026, 8:14 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69afce9f964081909e422aaf1f026dbb |
completed | March 10, 2026, 7:56 a.m. |
| NEDg | Description generation | batch_69afcf12e3a0819098f28d31434a0c5f |
completed | March 10, 2026, 7:58 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69afcf9c2d308190b111aa8038c9227a |
completed | March 10, 2026, 8 a.m. |
Created at: March 6, 2026, 9:59 p.m.