Triple
T2171615
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Riemann–Siegel formula |
E48437
|
entity |
| Predicate | standardReference |
P33736
|
FINISHED |
| Object |
E. C. Titchmarsh, The Theory of the Riemann Zeta-Function
"E. C. Titchmarsh, The Theory of the Riemann Zeta-Function" is a classic monograph in analytic number theory that provides a comprehensive and authoritative treatment of the Riemann zeta function and related topics.
|
E239281
|
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: E. C. Titchmarsh, The Theory of the Riemann Zeta-Function | Statement: [Riemann–Siegel formula, standardReference, E. C. Titchmarsh, The Theory of the Riemann Zeta-Function]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: E. C. Titchmarsh, The Theory of the Riemann Zeta-Function Context triple: [Riemann–Siegel formula, standardReference, E. C. Titchmarsh, The Theory of the Riemann Zeta-Function]
-
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.
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.
-
C.
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.
-
D.
Multiplicative Number Theory
Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
-
E.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
- 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: E. C. Titchmarsh, The Theory of the Riemann Zeta-Function Triple: [Riemann–Siegel formula, standardReference, E. C. Titchmarsh, The Theory of the Riemann Zeta-Function]
Generated description
"E. C. Titchmarsh, The Theory of the Riemann Zeta-Function" is a classic monograph in analytic number theory that provides a comprehensive and authoritative treatment of the Riemann zeta function and related topics.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: E. C. Titchmarsh, The Theory of the Riemann Zeta-Function Target entity description: "E. C. Titchmarsh, The Theory of the Riemann Zeta-Function" is a classic monograph in analytic number theory that provides a comprehensive and authoritative treatment of the Riemann zeta function and related topics.
-
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.
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.
-
C.
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.
-
D.
Multiplicative Number Theory
Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
-
E.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
- 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_69a88aa3faa48190995b233af6525815 |
completed | March 4, 2026, 7:40 p.m. |
| NER | Named-entity recognition | batch_69abbec7f9088190b32127421e340788 |
completed | March 7, 2026, 5:59 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ae58f6c8c8819081a06861f6133fe9 |
completed | March 9, 2026, 5:21 a.m. |
| NEDg | Description generation | batch_69ae5989f054819082f36e5515bec3ca |
completed | March 9, 2026, 5:24 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69ae5a12f11c81908cc345905f0a485e |
completed | March 9, 2026, 5:26 a.m. |
Created at: March 4, 2026, 7:45 p.m.