Triple
T10462110
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Selberg integral |
E246700
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Selberg trace formula |
E246698
|
NE FINISHED |
How this triple was built (2 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: Selberg trace formula | Statement: [Selberg integral, relatedTo, Selberg trace formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Selberg trace formula Context triple: [Selberg integral, relatedTo, Selberg trace formula]
-
A.
Selberg trace formula
chosen
The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
-
B.
Selberg class
The Selberg class is a collection of Dirichlet series with specific analytic properties introduced to generalize and axiomatize L-functions in number theory.
-
C.
Euler products for automorphic L-functions
Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
-
D.
Representation Theory and Automorphic Functions
"Representation Theory and Automorphic Functions" is a seminal mathematical work by Israel Gelfand that develops the connections between representation theory of groups and the theory of automorphic forms, with deep applications in number theory and harmonic analysis.
-
E.
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.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69d381c16c248190a2fe5b471e584e9c |
completed | April 6, 2026, 9:49 a.m. |
| NER | Named-entity recognition | batch_69d50884fac48190af22e181b1492557 |
completed | April 7, 2026, 1:37 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d89fcc84b48190a39de0d9b9111ebd |
completed | April 10, 2026, 6:59 a.m. |
Created at: April 6, 2026, 12:19 p.m.