Triple
T10462027
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Selberg trace formula |
E246698
|
entity |
| Predicate | generalizedBy |
P2372
|
FINISHED |
| Object | Arthur trace formula |
E865100
|
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: Arthur trace formula | Statement: [Selberg trace formula, generalizedBy, Arthur trace formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Arthur trace formula Context triple: [Selberg trace formula, generalizedBy, Arthur trace formula]
-
A.
Arthur trace formula
chosen
The Arthur trace formula is a far-reaching generalization of the Selberg trace formula that provides a powerful analytic tool for studying automorphic representations and establishing instances of the Langlands program.
-
B.
Selberg trace formula
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.
-
C.
Gutzwiller trace formula
The Gutzwiller trace formula is a semiclassical tool in quantum chaos that links the quantum energy spectrum of a system to the properties of its classical periodic orbits.
-
D.
Hecke operators
Hecke operators are algebraic operators acting on modular forms that play a central role in number theory, particularly in understanding congruences, L-functions, and the arithmetic of modular forms.
-
E.
Sato–Tate distribution (for families of elliptic curves)
The Sato–Tate distribution (for families of elliptic curves) is a probabilistic law describing how the normalized Frobenius traces (or equivalently, the angles in the Hasse bound) of elliptic curves are distributed, typically following a specific sine-squared measure on the interval [0, π].
- 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_69d8dc4fbc3481909b214137f26e243b |
completed | April 10, 2026, 11:17 a.m. |
Created at: April 6, 2026, 12:19 p.m.