Triple

T10641497
Position Surface form Disambiguated ID Type / Status
Subject Plancherel theorem for real reductive groups E250731 entity
Predicate isImportantFor P1887 FINISHED
Object the 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: the Arthur trace formula | Statement: [Plancherel theorem for real reductive groups, isImportantFor, the Arthur trace formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: the Arthur trace formula
Context triple: [Plancherel theorem for real reductive groups, isImportantFor, the 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. 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. 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.
  • E. 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.
  • 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_69d6aa5a4c4881908f39be6efe5981e5 completed April 8, 2026, 7:19 p.m.
NER Named-entity recognition batch_69d6dfcd19648190882380d2c90be486 completed April 8, 2026, 11:07 p.m.
NED1 Entity disambiguation (via context triple) batch_69d97a4555e48190be39c0a7698b4282 completed April 10, 2026, 10:31 p.m.
Created at: April 8, 2026, 9:05 p.m.