Triple

T5212075
Position Surface form Disambiguated ID Type / Status
Subject Weyl law E117656 entity
Predicate originallyFormulatedFor P53028 FINISHED
Object Dirichlet Laplacian on bounded domains in R^n E466251 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: Dirichlet Laplacian on bounded domains in R^n | Statement: [Weyl law, originallyFormulatedFor, Dirichlet Laplacian on bounded domains in R^n]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Dirichlet Laplacian on bounded domains in R^n
Context triple: [Weyl law, originallyFormulatedFor, Dirichlet Laplacian on bounded domains in R^n]
  • A. Neumann boundary conditions in potential theory
    Neumann boundary conditions in potential theory specify that the normal derivative of a potential function on a boundary is prescribed, modeling situations where flux across the boundary is controlled rather than the potential itself.
  • B. Dirichlet problem chosen
    The Dirichlet problem is a fundamental boundary value problem in potential theory and partial differential equations, asking for a function that solves a specified PDE inside a domain while taking prescribed values on the domain’s boundary.
  • C. Sobolev spaces
    Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
  • D. Hilbert–Schmidt operators
    Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
  • E. Monge–Ampère equation
    The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
  • 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_69bd4464ba3c8190bc16b2ebbe42ddb0 completed March 20, 2026, 12:58 p.m.
NER Named-entity recognition batch_69bd7a7166848190805152142e184529 completed March 20, 2026, 4:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69beefdee940819098e397ab50f57411 completed March 21, 2026, 7:22 p.m.
Created at: March 20, 2026, 1:47 p.m.