Triple

T8970014
Position Surface form Disambiguated ID Type / Status
Subject Fritz Noether E214240 entity
Predicate notableWork P4 FINISHED
Object Noether boundary value problems
Noether boundary value problems are a class of boundary value problems in the theory of partial differential equations characterized by conditions ensuring well-posedness and finite-dimensional solution spaces, developed by mathematician Fritz Noether.
E770192 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: Noether boundary value problems | Statement: [Fritz Noether, notableWork, Noether boundary value problems]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Noether boundary value problems
Context triple: [Fritz Noether, notableWork, Noether boundary value problems]
  • A. Hilbert’s nineteenth problem
    Hilbert’s nineteenth problem is one of David Hilbert’s famous list of 23 problems, asking whether solutions to regular variational problems are always analytic.
  • B. "Invariante Variationsprobleme"
    "Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
  • C. 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.
  • D. Morawetz inequalities
    Morawetz inequalities are fundamental energy and decay estimates in the study of partial differential equations, especially wave and dispersive equations, that provide control over the long-time behavior of solutions.
  • E. Sturm–Liouville problem
    The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
  • 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: Noether boundary value problems
Triple: [Fritz Noether, notableWork, Noether boundary value problems]
Generated description
Noether boundary value problems are a class of boundary value problems in the theory of partial differential equations characterized by conditions ensuring well-posedness and finite-dimensional solution spaces, developed by mathematician Fritz Noether.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Noether boundary value problems
Target entity description: Noether boundary value problems are a class of boundary value problems in the theory of partial differential equations characterized by conditions ensuring well-posedness and finite-dimensional solution spaces, developed by mathematician Fritz Noether.
  • A. Hilbert’s nineteenth problem
    Hilbert’s nineteenth problem is one of David Hilbert’s famous list of 23 problems, asking whether solutions to regular variational problems are always analytic.
  • B. "Invariante Variationsprobleme"
    "Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
  • C. 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.
  • D. Morawetz inequalities
    Morawetz inequalities are fundamental energy and decay estimates in the study of partial differential equations, especially wave and dispersive equations, that provide control over the long-time behavior of solutions.
  • E. Sturm–Liouville problem
    The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
  • 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_69ca839dbf608190a2f5990477115d29 completed March 30, 2026, 2:07 p.m.
NER Named-entity recognition batch_69cc6765babc8190a4a3b79aa21047c8 completed April 1, 2026, 12:31 a.m.
NED1 Entity disambiguation (via context triple) batch_69cfc96006e48190978e4ccdedc48b41 completed April 3, 2026, 2:06 p.m.
NEDg Description generation batch_69cfcb178d488190ab8ea897f964c10a completed April 3, 2026, 2:13 p.m.
NED2 Entity disambiguation (via description) batch_69cfcc1bb3248190ac94ed37be2dcde4 completed April 3, 2026, 2:18 p.m.
Created at: March 30, 2026, 7:02 p.m.