Triple

T6716266
Position Surface form Disambiguated ID Type / Status
Subject Salomon Bochner E153275 entity
Predicate notableFor P22 FINISHED
Object Bochner technique in Riemannian geometry
The Bochner technique in Riemannian geometry is a method that uses Bochner-type identities and curvature conditions to derive vanishing theorems and rigidity results for differential forms and harmonic maps on manifolds.
E613408 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: Bochner technique in Riemannian geometry | Statement: [Salomon Bochner, notableFor, Bochner technique in Riemannian geometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bochner technique in Riemannian geometry
Context triple: [Salomon Bochner, notableFor, Bochner technique in Riemannian geometry]
  • A. Nirenberg problem in differential geometry
    The Nirenberg problem in differential geometry is a classical question about prescribing Gaussian curvature on the 2-sphere via conformal deformations of the metric.
  • B. Perelman’s entropy functionals
    Perelman’s entropy functionals are analytic quantities introduced by Grigori Perelman to study the behavior and singularities of the Ricci flow, playing a central role in his proof of the Poincaré and geometrization conjectures.
  • C. 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.
  • D. Cartan theorems A and B
    Cartan theorems A and B are fundamental results in complex analytic geometry that characterize coherent analytic sheaves on Stein spaces by guaranteeing the existence of enough global sections and the vanishing of higher cohomology.
  • E. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • 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: Bochner technique in Riemannian geometry
Triple: [Salomon Bochner, notableFor, Bochner technique in Riemannian geometry]
Generated description
The Bochner technique in Riemannian geometry is a method that uses Bochner-type identities and curvature conditions to derive vanishing theorems and rigidity results for differential forms and harmonic maps on manifolds.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bochner technique in Riemannian geometry
Target entity description: The Bochner technique in Riemannian geometry is a method that uses Bochner-type identities and curvature conditions to derive vanishing theorems and rigidity results for differential forms and harmonic maps on manifolds.
  • A. Nirenberg problem in differential geometry
    The Nirenberg problem in differential geometry is a classical question about prescribing Gaussian curvature on the 2-sphere via conformal deformations of the metric.
  • B. Perelman’s entropy functionals
    Perelman’s entropy functionals are analytic quantities introduced by Grigori Perelman to study the behavior and singularities of the Ricci flow, playing a central role in his proof of the Poincaré and geometrization conjectures.
  • C. 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.
  • D. Cartan theorems A and B
    Cartan theorems A and B are fundamental results in complex analytic geometry that characterize coherent analytic sheaves on Stein spaces by guaranteeing the existence of enough global sections and the vanishing of higher cohomology.
  • E. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • 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_69c68809b4608190a2509ddb5ab87f05 completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d125db3c8190aad28919226a16da completed March 27, 2026, 6:49 p.m.
NED1 Entity disambiguation (via context triple) batch_69c700993128819081614ccfa68d7320 completed March 27, 2026, 10:11 p.m.
NEDg Description generation batch_69c70262f3e48190b544be536ee0b674 completed March 27, 2026, 10:19 p.m.
NED2 Entity disambiguation (via description) batch_69c70311418c8190a902cf21187fdc51 completed March 27, 2026, 10:22 p.m.
Created at: March 27, 2026, 2:07 p.m.