Triple

T10269761
Position Surface form Disambiguated ID Type / Status
Subject Shiing-Shen Chern E240802 entity
Predicate notableStudent P4838 FINISHED
Object S. S. Chern school of differential geometry
The S. S. Chern school of differential geometry is a mathematical tradition and research lineage in differential geometry founded and shaped by Shiing-Shen Chern and his students, known for its deep contributions to global differential geometry and characteristic classes.
E853115 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: S. S. Chern school of differential geometry | Statement: [Shiing-Shen Chern, notableStudent, S. S. Chern school of differential geometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: S. S. Chern school of differential geometry
Context triple: [Shiing-Shen Chern, notableStudent, S. S. Chern school of differential 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. Chern–Weil theory
    Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
  • C. Atiyah–Singer index theorem
    The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
  • D. Donaldson–Uhlenbeck–Yau theorem
    The Donaldson–Uhlenbeck–Yau theorem is a fundamental result in differential and algebraic geometry that characterizes when a holomorphic vector bundle over a compact Kähler manifold admits a Hermitian–Einstein metric, linking geometric stability with the existence of such metrics.
  • E. 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.
  • 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: S. S. Chern school of differential geometry
Triple: [Shiing-Shen Chern, notableStudent, S. S. Chern school of differential geometry]
Generated description
The S. S. Chern school of differential geometry is a mathematical tradition and research lineage in differential geometry founded and shaped by Shiing-Shen Chern and his students, known for its deep contributions to global differential geometry and characteristic classes.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: S. S. Chern school of differential geometry
Target entity description: The S. S. Chern school of differential geometry is a mathematical tradition and research lineage in differential geometry founded and shaped by Shiing-Shen Chern and his students, known for its deep contributions to global differential geometry and characteristic classes.
  • 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. Chern–Weil theory
    Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
  • C. Atiyah–Singer index theorem
    The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
  • D. Donaldson–Uhlenbeck–Yau theorem
    The Donaldson–Uhlenbeck–Yau theorem is a fundamental result in differential and algebraic geometry that characterizes when a holomorphic vector bundle over a compact Kähler manifold admits a Hermitian–Einstein metric, linking geometric stability with the existence of such metrics.
  • E. 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.
  • 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_69d381a94c1881908fc38fc263d9b9c2 completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4d270fb088190ba43b6f24e881b94 completed April 7, 2026, 9:46 a.m.
NED1 Entity disambiguation (via context triple) batch_69d6f80c25888190a3e8a2c513df7043 completed April 9, 2026, 12:51 a.m.
NEDg Description generation batch_69d6fcaca55c81908a48ac2a0ce24b85 completed April 9, 2026, 1:11 a.m.
NED2 Entity disambiguation (via description) batch_69d6fd772bc08190bf270f5fc767fb29 completed April 9, 2026, 1:14 a.m.
Created at: April 6, 2026, 11:35 a.m.