Triple

T4202362
Position Surface form Disambiguated ID Type / Status
Subject Solomon Lefschetz E86097 entity
Predicate familyName P18 FINISHED
Object Lefschetz
Lefschetz is a surname most notably associated with Solomon Lefschetz, a pioneering mathematician in algebraic topology and geometry.
E420791 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: Lefschetz | Statement: [Solomon Lefschetz, familyName, Lefschetz]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lefschetz
Context triple: [Solomon Lefschetz, familyName, Lefschetz]
  • A. Lefschetz operator
    The Lefschetz operator is a linear operator in Kähler geometry that acts on differential forms by wedging with the Kähler form, playing a central role in the Hard Lefschetz theorem and Hodge theory.
  • B. Lefschetz fixed-point theorem
    The Lefschetz fixed-point theorem is a fundamental result in algebraic topology that relates the number of fixed points of a continuous map on a topological space to traces of the induced maps on its homology groups.
  • C. Clebsch
    Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
  • D. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • E. Plücker
    Plücker is a German surname most notably associated with Julius Plücker, a 19th-century mathematician and physicist known for his contributions to analytic and projective geometry.
  • 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: Lefschetz
Triple: [Solomon Lefschetz, familyName, Lefschetz]
Generated description
Lefschetz is a surname most notably associated with Solomon Lefschetz, a pioneering mathematician in algebraic topology and geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lefschetz
Target entity description: Lefschetz is a surname most notably associated with Solomon Lefschetz, a pioneering mathematician in algebraic topology and geometry.
  • A. Lefschetz operator
    The Lefschetz operator is a linear operator in Kähler geometry that acts on differential forms by wedging with the Kähler form, playing a central role in the Hard Lefschetz theorem and Hodge theory.
  • B. Lefschetz fixed-point theorem
    The Lefschetz fixed-point theorem is a fundamental result in algebraic topology that relates the number of fixed points of a continuous map on a topological space to traces of the induced maps on its homology groups.
  • C. Clebsch
    Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
  • D. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • E. Plücker
    Plücker is a German surname most notably associated with Julius Plücker, a 19th-century mathematician and physicist known for his contributions to analytic and projective geometry.
  • 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_69aed93b89f48190a31f6d57c760e42f completed March 9, 2026, 2:29 p.m.
NER Named-entity recognition batch_69af037f1de4819088d6bf544317a694 completed March 9, 2026, 5:29 p.m.
NED1 Entity disambiguation (via context triple) batch_69b58a173a78819094915f63c8411602 completed March 14, 2026, 4:17 p.m.
NEDg Description generation batch_69b58e1e7bc08190b75486c74953f609 completed March 14, 2026, 4:34 p.m.
NED2 Entity disambiguation (via description) batch_69b58e7a208481909056b6fba4597bf4 completed March 14, 2026, 4:36 p.m.
Created at: March 9, 2026, 3:49 p.m.