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.