Triple

T2689819
Position Surface form Disambiguated ID Type / Status
Subject Julius Plücker E57572 entity
Predicate notableWork P4 FINISHED
Object Plücker formulas
Plücker formulas are classical algebraic geometry relations that connect the degree and singularities of plane algebraic curves with the invariants of their dual curves.
E291201 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: Plücker formulas | Statement: [Julius Plücker, notableWork, Plücker formulas]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Plücker formulas
Context triple: [Julius Plücker, notableWork, Plücker formulas]
  • A. Clebsch–Aronhold invariants
    The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
  • B. Clebsch diagonal surfaces
    Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
  • C. 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.
  • D. Brill–Noether theory
    Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
  • E. Riemann–Hurwitz formula
    The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
  • 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: Plücker formulas
Triple: [Julius Plücker, notableWork, Plücker formulas]
Generated description
Plücker formulas are classical algebraic geometry relations that connect the degree and singularities of plane algebraic curves with the invariants of their dual curves.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Plücker formulas
Target entity description: Plücker formulas are classical algebraic geometry relations that connect the degree and singularities of plane algebraic curves with the invariants of their dual curves.
  • A. Clebsch–Aronhold invariants
    The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
  • B. Clebsch diagonal surfaces
    Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
  • C. 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.
  • D. Brill–Noether theory
    Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
  • E. Riemann–Hurwitz formula
    The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
  • 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_69ab4a5028388190a36f3baf1588309e completed March 6, 2026, 9:42 p.m.
NER Named-entity recognition batch_69abd9f380d48190953529d23688a328 completed March 7, 2026, 7:55 a.m.
NED1 Entity disambiguation (via context triple) batch_69afaf5e85bc81908ba1b1968cfa440a completed March 10, 2026, 5:42 a.m.
NEDg Description generation batch_69afafddb2a081909b891eed7ba5411d completed March 10, 2026, 5:45 a.m.
NED2 Entity disambiguation (via description) batch_69afb10304488190a1129efae36b3c4e completed March 10, 2026, 5:49 a.m.
Created at: March 6, 2026, 9:54 p.m.