Triple

T10389148
Position Surface form Disambiguated ID Type / Status
Subject Weil divisor E244844 entity
Predicate relatedTo P37 FINISHED
Object Cartier divisor
A Cartier divisor is a type of divisor on an algebraic variety defined locally by a single rational function, corresponding to an invertible sheaf and generalizing the notion of a principal divisor.
E860118 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: Cartier divisor | Statement: [Weil divisor, relatedTo, Cartier divisor]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cartier divisor
Context triple: [Weil divisor, relatedTo, Cartier divisor]
  • A. Weil divisor
    A Weil divisor is a formal integer linear combination of irreducible subvarieties of codimension one on an algebraic variety, used to study its geometric and arithmetic properties.
  • B. 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.
  • C. Lefschetz pencil
    A Lefschetz pencil is a geometric structure on an algebraic variety given by a one-parameter family of hyperplane sections with only isolated, well-controlled singularities, fundamental in the study of its topology and geometry.
  • D. Chern classes
    Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
  • E. 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.
  • 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: Cartier divisor
Triple: [Weil divisor, relatedTo, Cartier divisor]
Generated description
A Cartier divisor is a type of divisor on an algebraic variety defined locally by a single rational function, corresponding to an invertible sheaf and generalizing the notion of a principal divisor.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cartier divisor
Target entity description: A Cartier divisor is a type of divisor on an algebraic variety defined locally by a single rational function, corresponding to an invertible sheaf and generalizing the notion of a principal divisor.
  • A. Weil divisor
    A Weil divisor is a formal integer linear combination of irreducible subvarieties of codimension one on an algebraic variety, used to study its geometric and arithmetic properties.
  • B. 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.
  • C. Lefschetz pencil
    A Lefschetz pencil is a geometric structure on an algebraic variety given by a one-parameter family of hyperplane sections with only isolated, well-controlled singularities, fundamental in the study of its topology and geometry.
  • D. Chern classes
    Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
  • E. 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.
  • 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_69d381b5116081908d85227bab6d3c0c completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4e9b40dd8819080ac839487020a44 completed April 7, 2026, 11:25 a.m.
NED1 Entity disambiguation (via context triple) batch_69d795b2423c8190a7c0e9b6fcbcc6db completed April 9, 2026, 12:04 p.m.
NEDg Description generation batch_69d7998acbf881909b6f063c4bf2d0a6 completed April 9, 2026, 12:20 p.m.
NED2 Entity disambiguation (via description) batch_69d79aa0cc5481908bc14cda8fb6e8b1 completed April 9, 2026, 12:25 p.m.
Created at: April 6, 2026, 12:05 p.m.