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.