Triple
T2228054
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | André Weil |
E48698
|
entity |
| Predicate | notableConcept |
P201
|
FINISHED |
| Object |
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.
|
E244844
|
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: Weil divisor | Statement: [André Weil, notableConcept, Weil divisor]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Weil divisor Context triple: [André Weil, notableConcept, Weil divisor]
-
A.
Riemann–Roch theorem
The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
-
B.
Hasse–Weil zeta function
The Hasse–Weil zeta function is an analytic object in number theory that encodes arithmetic information about algebraic varieties over number fields, generalizing the Riemann zeta function and playing a central role in modern arithmetic geometry and conjectures like the Weil conjectures and the Birch–Swinnerton-Dyer conjecture.
-
C.
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.
-
D.
Zariski topology
The Zariski topology is a fundamental topology in algebraic geometry, defined on the spectrum of a ring or an algebraic variety, whose closed sets correspond to solution sets of polynomial equations.
-
E.
Deuring reduction theorem
The Deuring reduction theorem is a result in number theory that relates the reduction of elliptic curves with complex multiplication modulo primes to the theory of quaternion algebras and endomorphism rings.
- 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: Weil divisor Triple: [André Weil, notableConcept, Weil divisor]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Weil divisor Target entity description: 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.
-
A.
Riemann–Roch theorem
The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
-
B.
Hasse–Weil zeta function
The Hasse–Weil zeta function is an analytic object in number theory that encodes arithmetic information about algebraic varieties over number fields, generalizing the Riemann zeta function and playing a central role in modern arithmetic geometry and conjectures like the Weil conjectures and the Birch–Swinnerton-Dyer conjecture.
-
C.
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.
-
D.
Zariski topology
The Zariski topology is a fundamental topology in algebraic geometry, defined on the spectrum of a ring or an algebraic variety, whose closed sets correspond to solution sets of polynomial equations.
-
E.
Deuring reduction theorem
The Deuring reduction theorem is a result in number theory that relates the reduction of elliptic curves with complex multiplication modulo primes to the theory of quaternion algebras and endomorphism rings.
- 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_69a88aa51b388190949868ec9766e587 |
completed | March 4, 2026, 7:40 p.m. |
| NER | Named-entity recognition | batch_69abc0670ce48190b98814064bff0517 |
completed | March 7, 2026, 6:06 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ae6567b64c8190ab718f20bbf033df |
completed | March 9, 2026, 6:15 a.m. |
| NEDg | Description generation | batch_69ae666bd32c81909ff15201757a6c76 |
completed | March 9, 2026, 6:19 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69ae66d8ba688190a2102c00fc6231c4 |
completed | March 9, 2026, 6:21 a.m. |
Created at: March 4, 2026, 7:47 p.m.