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.