Triple

T10389151
Position Surface form Disambiguated ID Type / Status
Subject Weil divisor E244844 entity
Predicate relatedTo P37 FINISHED
Object Picard group
The Picard group is an algebraic invariant of a variety or scheme that classifies line bundles (or divisor classes) up to isomorphism, playing a central role in algebraic geometry.
E860119 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: Picard group | Statement: [Weil divisor, relatedTo, Picard group]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Picard group
Context triple: [Weil divisor, relatedTo, Picard group]
  • A. Grothendieck group
    The Grothendieck group is an algebraic construction that formally turns a commutative monoid (often arising from isomorphism classes of objects like vector bundles or modules) into an abelian group, playing a central role in K-theory and modern algebraic geometry.
  • B. Brauer group
    The Brauer group is an algebraic structure that classifies equivalence classes of central simple algebras over a field (or more general schemes), playing a key role in number theory, algebraic geometry, and cohomology.
  • C. Weil group
    The Weil group is an extension of the absolute Galois group introduced by André Weil to refine class field theory and play a central role in the formulation of the local and global Langlands correspondences.
  • D. Pontryagin classes
    Pontryagin classes are characteristic classes associated with real vector bundles that capture topological information about the bundle’s curvature and play a central role in differential topology and geometry.
  • E. Alexander–Spanier cohomology
    Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
  • 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: Picard group
Triple: [Weil divisor, relatedTo, Picard group]
Generated description
The Picard group is an algebraic invariant of a variety or scheme that classifies line bundles (or divisor classes) up to isomorphism, playing a central role in algebraic geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Picard group
Target entity description: The Picard group is an algebraic invariant of a variety or scheme that classifies line bundles (or divisor classes) up to isomorphism, playing a central role in algebraic geometry.
  • A. Grothendieck group
    The Grothendieck group is an algebraic construction that formally turns a commutative monoid (often arising from isomorphism classes of objects like vector bundles or modules) into an abelian group, playing a central role in K-theory and modern algebraic geometry.
  • B. Brauer group
    The Brauer group is an algebraic structure that classifies equivalence classes of central simple algebras over a field (or more general schemes), playing a key role in number theory, algebraic geometry, and cohomology.
  • C. Weil group
    The Weil group is an extension of the absolute Galois group introduced by André Weil to refine class field theory and play a central role in the formulation of the local and global Langlands correspondences.
  • D. Pontryagin classes
    Pontryagin classes are characteristic classes associated with real vector bundles that capture topological information about the bundle’s curvature and play a central role in differential topology and geometry.
  • E. Alexander–Spanier cohomology
    Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
  • 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.