Triple

T19370557
Position Surface form Disambiguated ID Type / Status
Subject Cartan theorems A and B E484523 entity
Predicate influenced P9 FINISHED
Object Serre’s GAGA theorem — NE NERFINISHED

How this triple was built (2 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: Serre’s GAGA theorem | Statement: [Cartan theorems A and B, influenced, Serre’s GAGA theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Serre’s GAGA theorem
Context triple: [Cartan theorems A and B, influenced, Serre’s GAGA theorem]
  • A. Serre’s cohomological methods in algebraic geometry chosen
    Serre’s cohomological methods in algebraic geometry are foundational techniques that use sheaf cohomology to relate and study algebraic and analytic geometry, profoundly influencing modern algebraic geometry and complex geometry.
  • B. Serre’s theorem on projective embeddings via ample line bundles
    Serre’s theorem on projective embeddings via ample line bundles is a foundational result in algebraic geometry that characterizes when a variety can be embedded into projective space using sufficiently high tensor powers of an ample line bundle.
  • C. Zariski’s Main Theorem
    Zariski’s Main Theorem is a fundamental result in algebraic geometry that characterizes finite-type morphisms between varieties by relating birationality, normality, and the structure of fibers.
  • D. 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.
  • E. The Geometry of Schemes
    The Geometry of Schemes is a graduate-level textbook by David Eisenbud and Joe Harris that provides an accessible, example-driven introduction to the language and techniques of scheme theory in modern algebraic geometry.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8e8d305088190ad13571532aa454c completed April 10, 2026, 12:10 p.m.
NER Named-entity recognition batch_69e619af33e481908643f8beb2f498dc completed April 20, 2026, 12:18 p.m.
Created at: April 10, 2026, 1:35 p.m.