Triple

T7997786
Position Surface form Disambiguated ID Type / Status
Subject Noether’s AF+BG theorem E186169 entity
Predicate alsoKnownAs P39 FINISHED
Object Noether’s theorem in algebraic geometry E186169 NE FINISHED

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: Noether’s theorem in algebraic geometry | Statement: [Noether’s AF+BG theorem, alsoKnownAs, Noether’s theorem in algebraic geometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Noether’s theorem in algebraic geometry
Context triple: [Noether’s AF+BG theorem, alsoKnownAs, Noether’s theorem in algebraic geometry]
  • A. Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem) chosen
    Noether’s AF+BG theorem is a foundational result in algebraic geometry that provides conditions under which a polynomial vanishing on the intersection of two plane curves can be expressed as a linear combination of their defining equations.
  • B. Chevalley’s theorem in algebraic geometry
    Chevalley’s theorem in algebraic geometry is a fundamental result stating that the image of a morphism of finite type between schemes (or varieties) is a constructible set, playing a key role in understanding how geometric properties behave under mappings.
  • C. Topological Methods in Algebraic Geometry
    Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
  • D. Adeles and Algebraic Groups
    "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
  • E. Grothendieck’s scheme-theoretic framework
    Grothendieck’s scheme-theoretic framework is a foundational reformulation of algebraic geometry that generalizes varieties using schemes, enabling powerful tools like sheaf theory, cohomology, and modern number-theoretic applications.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69ca829c6c308190ab05b43d234c52b2 completed March 30, 2026, 2:03 p.m.
NER Named-entity recognition batch_69cb3c98e39081908904d36a31bd6768 completed March 31, 2026, 3:16 a.m.
NED1 Entity disambiguation (via context triple) batch_69cbe10d5eb081909f257390094de442 completed March 31, 2026, 2:58 p.m.
Created at: March 30, 2026, 5:17 p.m.