Triple

T7997787
Position Surface form Disambiguated ID Type / Status
Subject Noether’s AF+BG theorem E186169 entity
Predicate alsoKnownAs P39 FINISHED
Object Noether’s AF+BG theorem in plane curves 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 AF+BG theorem in plane curves | Statement: [Noether’s AF+BG theorem, alsoKnownAs, Noether’s AF+BG theorem in plane curves]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Noether’s AF+BG theorem in plane curves
Context triple: [Noether’s AF+BG theorem, alsoKnownAs, Noether’s AF+BG theorem in plane curves]
  • 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. Theorie der algebraischen Kurven
    "Theorie der algebraischen Kurven" is a foundational 19th-century mathematical treatise by Julius Plücker that systematically develops the geometry and classification of algebraic curves.
  • C. Clebsch–Aronhold invariants
    The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
  • D. 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.
  • E. Clebsch diagonal surfaces
    Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
  • 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.