Triple

T14265261
Position Surface form Disambiguated ID Type / Status
Subject Tarski’s theorem on the completeness of elementary algebra and geometry E353627 entity
Predicate field P3 FINISHED
Object real algebraic geometry E761266 NE FINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

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: real algebraic geometry | Statement: [Tarski’s theorem on the completeness of elementary algebra and geometry, field, real algebraic geometry]

Disambiguation candidates (1 decision)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: real algebraic geometry
Context triple: [Tarski’s theorem on the completeness of elementary algebra and geometry, field, real algebraic geometry]
  • A. Géométrie algébrique
    Géométrie algébrique is a French-language textbook that introduces the fundamental concepts and methods of modern algebraic geometry.
  • B. Positivstellensatz chosen
    The Positivstellensatz is a fundamental result in real algebraic geometry that characterizes when a polynomial that is positive on a semialgebraic set can be represented using sums of squares and polynomial inequalities.
  • C. Hilbert’s Nullstellensatz
    Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
  • D. Foundations of Algebraic Geometry
    Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 batches)

Stage Batch ID Job type Status
creating batch_69d8278c43e08190824146f4632b89a5 elicitation completed
NER batch_69de6357a8188190ba518a486521052b ner completed
NED1 batch_69fd326551b08190ae8fe220a6422339 ned_source_triple completed
Created at: April 10, 2026, 1:09 a.m.