Triple

T8850262

Position	Surface form	Disambiguated ID	Type / Status
Subject	Hilbert’s seventeenth problem	`E210619`	entity
Predicate	relatedTo	`P37`	FINISHED
Object	Positivstellensatz 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.	`E761266`	NE FINISHED

Disambiguation candidates (2 decisions)

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: Positivstellensatz
Context triple: [Hilbert’s seventeenth problem, relatedTo, Positivstellensatz]

A. 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.
B. Hilbert’s seventeenth problem
Hilbert’s seventeenth problem is a famous question in real algebraic geometry asking whether every nonnegative polynomial can be represented as a sum of squares of rational functions.
C. Chevalley–Warning theorem
The Chevalley–Warning theorem is a result in number theory and algebraic geometry that gives conditions under which systems of polynomial equations over finite fields must have nontrivial solutions.
D. Hilbert’s fourteenth problem
Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
E. Hilbert basis theorem
The Hilbert basis theorem is a fundamental result in commutative algebra stating that if a ring is Noetherian then any polynomial ring over it is also Noetherian, ensuring that ideals in such rings are finitely generated.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Positivstellensatz
Target entity description: 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.

A. 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.
B. Hilbert’s seventeenth problem
Hilbert’s seventeenth problem is a famous question in real algebraic geometry asking whether every nonnegative polynomial can be represented as a sum of squares of rational functions.
C. Chevalley–Warning theorem
The Chevalley–Warning theorem is a result in number theory and algebraic geometry that gives conditions under which systems of polynomial equations over finite fields must have nontrivial solutions.
D. Hilbert’s fourteenth problem
Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
E. Hilbert basis theorem
The Hilbert basis theorem is a fundamental result in commutative algebra stating that if a ring is Noetherian then any polynomial ring over it is also Noetherian, ensuring that ideals in such rings are finitely generated.
F. None of above. chosen

Provenance (5 batches)

Stage	Batch ID	Job type	Status
creating	`batch_69ca838a424c8190b1ecac115c2927e7`	elicitation	completed
NER	`batch_69cc60abb0748190af41d4e1f419e39c`	ner	completed
NED1	`batch_69cf89cb853c8190a7664f2e7de0de87`	ned_source_triple	completed
NED2	`batch_69cf8bd252a4819098891bbb67baf897`	ned_description	completed
NEDg	`batch_69cf8ab7da348190b423f0768fe9dc1a`	nedg	completed

Created at: March 30, 2026, 6:49 p.m.