Triple
T1859189
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hilbert problems |
E41774
|
entity |
| Predicate | hasPart |
P35
|
FINISHED |
| Object |
Hilbert’s fifteenth problem
Hilbert’s fifteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the rigorous mathematical foundation and general theory of Schubert’s enumerative calculus in algebraic geometry.
|
E41774
|
NE FINISHED |
How this triple was built (4 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: Hilbert’s fifteenth problem | Statement: [Hilbert problems, hasPart, Hilbert’s fifteenth problem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hilbert’s fifteenth problem Context triple: [Hilbert problems, hasPart, Hilbert’s fifteenth problem]
-
A.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
-
B.
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.
-
C.
Hilbert’s tenth problem
Hilbert’s tenth problem is a famous unsolved question in mathematics that asked for a general algorithm to determine whether any given Diophantine equation has an integer solution, and whose negative answer helped establish fundamental limits of computability.
-
D.
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.
-
E.
Hilbert’s irreducibility theorem
Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Hilbert’s fifteenth problem Triple: [Hilbert problems, hasPart, Hilbert’s fifteenth problem]
Generated description
Hilbert’s fifteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the rigorous mathematical foundation and general theory of Schubert’s enumerative calculus in algebraic geometry.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hilbert’s fifteenth problem Target entity description: Hilbert’s fifteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the rigorous mathematical foundation and general theory of Schubert’s enumerative calculus in algebraic geometry.
-
A.
Hilbert problems
chosen
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
-
B.
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.
-
C.
Hilbert’s tenth problem
Hilbert’s tenth problem is a famous unsolved question in mathematics that asked for a general algorithm to determine whether any given Diophantine equation has an integer solution, and whose negative answer helped establish fundamental limits of computability.
-
D.
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.
-
E.
Hilbert’s irreducibility theorem
Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
- F. None of above.
Provenance (5 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_69a8864a83848190a4ec02721306c511 |
completed | March 4, 2026, 7:21 p.m. |
| NER | Named-entity recognition | batch_69abb0829f1481908d2b389d20827417 |
completed | March 7, 2026, 4:58 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69addf4ecdc08190a264b358d3883f70 |
completed | March 8, 2026, 8:42 p.m. |
| NEDg | Description generation | batch_69ade0628a3881908443346eab47656e |
completed | March 8, 2026, 8:47 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69ade0c545e08190b4469e93922d9b4b |
completed | March 8, 2026, 8:49 p.m. |
Created at: March 4, 2026, 7:33 p.m.