H10
E838585
H10 is the shorthand name for Hilbert’s tenth problem, a famous decision problem in number theory concerning the solvability of Diophantine equations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| H10 canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10055466 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: H10 Context triple: [Hilbert’s tenth problem, alsoKnownAs, H10]
-
A.
FH10
FH10 is a proprietary vector graphics file format associated with Macromedia FreeHand version 10, used for storing illustrations and page layouts.
-
B.
H130
The H130 is a light single-engine helicopter developed by Airbus Helicopters, widely used for passenger transport, sightseeing, and medical evacuation due to its spacious cabin and low noise levels.
-
C.
H160
The H160 is a next-generation medium twin-engine helicopter developed by Airbus Helicopters, designed for versatile missions such as offshore transport, emergency medical services, and corporate aviation.
-
D.
H 111
H 111 is the catalogue number assigned to Hector Berlioz’s dramatic legend "La damnation de Faust."
-
E.
H-1
H-1 is a major east–west Interstate highway on the island of Oʻahu in Hawaii, serving as a primary transportation corridor through Honolulu and surrounding areas.
- 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: H10 Target entity description: H10 is the shorthand name for Hilbert’s tenth problem, a famous decision problem in number theory concerning the solvability of Diophantine equations.
-
A.
FH10
FH10 is a proprietary vector graphics file format associated with Macromedia FreeHand version 10, used for storing illustrations and page layouts.
-
B.
H130
The H130 is a light single-engine helicopter developed by Airbus Helicopters, widely used for passenger transport, sightseeing, and medical evacuation due to its spacious cabin and low noise levels.
-
C.
H160
The H160 is a next-generation medium twin-engine helicopter developed by Airbus Helicopters, designed for versatile missions such as offshore transport, emergency medical services, and corporate aviation.
-
D.
H 111
H 111 is the catalogue number assigned to Hector Berlioz’s dramatic legend "La damnation de Faust."
-
E.
H-1
The H-1 was a liquid-fueled rocket engine developed in the United States and used on early Saturn launch vehicles during the Apollo era.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
Hilbert's tenth problem
ⓘ
mathematical problem ⓘ |
| alsoKnownAs |
Hilbert's tenth problem
ⓘ
linked to:
Hilbert’s tenth problem
|
| answerType | negative ⓘ |
| asksAbout |
existence of an algorithm for Diophantine solvability
ⓘ
solvability of Diophantine equations ⓘ |
| classification | undecidable problem ⓘ |
| concerns |
Diophantine equations
ⓘ
algorithmic decidability ⓘ recursively enumerable sets ⓘ undecidability ⓘ |
| field |
mathematical logic
ⓘ
number theory ⓘ |
| hasComplexityProperty | recursively unsolvable ⓘ |
| historicalContext | turn of the 20th century foundational questions in mathematics ⓘ |
| implies | undecidability of Diophantine equation solvability ⓘ |
| influenceOn |
computability in number theory
ⓘ
logic and foundations of mathematics ⓘ |
| involves |
integer solutions
ⓘ
polynomial equations with integer coefficients ⓘ |
| keyResult | every recursively enumerable set is Diophantine ⓘ |
| language | originally formulated in German ⓘ |
| notation | H10 ⓘ |
| openVariant |
Hilbert's tenth problem over number fields
ⓘ
linked to:
Hilbert’s tenth problem
Hilbert's tenth problem over the rationals ⓘ
linked to:
Hilbert’s tenth problem
|
| originalQuestion | To devise a process according to which it can be determined in a finite number of operations whether a given Diophantine equation is solvable in integers ⓘ |
| partOf |
Hilbert's problems
ⓘ
linked to:
Hilbert problems
|
| posedBy | David Hilbert ⓘ |
| positionInSeries | 10 ⓘ |
| presentedAt |
International Congress of Mathematicians 1900
ⓘ
linked to:
International Congress of Mathematicians
|
| relatedTo |
Church–Turing thesis
ⓘ
Davis–Putnam–Robinson–Matiyasevich theorem ⓘ Hilbert's problems ⓘ
linked to:
Hilbert problems
Turing machines ⓘ
linked to:
Turing machine
computability theory ⓘ |
| solutionCollectiveName | MRDP theorem ⓘ |
| solutionProperty | no algorithm exists that decides solvability of all Diophantine equations in integers ⓘ |
| solutionYear | 1970 ⓘ |
| solvedBy |
Hilary Putnam
ⓘ
Julia Robinson ⓘ Martin Davis ⓘ Yuri Matiyasevich ⓘ |
| status | unsolvable as stated ⓘ |
| yearPosed | 1900 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: H10 Description of subject: H10 is the shorthand name for Hilbert’s tenth problem, a famous decision problem in number theory concerning the solvability of Diophantine equations.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.