Gauss code
E656663
Gauss code is a combinatorial encoding of a knot or plane curve that records the sequence of crossings encountered along the curve.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Gauss code canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7338184 — 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: Gauss code Context triple: [Dowker–Thistlethwaite notation, relatedTo, Gauss code]
-
A.
Conway notation for knots
Conway notation for knots is a mathematical system introduced by John H. Conway that encodes knot and link diagrams into concise symbolic expressions to classify and study them.
-
B.
Gödel numbering
Gödel numbering is a method in mathematical logic that encodes symbols, formulas, and proofs as unique natural numbers, enabling arithmetic to represent and reason about syntactic statements.
-
C.
Golomb
Golomb is a station on the Carmelit underground funicular system in Haifa, Israel.
-
D.
gauss
The gauss is a unit of magnetic flux density in the centimeter–gram–second (CGS) system, commonly used in physics to measure the strength of magnetic fields.
-
E.
Alexander–Briggs notation
Alexander–Briggs notation is a classical system for naming and classifying knots in knot theory, assigning each distinct knot a unique label based on its crossing number and order in knot tables.
- 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: Gauss code Target entity description: Gauss code is a combinatorial encoding of a knot or plane curve that records the sequence of crossings encountered along the curve.
-
A.
Conway notation for knots
Conway notation for knots is a mathematical system introduced by John H. Conway that encodes knot and link diagrams into concise symbolic expressions to classify and study them.
-
B.
Gödel numbering
Gödel numbering is a method in mathematical logic that encodes symbols, formulas, and proofs as unique natural numbers, enabling arithmetic to represent and reason about syntactic statements.
-
C.
Golomb
Golomb is a station on the Carmelit underground funicular system in Haifa, Israel.
-
D.
gauss
The gauss is a unit of magnetic flux density in the centimeter–gram–second (CGS) system, commonly used in physics to measure the strength of magnetic fields.
-
E.
Alexander–Briggs notation
Alexander–Briggs notation is a classical system for naming and classifying knots in knot theory, assigning each distinct knot a unique label based on its crossing number and order in knot tables.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial encoding
ⓘ
knot invariant ⓘ |
| alternativeTo |
Dowker code
NERFINISHED
ⓘ
planar diagram notation ⓘ |
| appliesTo |
generic immersed closed curves in the plane
ⓘ
knot projections with transverse double points ⓘ |
| basedOn |
traversal of a knot diagram
ⓘ
traversal of a plane curve ⓘ |
| canBeExtendedTo | virtual knot theory ⓘ |
| captures | combinatorial structure of crossings ⓘ |
| constraint | each crossing label appears exactly twice ⓘ |
| describes |
knot
ⓘ
plane curve ⓘ |
| doesNotFullyDetermine | embedding in three-dimensional space ⓘ |
| encodes |
order of crossings along a curve
ⓘ
orientation information of a knot diagram ⓘ over-under information at crossings ⓘ sequence of crossings ⓘ |
| field |
combinatorics
ⓘ
knot theory ⓘ topology ⓘ |
| limitation | not every abstract Gauss code is realizable as a planar knot diagram ⓘ |
| namedAfter | Carl Friedrich Gauss NERFINISHED ⓘ |
| relatedTo |
Dowker–Thistlethwaite code
NERFINISHED
ⓘ
Gauss diagram NERFINISHED ⓘ Reidemeister moves NERFINISHED ⓘ knot diagram ⓘ oriented Gauss code ⓘ planar graph embeddings ⓘ signed Gauss code ⓘ |
| representationForm |
sequence of labels
ⓘ
word over an alphabet of crossing labels ⓘ |
| requires |
choice of orientation of the curve
ⓘ
choice of starting point on the curve ⓘ |
| studiedIn |
knot tabulation
ⓘ
topological graph theory ⓘ |
| usedFor |
algorithmic manipulation of knots
ⓘ
classification of knots ⓘ computer representation of knot diagrams ⓘ reconstruction of knot diagrams up to equivalence ⓘ |
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: Gauss code Description of subject: Gauss code is a combinatorial encoding of a knot or plane curve that records the sequence of crossings encountered along the curve.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.