Hermite constant
E502193
The Hermite constant is a number in each dimension that measures the densest possible lattice sphere packing, playing a central role in the geometry of numbers and lattice theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Hermite constant canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5191867 — 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: Hermite constant Context triple: [Charles Hermite, hasConceptNamedAfter, Hermite constant]
-
A.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
-
B.
Khinchin–Lévy constant
The Khinchin–Lévy constant is a mathematical constant arising in metric number theory and continued fractions, describing the typical exponential growth rate of the denominators of convergents for almost all real numbers.
-
C.
Khinchin's constant
Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
-
D.
Waring's problem
Waring's problem is a famous conjecture in number theory that concerns representing natural numbers as sums of fixed powers of integers and determining how many such powers are needed.
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E.
Deuring–Heilbronn phenomenon
The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
- 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: Hermite constant Target entity description: The Hermite constant is a number in each dimension that measures the densest possible lattice sphere packing, playing a central role in the geometry of numbers and lattice theory.
-
A.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
-
B.
Khinchin–Lévy constant
The Khinchin–Lévy constant is a mathematical constant arising in metric number theory and continued fractions, describing the typical exponential growth rate of the denominators of convergents for almost all real numbers.
-
C.
Khinchin's constant
Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
-
D.
Waring's problem
Waring's problem is a famous conjecture in number theory that concerns representing natural numbers as sums of fixed powers of integers and determining how many such powers are needed.
-
E.
Deuring–Heilbronn phenomenon
The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
invariant in the geometry of numbers
ⓘ
mathematical constant ⓘ |
| achievedBy |
D_4 root lattice in dimension 4
ⓘ
E_8 root lattice in dimension 8 ⓘ Leech lattice in dimension 24 NERFINISHED ⓘ face-centered cubic lattice in dimension 3 ⓘ hexagonal lattice in dimension 2 ⓘ |
| appearsIn |
Hermite–Minkowski theorem
NERFINISHED
ⓘ
bounds for discriminants of number fields ⓘ |
| classificationStatus | exact values known only for finitely many dimensions ⓘ |
| codomain | positive real numbers ⓘ |
| definitionUses |
determinant of a lattice
ⓘ
shortest nonzero lattice vector ⓘ |
| dependsOn | dimension n ⓘ |
| describes | densest possible lattice sphere packing in dimension n ⓘ |
| domain | positive integers n ≥ 1 ⓘ |
| field |
geometry of numbers
ⓘ
lattice theory ⓘ |
| introducedInContextOf | reduction theory of positive definite quadratic forms ⓘ |
| isSequence | {γ_n}_n ⓘ |
| lowerBoundGrowth | Ω(n / log n) ⓘ |
| monotonicity | nondecreasing in n ⓘ |
| namedAfter | Charles Hermite NERFINISHED ⓘ |
| relatedTo |
E_8 lattice
NERFINISHED
ⓘ
Leech lattice NERFINISHED ⓘ Minkowski’s theorem NERFINISHED ⓘ covering radius of lattices ⓘ kissing number problem ⓘ lattices in Euclidean space ⓘ root lattices ⓘ sphere packing density ⓘ successive minima of lattices ⓘ |
| researchStatus | subject of ongoing research in high dimensions ⓘ |
| symbol | γ_n ⓘ |
| upperBoundGrowth | O(n) ⓘ |
| usedFor |
Minkowski-type inequalities
NERFINISHED
ⓘ
bounding minima of quadratic forms ⓘ studying densest lattice sphere packings ⓘ transference theorems in geometry of numbers ⓘ |
| usedIn |
coding theory via lattice codes
ⓘ
cryptography based on lattices ⓘ |
| γ_1 | 1 ⓘ |
| γ_2 | 2/√3 ⓘ |
| γ_24 | 4 ⓘ |
| γ_3 | 2^{1/3} ⓘ |
| γ_4 | 2^{1/2} ⓘ |
| γ_8 | 2 ⓘ |
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: Hermite constant Description of subject: The Hermite constant is a number in each dimension that measures the densest possible lattice sphere packing, playing a central role in the geometry of numbers and lattice theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.