holdsFor
P12018
predicate
Indicates that a particular relationship or condition remains true over a specified interval or duration of time.
All labels observed (5)
| Label | Occurrences |
|---|---|
| holdsFor canonical | 180 |
| holdsOn | 11 |
| giltFür | 8 |
| trueFor | 8 |
| hedgingHorizon | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: holdsFor
Generated description
Indicates that a particular relationship or condition remains true over a specified interval or duration of time.
Sample triples (208)
| Subject | Object |
|---|---|
| black hole no-hair theorem | uncharged rotating black holes described by the Kerr metric ⓘ |
| black hole no-hair theorem | charged rotating black holes described by the Kerr–Newman metric ⓘ |
| black hole no-hair theorem | non-rotating uncharged black holes described by the Schwarzschild metric ⓘ |
| Whitney embedding theorem | non-compact smooth manifolds ⓘ |
| Whitney embedding theorem | compact smooth manifolds ⓘ |
| Girsanov theorem | filtered probability spaces via predicate surface "holdsOn" ⓘ |
| Eurodollar futures | short-term interest rate exposures up to several years ahead via predicate surface "hedgingHorizon" ⓘ |
| Pauli exclusion principle | electrons ⓘ |
| Pauli exclusion principle | protons ⓘ |
| Pauli exclusion principle | neutrons ⓘ |
| Pauli exclusion principle | quarks ⓘ |
| Pauli exclusion principle | any half-integer spin particle ⓘ |
| Pascal's identity | integers n ≥ 1 ⓘ |
| Pascal's identity | integers k with 0 ≤ k ≤ n ⓘ |
|
Gauss’s lemma (number theory)
linked to:
Gauss’s lemma in number theory
|
integers a with gcd(a,p)=1 ⓘ |
| Hilbert basis theorem | R[x] when R is Noetherian ⓘ |
| Hilbert basis theorem | R[x_1,\dots,x_n] when R is Noetherian ⓘ |
| Hilbert’s syzygy theorem | polynomial rings in finitely many variables over a field ⓘ |
| Hilbert’s syzygy theorem | finitely generated graded modules over a standard graded polynomial ring ⓘ |
| Riemann–Lebesgue lemma | compactly supported integrable functions ⓘ |
| Riemann–Lebesgue lemma | absolutely integrable functions ⓘ |
| Permanent Representative of the People’s Republic of China to the United Nations |
People’s Republic of China’s seat on the United Nations Security Council
ⓘ
linked to:
United Nations Security Council
|
| LSZ reduction formula | in and out asymptotic fields ⓘ |
| Whitney approximation theorem | maps between manifolds with boundary under suitable compatibility conditions ⓘ |
| Euler’s polyhedron formula | Platonic solids ⓘ |
| Euler’s polyhedron formula | tetrahedron ⓘ |
| Euler’s polyhedron formula | cube ⓘ |
| Euler’s polyhedron formula | octahedron ⓘ |
| Euler’s polyhedron formula | dodecahedron ⓘ |
| Euler’s polyhedron formula | icosahedron ⓘ |
| Bianchi identities | Levi-Civita connection of any metric ⓘ |
| Bianchi identities | curvature of any linear connection ⓘ |
| Cameron–Martin theorem | centered Gaussian measures ⓘ |
| Cameron–Martin theorem | non-degenerate Gaussian measures ⓘ |
| Tucker’s lemma | triangulations of the n-dimensional sphere via predicate surface "holdsOn" ⓘ |
|
Jensen's inequality
linked to:
Jensen inequality
|
finite sums ⓘ |
|
Jensen's inequality
linked to:
Jensen inequality
|
integrals ⓘ |
|
Jensen's inequality
linked to:
Jensen inequality
|
probability measures ⓘ |
|
Jensen's inequality
linked to:
Jensen inequality
|
discrete distributions ⓘ |
|
Jensen's inequality
linked to:
Jensen inequality
|
continuous distributions ⓘ |
| all-or-none principle in nerve excitation | individual axons ⓘ |
| Wigner–Eckart theorem | discrete angular momentum spectra ⓘ |
| uncertainty principle | all quantum systems ⓘ |
| Weyl character formula | complex semisimple Lie algebras ⓘ |
| Weyl character formula | connected compact Lie groups ⓘ |
| Lagrange's four-square theorem | 0 as 0^2 + 0^2 + 0^2 + 0^2 ⓘ |
| Poincaré–Bendixson theorem | plane via predicate surface "holdsOn" ⓘ |
| Poincaré–Bendixson theorem | two-dimensional sphere via predicate surface "holdsOn" ⓘ |
| Poincaré–Hopf theorem | compact oriented manifolds ⓘ |
| Poincaré–Hopf theorem | compact manifolds with boundary under suitable conditions ⓘ |