coreCondition
P19924
predicate
Indicates that something serves as the primary or fundamental condition that must hold for a situation, process, or relationship to apply.
All labels observed (16)
| Label | Occurrences |
|---|---|
| domainCondition | 43 |
| conditionFor | 30 |
| coreRequirement | 28 |
| equivalentCondition | 24 |
| givesConditionFor | 14 |
| coreCondition canonical | 12 |
| equilibriumCondition | 10 |
| definitionCondition | 8 |
| stabilityCondition | 5 |
| coreCriterion | 4 |
| definingCondition | 3 |
| requiresConditionOn | 3 |
| theoreticalCondition | 3 |
| الشرط_الأساسي | 2 |
| matrixCondition | 1 |
| unitCondition | 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: coreCondition
Generated description
Indicates that something serves as the primary or fundamental condition that must hold for a situation, process, or relationship to apply.
Sample triples (191)
| Subject | Object |
|---|---|
| Voting Rights Act requirements | prohibition of vote buying via predicate surface "coreRequirement" ⓘ |
| Voting Rights Act requirements | prohibition of threats against voters via predicate surface "coreRequirement" ⓘ |
| Lucas tree model | market clearing via predicate surface "equilibriumCondition" ⓘ |
| Lucas tree model | optimal consumption choice via predicate surface "equilibriumCondition" ⓘ |
| Lucas tree model | no-arbitrage pricing via predicate surface "equilibriumCondition" ⓘ |
| Dirichlet convolution | an arithmetic function is a unit iff f(1) ≠ 0 via predicate surface "unitCondition" ⓘ |
| Riemann ellipsoid | balance of self-gravity, pressure, and inertial forces via predicate surface "equilibriumCondition" ⓘ |
| Riemann ellipsoid | ellipsoidal surfaces of constant density and pressure via predicate surface "equilibriumCondition" ⓘ |
| tangent half-angle substitution | x not equal to odd multiples of π via predicate surface "domainCondition" ⓘ |
| Yao’s next-bit test | no efficient algorithm can predict the next bit significantly better than random guessing via predicate surface "coreRequirement" ⓘ |
| Carathéodory measurability criterion | additivity over intersections and complements ⓘ |
| Carathéodory measurability criterion | additivity over disjoint unions ⓘ |
| Carathéodory measurability criterion | Carathéodory condition for measurability ⓘ |
| Helly’s theorem | nonempty common intersection via predicate surface "givesConditionFor" ⓘ |
| open mapping theorem | continuous linear operator between Banach spaces via predicate surface "domainCondition" ⓘ |
| open mapping theorem | operator is surjective via predicate surface "domainCondition" ⓘ |
| Fermat primality test | a^(n-1) ≡ 1 (mod n) ⓘ |
| Wilson's theorem | n to be prime via predicate surface "givesConditionFor" ⓘ |
| Article 102 of the Charter of the United Nations | invoking treaties and international agreements before any organ of the United Nations via predicate surface "conditionFor" ⓘ |
| Artin–Wedderburn theorem | ring is semisimple if and only if it is isomorphic to a finite direct product of matrix rings over division rings via predicate surface "equivalentCondition" ⓘ |
| Artin–Wedderburn theorem | ring is semisimple if and only if its Jacobson radical is zero and it is Artinian via predicate surface "equivalentCondition" ⓘ |
| Jury test | all roots of the characteristic polynomial lie inside the unit circle via predicate surface "stabilityCondition" ⓘ |
| tâtonnement process | market demand equals market supply in all markets via predicate surface "equilibriumCondition" ⓘ |
| Euler’s reflection formula | z ∉ ℤ via predicate surface "domainCondition" ⓘ |
| Euler’s reflection formula | z not an integer via predicate surface "domainCondition" ⓘ |
| Bochner–Martinelli formula | bounded domain in \mathbb{C}^n with sufficiently smooth boundary via predicate surface "domainCondition" ⓘ |
| Dedekind domain | Noetherian + integrally closed + Krull dimension 1 via predicate surface "equivalentCondition" ⓘ |
| Dedekind domain | every nonzero ideal factors uniquely as a product of prime ideals via predicate surface "equivalentCondition" ⓘ |
| Dedekind domain | every localization at a nonzero prime ideal is a discrete valuation ring via predicate surface "equivalentCondition" ⓘ |
| Dedekind domain | every nonzero fractional ideal is invertible via predicate surface "equivalentCondition" ⓘ |
| Artinian ring | left Artinian and right Artinian are equivalent for semiprimary rings via predicate surface "equivalentCondition" ⓘ |
| Artinian ring | commutative Artinian ring is Noetherian with dimension zero via predicate surface "equivalentCondition" ⓘ |
| Artinian ring | commutative Artinian ring is Noetherian and has finitely many prime ideals via predicate surface "equivalentCondition" ⓘ |
| Artinian ring | commutative Artinian ring is Noetherian and every prime ideal is maximal via predicate surface "equivalentCondition" ⓘ |
| Freyd adjoint functor theorem | existence of left adjoint functor via predicate surface "givesConditionFor" ⓘ |
| Freyd adjoint functor theorem | existence of right adjoint functor via predicate surface "givesConditionFor" ⓘ |
| Jacobson radical | R/J(R) being semisimple Artinian when R is left Artinian via predicate surface "conditionFor" ⓘ |
| Jacobson radical | R/J(R) being semisimple when R is semiprimary via predicate surface "conditionFor" ⓘ |
| Medicaid Drug Rebate Program | Medicaid coverage of manufacturers’ outpatient drugs via predicate surface "conditionFor" ⓘ |
| Segré–Silberberg effect | net lateral force on particle equals zero via predicate surface "equilibriumCondition" ⓘ |
| Lusin–Souslin theorem | domain is a Borel subset of a Polish space via predicate surface "domainCondition" ⓘ |
| Legendre’s relation for elliptic integrals | 0 < k < 1 via predicate surface "domainCondition" ⓘ |
| Tinker substantial disruption test | material and substantial disruption to school operations via predicate surface "coreRequirement" ⓘ |
| Tinker substantial disruption test | infringement on the rights of others via predicate surface "coreRequirement" ⓘ |
| Riesz lemma | infinite-dimensional normed space via predicate surface "domainCondition" ⓘ |
| Riesz lemma | proper closed subspace via predicate surface "domainCondition" ⓘ |
| Brauer–Manin obstruction | existence of rational points via predicate surface "givesConditionFor" ⓘ |
| Brauer–Manin obstruction | density of rational points in adelic points via predicate surface "givesConditionFor" ⓘ |
| Federal-Aid Highway Act of 1962 | federal highway funding via predicate surface "conditionFor" ⓘ |
| Libya to cooperate with France, the United Kingdom and the United States | suspension of UN sanctions on Libya via predicate surface "conditionFor" ⓘ |