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 |
|---|---|
| Schauder fixed-point theorem | convex subset via predicate surface "domainCondition" ⓘ |
| Schauder fixed-point theorem | subset is nonempty, closed, bounded, and convex via predicate surface "domainCondition" ⓘ |
| Boy Scouts of America Equal Access Act | receipt of certain federal education funds via predicate surface "conditionFor" ⓘ |
| Bragg's law | constructive interference of scattered waves via predicate surface "conditionFor" ⓘ |
| Lyapunov equation | existence of quadratic Lyapunov functions via predicate surface "conditionFor" ⓘ |
| Jacobi symbol | n is a positive odd integer via predicate surface "domainCondition" ⓘ |
|
Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem)
surface form:
Noether’s AF+BG theorem
|
membership in the ideal generated by two polynomials via predicate surface "givesConditionFor" ⓘ |
|
Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem)
surface form:
Noether’s AF+BG theorem
|
expressing a polynomial as AF+BG via predicate surface "givesConditionFor" ⓘ |
| small-gain theorem | product of gains less than one via predicate surface "coreRequirement" ⓘ |
| small-gain theorem | loop gain less than one via predicate surface "coreRequirement" ⓘ |
| Juvenile Justice and Delinquency Prevention Act of 1974 | deinstitutionalization of status offenders via predicate surface "coreRequirement" ⓘ |
| Juvenile Justice and Delinquency Prevention Act of 1974 | separation of juveniles from adult inmates in secure facilities via predicate surface "coreRequirement" ⓘ |
| Juvenile Justice and Delinquency Prevention Act of 1974 | removal of juveniles from adult jails and lockups via predicate surface "coreRequirement" ⓘ |
| Juvenile Justice and Delinquency Prevention Act of 1974 | reduction of disproportionate minority contact in juvenile justice systems via predicate surface "coreRequirement" ⓘ |
| Grothendieck category | is an abelian category with exact filtered colimits and a generator via predicate surface "definitionCondition" ⓘ |
| Grothendieck category | every object is a quotient of a coproduct of copies of a generator via predicate surface "definitionCondition" ⓘ |
| Grothendieck category | filtered colimits of exact sequences are exact via predicate surface "definitionCondition" ⓘ |
|
Hausdorff
surface form:
Hausdorff space
|
X is Hausdorff iff the diagonal Δ = {(x,x) : x ∈ X} is closed in X × X via predicate surface "equivalentCondition" ⓘ |
| Schwarz lemma | function holomorphic on the open unit disk via predicate surface "domainCondition" ⓘ |
| Dehn lemma | when a loop on the boundary of a 3-manifold bounds an embedded disk via predicate surface "givesConditionFor" ⓘ |
| Gibbs free energy | ΔG = 0 via predicate surface "equilibriumCondition" ⓘ |
| Pigouvian subsidy | optimal subsidy equals marginal external benefit at socially optimal quantity via predicate surface "theoreticalCondition" ⓘ |
| Pigouvian subsidy | requires knowledge of marginal social benefit curve via predicate surface "theoreticalCondition" ⓘ |
| Pigouvian subsidy | requires knowledge of marginal private benefit or cost via predicate surface "theoreticalCondition" ⓘ |
| Ledoux criterion | layer stable if stabilizing composition gradient overcomes destabilizing temperature gradient via predicate surface "stabilityCondition" ⓘ |
| Kruskal–Shafranov instability criterion | safety factor q must exceed 1 for stability against m=1 kink mode in a tokamak ⓘ |
| Kruskal–Shafranov instability criterion | plasma column becomes kink‑unstable when twist of field lines exceeds about one turn over column length ⓘ |
| Kruskal–Shafranov instability criterion | instability occurs when parallel current is too large relative to confining magnetic field ⓘ |
| Multistate Professional Responsibility Examination (MPRE) requirement | eligibility for bar admission via predicate surface "conditionFor" ⓘ |
| Multistate Professional Responsibility Examination (MPRE) requirement | swearing-in as an attorney in many jurisdictions via predicate surface "conditionFor" ⓘ |
| Disaster Mitigation Act of 2000 | eligibility for certain FEMA hazard mitigation grants via predicate surface "conditionFor" ⓘ |
| Karamata's inequality | finite sequences of real numbers via predicate surface "domainCondition" ⓘ |
| Karamata's inequality | sequences sorted in decreasing order via predicate surface "domainCondition" ⓘ |
| Closed Graph Theorem | domain is a Banach space via predicate surface "domainCondition" ⓘ |
| must be approved by Andorra Telecom | obtaining a .ad domain name via predicate surface "conditionFor" ⓘ |
| must be approved by Andorra Telecom | maintaining a .ad domain name via predicate surface "conditionFor" ⓘ |
| roentgen (unit) | standard temperature and pressure via predicate surface "definitionCondition" ⓘ |
| roentgen (unit) | dry air via predicate surface "definitionCondition" ⓘ |
| Banach–Stone theorem | X compact Hausdorff space via predicate surface "domainCondition" ⓘ |
| Banach–Stone theorem | Y compact Hausdorff space via predicate surface "domainCondition" ⓘ |
| Voting Rights Act requirements | ban on voting qualifications that discriminate on the basis of race or color via predicate surface "coreRequirement" ⓘ |
| Voting Rights Act requirements | ban on standards or procedures that result in denial or abridgment of the right to vote via predicate surface "coreRequirement" ⓘ |
| Voting Rights Act requirements | prohibition of literacy tests in covered jurisdictions via predicate surface "coreRequirement" ⓘ |
| Voting Rights Act requirements | prohibition of other discriminatory tests or devices via predicate surface "coreRequirement" ⓘ |
| Voting Rights Act requirements | requirement that voting changes not be adopted with discriminatory purpose via predicate surface "coreRequirement" ⓘ |
| Voting Rights Act requirements | requirement that voting changes not be adopted with discriminatory effect via predicate surface "coreRequirement" ⓘ |
| Voting Rights Act requirements | requirement to provide language assistance to certain language minority groups via predicate surface "coreRequirement" ⓘ |
| Voting Rights Act requirements | protection of assistance for voters who need help casting a ballot via predicate surface "coreRequirement" ⓘ |
| Voting Rights Act requirements | prohibition of voter intimidation via predicate surface "coreRequirement" ⓘ |
| Voting Rights Act requirements | prohibition of voter coercion via predicate surface "coreRequirement" ⓘ |