keyFormula
P2310
predicate
Indicates that a formula serves as the primary or defining expression associated with an entity or relationship.
All labels observed (35)
| Label | Occurrences |
|---|---|
| mathematicalForm | 239 |
| hasFormula | 74 |
| formula | 24 |
| openingFormula | 15 |
| hasKeyFormula | 14 |
| containsFormula | 10 |
| coreFormula | 7 |
| satisfiesEquation | 7 |
| coreEquation | 6 |
| keyFormula canonical | 4 |
| mathematicalExpression | 4 |
| costSharingFormula | 3 |
| definitionFormula | 3 |
| famousFormula | 3 |
| keyFormulaOfCategoricalImperative | 3 |
| typicalFormula | 3 |
| centralFormula | 2 |
| standardFormula | 2 |
| GOEFormula | 1 |
| GUEFormula | 1 |
| bracketFormula | 1 |
| codeRateFormula | 1 |
| combinedFormula | 1 |
| commonFormula | 1 |
| definedByFormula | 1 |
| establishedFormula | 1 |
| formulaInFrequencyForm | 1 |
| hasEntropyFormula | 1 |
| hasFormulaForShift | 1 |
| kernelFormula | 1 |
| keyStatementFormula | 1 |
| mainFormula | 1 |
| originalFormulaFor | 1 |
| primeFormula | 1 |
| usesSchedulingFormula | 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: keyFormula
Generated description
Indicates that a formula serves as the primary or defining expression associated with an entity or relationship.
Sample triples (440)
| Subject | Object |
|---|---|
| Landau collision operator | velocity-space divergence of a flux in velocity space via predicate surface "mathematicalForm" ⓘ |
| Burkert profile | two-parameter density profile via predicate surface "mathematicalForm" ⓘ |
| Sérsic profile | I(R) = I_e * exp{-b_n[(R/R_e)^{1/n} - 1]} via predicate surface "mathematicalForm" ⓘ |
| Shephard’s lemma | ∂C(w,y)/∂w_i = x_i(w,y) via predicate surface "mathematicalForm" ⓘ |
| Shephard’s lemma | ∂e(p,u)/∂p_i = h_i(p,u) via predicate surface "mathematicalForm" ⓘ |
| Jensen–Shannon divergence | JSD(P‖Q) = 1/2 KL(P‖M) + 1/2 KL(Q‖M) via predicate surface "formula" ⓘ |
| Herbrand quotient | h(G,M) = |H^0(G,M)| / |H^1(G,M)| when both groups are finite via predicate surface "hasFormula" ⓘ |
| Wright's law | power law relationship between cost and cumulative production via predicate surface "mathematicalForm" ⓘ |
| Sachs–Wolfe effect | temperature fluctuation proportional to gravitational potential divided by c squared via predicate surface "mathematicalForm" ⓘ |
| zeroth law of thermodynamics | equivalence relation on thermal equilibrium states via predicate surface "mathematicalForm" ⓘ |
|
The Matching Law
surface form:
Matching Law
|
R1/(R1+R2) = r1/(r1+r2) via predicate surface "mathematicalForm" ⓘ |
|
The Matching Law
surface form:
Matching Law
|
B1/(B1+B2) = R1/(R1+R2) via predicate surface "mathematicalForm" ⓘ |
| PMNS matrix | 3×3 complex matrix via predicate surface "mathematicalForm" ⓘ |
| Joule’s law of heating | Q = I^2 R t via predicate surface "hasFormula" ⓘ |
| Joule’s law of heating | Q ∝ I^2 R t via predicate surface "mathematicalForm" ⓘ |
| Chabrier initial mass function | log-normal plus power-law function of stellar mass via predicate surface "mathematicalForm" ⓘ |
|
Laplace's rule of succession (as a special case)
surface form:
Laplace's rule of succession
|
(s+1)/(n+2) via predicate surface "formula" ⓘ |
|
Laplace's rule of succession (as a special case)
surface form:
Laplace's rule of succession
|
posterior mean of Beta(s+1,n-s+1) distribution via predicate surface "mathematicalForm" ⓘ |
| Transverse Mercator | spherical formulation via predicate surface "mathematicalForm" ⓘ |
| Transverse Mercator | ellipsoidal formulation via predicate surface "mathematicalForm" ⓘ |
| Schuster–Schwarzschild theorem | solution of the radiative transfer equation with simplified boundary conditions via predicate surface "mathematicalForm" ⓘ |
| -5/3 law | E(k) ∝ ε^(2/3) k^(-5/3) via predicate surface "mathematicalForm" ⓘ |
|
Bell’s theorem
surface form:
Bell's theorem
|
Bell inequalities on correlation functions via predicate surface "mathematicalForm" ⓘ |
|
FTC
surface form:
Fundamental Theorem of Calculus
|
If F is an antiderivative of f on [a,b], then ∫_a^b f(x) dx = F(b) − F(a) via predicate surface "hasFormula" ⓘ |
|
FTC
surface form:
Fundamental Theorem of Calculus
|
If f is continuous on [a,b] and F(x)=∫_a^x f(t) dt, then F′(x)=f(x) via predicate surface "hasFormula" ⓘ |
| Koebe function | k(z) = z / (1 - z)^2 via predicate surface "hasFormula" ⓘ |
| Shields number | θ = τ / [(ρ_s − ρ) g d] via predicate surface "mathematicalForm" ⓘ |
| Kuznets curve | nonlinear relationship via predicate surface "mathematicalForm" ⓘ |
| New Keynesian Phillips Curve | current inflation depends on expected future inflation and real marginal cost via predicate surface "coreEquation" ⓘ |
| Shapiro delay | logarithmic dependence on impact parameter in weak-field limit via predicate surface "mathematicalForm" ⓘ |
| Varignon’s theorem in statics | M_O(F) = r × F via predicate surface "mathematicalForm" ⓘ |
| Varignon’s theorem in statics | M_O(F) = Σ M_O(F_i) via predicate surface "mathematicalForm" ⓘ |
| Israeli policy of nuclear ambiguity | Israel will not be the first to introduce nuclear weapons into the Middle East via predicate surface "keyStatementFormula" ⓘ |
| Cramér–Wold theorem | If a^T X and a^T Y have the same distribution for all a in R^n, then X and Y have the same distribution via predicate surface "mathematicalForm" ⓘ |
| Phong reflection model | sum of ambient, diffuse, and specular terms via predicate surface "mathematicalForm" ⓘ |
| Schwarz–Christoffel mapping | f(z)=A∫∏(ζ−z_k)^{α_k−1} dζ + B, where α_k are interior angle parameters via predicate surface "hasFormula" ⓘ |
| Triratna | I take refuge in the Buddha via predicate surface "hasFormula" ⓘ |
| Triratna | I take refuge in the Dharma via predicate surface "hasFormula" ⓘ |
| Triratna | I take refuge in the Sangha via predicate surface "hasFormula" ⓘ |
| Lefschetz number | L(f) = Σ_k (-1)^k tr(f_* | H_k(X)) via predicate surface "definitionFormula" ⓘ |