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 |
|---|---|
| law of mass action | rate = k ∏[reactant_i]^{ν_i} via predicate surface "mathematicalForm" ⓘ |
| law of mass action | K = ∏a_product^{ν_product} / ∏a_reactant^{ν_reactant} via predicate surface "mathematicalForm" ⓘ |
| Poisson kernel | P_r(θ) = (1 - r^2) / (1 - 2r cos θ + r^2) for 0 ≤ r < 1 via predicate surface "hasFormula" ⓘ |
| Poisson kernel | P(x,y) = (1/π) · y / (x^2 + y^2) for the upper half-plane via predicate surface "hasFormula" ⓘ |
| Poisson integral | P_r(\theta) = \frac{1-r^2}{1-2r\cos\theta + r^2} via predicate surface "kernelFormula" ⓘ |
| Flory–Huggins solution theory | Gm/RT = φ1 ln φ1 + φ2 ln φ2 + χ φ1 φ2 for binary mixtures via predicate surface "mathematicalForm" ⓘ |
| Sylvester sequence | \sum_{n=1}^{\infty} 1/a_n = 1 via predicate surface "formula" ⓘ |
| Carothers equation | X_n = 1 / (1 - p) via predicate surface "mathematicalForm" ⓘ |
| Bergson–Samuelson social welfare function | real-valued function of individual utilities W(u1, u2, …, un) via predicate surface "mathematicalForm" ⓘ |
| Zames–Falb multipliers | convolution operators in time domain via predicate surface "mathematicalForm" ⓘ |
| Zames–Falb multipliers | multiplicative frequency-domain transfer functions via predicate surface "mathematicalForm" ⓘ |
| Casimir operator | C = \sum_i X_i X^i for basis {X_i} and dual basis {X^i} via predicate surface "hasFormula" ⓘ |
|
papal bull Unam Sanctam
surface form:
Unam Sanctam
|
Unam sanctam ecclesiam catholicam et ipsam apostolicam via predicate surface "openingFormula" ⓘ |
| Leibniz rule | (f g)' = f' g + f g' via predicate surface "hasFormula" ⓘ |
| Burnside's lemma | |X/G| = (1/|G|) * Σ_{g∈G} |Fix(g)| via predicate surface "formula" ⓘ |
| Casimir effect | F = -\frac{\pi^2 \hbar c}{240 a^4} for ideal parallel plates via predicate surface "hasFormula" ⓘ |
| Rindler wedge | subset of Minkowski spacetime defined by |t| < x in 1+1 dimensions (right wedge) via predicate surface "mathematicalForm" ⓘ |
| Rindler wedge | subset of Minkowski spacetime defined by x > |t| in 1+1 dimensions (right wedge) via predicate surface "mathematicalForm" ⓘ |
|
Zipf
surface form:
Zipf's law
|
frequency is inversely proportional to rank via predicate surface "hasFormula" ⓘ |
| Zipf's law | f(r) ∝ 1/r via predicate surface "mathematicalForm" ⓘ |
| Zipf's law | f(r) = C / r^s via predicate surface "mathematicalForm" ⓘ |
| Mersenne’s laws of vibrating strings | f ∝ 1 / L via predicate surface "mathematicalForm" ⓘ |
| Mersenne’s laws of vibrating strings | f ∝ √T via predicate surface "mathematicalForm" ⓘ |
| Mersenne’s laws of vibrating strings | f ∝ 1 / √μ via predicate surface "mathematicalForm" ⓘ |
| Mersenne’s laws of vibrating strings | f = (1 / 2L) · √(T / μ) via predicate surface "combinedFormula" ⓘ |
| Liouville's theorem in Hamiltonian mechanics | volume-preserving flow on a symplectic manifold via predicate surface "mathematicalForm" ⓘ |
| Reynolds number | Re = (ρ v L) / μ via predicate surface "formula" ⓘ |
| Reynolds number | Re = (v L) / ν via predicate surface "formula" ⓘ |
| Landen transformations | transformation mapping k to 2√k/(1+k) via predicate surface "hasFormula" ⓘ |
| Landen transformations | transformation mapping k to (1−√(1−k^2))/(1+√(1−k^2)) via predicate surface "hasFormula" ⓘ |
| Rossby number | Ro = U / (f L) via predicate surface "typicalFormula" ⓘ |
| Spearman–Brown prophecy formula | ρ_new = (k · ρ_old) / (1 + (k − 1) · ρ_old) via predicate surface "hasFormula" ⓘ |
| source coding theorem | L̄ ≥ H(X) for any uniquely decodable code via predicate surface "mathematicalForm" ⓘ |
| source coding theorem | for every ε > 0 there exists a code with L̄ < H(X) + ε via predicate surface "mathematicalForm" ⓘ |
| R_K | R_K = h / e^2 via predicate surface "hasFormula" ⓘ |
| Rydberg–Ritz combination principle | ν_ij = T_i − T_j via predicate surface "mathematicalForm" ⓘ |
| Paschen series | 1/λ = R_H (1/3² − 1/n²), n>3 via predicate surface "formula" ⓘ |
| Hamilton's rule | rb > c via predicate surface "coreFormula" ⓘ |
| Kohlrausch law of independent migration of ions | Λm∞ = λ+∞ + λ−∞ for a 1:1 electrolyte via predicate surface "mathematicalForm" ⓘ |
| Kohlrausch law of independent migration of ions | Λm∞ = ν+ λ+∞ + ν− λ−∞ for a ν+:ν− electrolyte via predicate surface "mathematicalForm" ⓘ |
| Buffon’s needle problem | P(cross) = 2L / (πT) for L ≤ T via predicate surface "hasFormula" ⓘ |
| Taylor–Proudman theorem | Coriolis term balances pressure gradient in the momentum equations via predicate surface "mathematicalForm" ⓘ |
| Taylor–Proudman theorem | derivative of velocity along rotation axis is approximately zero via predicate surface "mathematicalForm" ⓘ |
| Cover’s theorem | bound on number of linearly separable labelings of points via predicate surface "mathematicalForm" ⓘ |
| Planck power | P_P = c^5 / G via predicate surface "hasFormula" ⓘ |
| International Geomagnetic Reference Field | spherical harmonic expansion via predicate surface "mathematicalForm" ⓘ |
| Bloch–Torrey equation | time derivative of magnetization equals Bloch terms plus diffusion term via predicate surface "mathematicalForm" ⓘ |
| Liouville–von Neumann equation | operator differential equation via predicate surface "mathematicalForm" ⓘ |
| Fellgett advantage | SNR improvement proportional to square root of number of multiplexed channels (under ideal conditions) via predicate surface "mathematicalForm" ⓘ |
| Darcy’s law | linear relationship between flux and pressure gradient via predicate surface "mathematicalForm" ⓘ |