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 |
|---|---|
| Randles–Ševčík equation | peak current proportional to square root of scan rate via predicate surface "mathematicalForm" ⓘ |
| Randles–Ševčík equation | peak current proportional to square root of diffusion coefficient via predicate surface "mathematicalForm" ⓘ |
| Randles–Ševčík equation | peak current proportional to concentration of electroactive species via predicate surface "mathematicalForm" ⓘ |
| modular j-invariant | j(τ) = 1728 E4(τ)^3 / (E4(τ)^3 - E6(τ)^2) via predicate surface "hasFormula" ⓘ |
| modular j-invariant | j(τ) = 1728 g_2(τ)^3 / (g_2(τ)^3 - 27 g_3(τ)^2) via predicate surface "hasFormula" ⓘ |
| Memorial Acclamation | We proclaim your Death, O Lord, and profess your Resurrection until you come again. via predicate surface "hasFormula" ⓘ |
| Memorial Acclamation | When we eat this Bread and drink this Cup, we proclaim your Death, O Lord, until you come again. via predicate surface "hasFormula" ⓘ |
| Memorial Acclamation | Save us, Savior of the world, for by your Cross and Resurrection you have set us free. via predicate surface "hasFormula" ⓘ |
| Euler–Poisson equations | first-order nonlinear ordinary differential equations via predicate surface "mathematicalForm" ⓘ |
| Kovalevskaya integral | quartic polynomial in phase-space variables (up to canonical transformations) via predicate surface "mathematicalForm" ⓘ |
| Krating Daeng | Red Bull via predicate surface "originalFormulaFor" NERFINISHED ⓘ |
| Pearson correlation coefficient | r = cov(X,Y) / (σ_X σ_Y) via predicate surface "formula" ⓘ |
| Pearson correlation coefficient | r = Σ[(x_i - x̄)(y_i - ȳ)] / sqrt[Σ(x_i - x̄)² Σ(y_i - ȳ)²] via predicate surface "formula" ⓘ |
| Hill muscle model | differential equations via predicate surface "mathematicalForm" ⓘ |
| Hill muscle model | algebraic equations via predicate surface "mathematicalForm" ⓘ |
| Löwdin partitioning | block-partitioned Schrödinger equation via predicate surface "mathematicalForm" ⓘ |
| Coleman–Glashow mass formula | linear relation among hadron masses via predicate surface "mathematicalForm" ⓘ |
| Brillouin function | B_J(x) = (2J+1)/(2J) coth[(2J+1)x/(2J)] - (1/(2J)) coth[x/(2J)] via predicate surface "hasFormula" ⓘ |
| Brillouin theorem | ⟨Φ₀|H|Φᵢᵃ⟩ = 0 for all single excitations |Φᵢᵃ⟩ from the Hartree–Fock determinant |Φ₀⟩ via predicate surface "mathematicalForm" ⓘ |
| Reiner–Rivlin fluid model | stress expressed as polynomial in invariants of rate-of-deformation tensor via predicate surface "mathematicalForm" ⓘ |
| Bayes factor | B_10 = p(y | M_1) / p(y | M_0) via predicate surface "hasFormula" ⓘ |
| Goldman–Hodgkin–Katz equation | logarithmic via predicate surface "mathematicalForm" ⓘ |
| second law of thermodynamics | dS ≥ δQ_rev / T for closed systems via predicate surface "mathematicalForm" ⓘ |
| Euler’s identity for sine product | \sin(\pi z) = \pi z \prod_{n=1}^{\infty} \left(1 - \frac{z^{2}}{n^{2}}\right) via predicate surface "hasFormula" ⓘ |
| Jacobi manifold | {f,g} = Λ(df,dg) + fE(g) − gE(f) via predicate surface "bracketFormula" ⓘ |
| Letter of Dedication to the Sorbonne | formal dedication to the most distinguished theologians of Paris via predicate surface "openingFormula" ⓘ |
| R-squared inflation | Einstein–Hilbert action plus R^2 correction term via predicate surface "mathematicalForm" ⓘ |
| Ehrenfest theorem | d⟨A⟩/dt = (i/ħ)⟨[H,A]⟩ + ⟨∂A/∂t⟩ via predicate surface "hasFormula" ⓘ |
| Hammett acidity function | H0 = pKBH+ + log([B]/[BH+]) via predicate surface "hasFormula" ⓘ |
| Marshallian demand | x_i(p,w) via predicate surface "mathematicalForm" ⓘ |
| Slutsky substitution matrix is negative semidefinite | Slutsky matrix is symmetric and negative semidefinite via predicate surface "mathematicalForm" NERFINISHED ⓘ |
| Harrod–Domar growth model | linear differential equations in capital and output via predicate surface "mathematicalForm" ⓘ |
| Price equation | Δz̄ = Cov(wᵢ, zᵢ)/w̄ + E(wᵢΔzᵢ)/w̄ via predicate surface "mathematicalForm" ⓘ |
| Kaldor’s theory of distribution | profit share as function of investment rate and saving propensities via predicate surface "mathematicalForm" ⓘ |
| Perceptual Quantizer | logarithmic-like nonlinearity via predicate surface "mathematicalForm" ⓘ |
| Hospital Insurance and Diagnostic Services Act 1957 | federal government paid approximately half of eligible provincial hospital costs via predicate surface "costSharingFormula" ⓘ |
| Kalimat-i-Maknúnih | O Son of Spirit via predicate surface "openingFormula" ⓘ |
| Kalimat-i-Maknúnih | O Son of Man via predicate surface "openingFormula" ⓘ |
| Kalimat-i-Maknúnih | O Son of Being via predicate surface "openingFormula" ⓘ |
| Carter constant | quadratic in momenta via predicate surface "mathematicalForm" ⓘ |
| Foster-Greer-Thorbecke poverty measures | FGT(alpha) = (1/N) * Σ[(z - y_i)/z]^alpha for all poor i via predicate surface "hasFormula" ⓘ |
| Trouton’s rule | ΔSvap = ΔHvap / Tb via predicate surface "mathematicalForm" ⓘ |
| baryonic Tully–Fisher relation (in MOND context) | M_b ∝ V_f^4 via predicate surface "mathematicalForm" ⓘ |
| baryonic Tully–Fisher relation (in MOND context) | M_b = (V_f^4) / (G a_0) in the deep-MOND limit via predicate surface "mathematicalForm" ⓘ |
|
Larmor theorem in classical electrodynamics
surface form:
Larmor theorem
|
ω_L = −(q B)/(2 m c) in Gaussian units for orbital motion via predicate surface "mathematicalForm" ⓘ |
|
Larmor theorem in classical electrodynamics
surface form:
Larmor theorem
|
ω_L = −(q B)/(2 m) in SI units for orbital motion without c factor via predicate surface "mathematicalForm" ⓘ |
| Einstein–Infeld–Hoffmann equations | coupled ordinary differential equations for particle trajectories via predicate surface "mathematicalForm" ⓘ |
| Heisenberg–Euler effective Lagrangian | nonlinear function of F_{\ via predicate surface "mathematicalForm" ⓘ |
| Heisenberg–Euler effective Lagrangian | nonlinear function of F_{\mu\nu}F^{\mu\nu} and F_{\mu\nu}\tilde F^{\mu\nu} via predicate surface "mathematicalForm" ⓘ |
| Cabibbo theory | rotation in two-dimensional flavor space via predicate surface "mathematicalForm" ⓘ |