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 |
|---|---|
| Wheeler–DeWitt equation | HΨ = 0 via predicate surface "mathematicalForm" ⓘ |
| Pascal's law | P = F / A via predicate surface "mathematicalForm" ⓘ |
|
Tolman length in thermodynamics of curved interfaces
surface form:
Tolman length
|
Tolman length in thermodynamics of curved interfaces
via predicate surface "mathematicalForm"
self-linksurface differs
ⓘ
surface form:
appears in first-order curvature correction to surface tension γ(R) = γ∞ (1 - 2δ/R + …)
|
| Tolman–Ehrenfest effect | T(r)·sqrt(g00(r)) = constant in static spacetime via predicate surface "mathematicalForm" ⓘ |
| Condon approximation | transition dipole moment treated as constant with respect to nuclear coordinates via predicate surface "mathematicalForm" ⓘ |
| theosis | God became man so that man might become god via predicate surface "famousFormula" ⓘ |
| Bayes’ theorem | P(A|B) = P(B|A) P(A) / P(B) via predicate surface "coreFormula" ⓘ |
| Bayes’ theorem | P(H|E) = P(E|H) P(H) / P(E) via predicate surface "coreFormula" ⓘ |
| Bernoulli numbers | x/(e^x - 1) = \sum_{n=0}^{\infty} B_n x^n / n! via predicate surface "definitionFormula" ⓘ |
| stars and bars method | C(n + k - 1, k - 1) for nonnegative solutions of x1 + ... + xk = n via predicate surface "typicalFormula" ⓘ |
| stars and bars method | C(n - 1, k - 1) for positive solutions of x1 + ... + xk = n via predicate surface "typicalFormula" ⓘ |
| Frisch–Waugh–Lovell theorem | partitioned regression formula via predicate surface "mathematicalForm" ⓘ |
| Frisch–Waugh–Lovell theorem | Y = X1β1 + X2β2 + u with partitioned regressors via predicate surface "mathematicalForm" ⓘ |
| Schrödinger equation | iℏ ∂ψ/∂t = Ĥψ via predicate surface "mathematicalForm" ⓘ |
| Schrödinger equation | Ĥψ = Eψ via predicate surface "mathematicalForm" ⓘ |
| Unruh effect | T = \frac{\hbar a}{2 \pi c k_B} via predicate surface "hasFormula" ⓘ |
|
Newton's laws of motion
surface form:
Newton's second law of motion
|
F = ma via predicate surface "hasFormula" ⓘ |
| newton | 1 N = 1 kg·m/s² via predicate surface "definitionFormula" ⓘ |
| Newton's third law of motion | F_AB = - F_BA via predicate surface "mathematicalForm" ⓘ |
| Pochhammer symbol | (a)_n = \frac{\Gamma(a+n)}{\Gamma(a)} when a is not a nonpositive integer and n is a nonnegative integer via predicate surface "hasFormula" ⓘ |
| Lenz's law | minus sign in Faraday's law of induction via predicate surface "mathematicalForm" ⓘ |
| Avogadro's law | V ∝ n at constant T and P via predicate surface "mathematicalForm" ⓘ |
| Avogadro's law | V1 / n1 = V2 / n2 at constant T and P via predicate surface "mathematicalForm" ⓘ |
| Avogadro's law | V = k n at constant T and P via predicate surface "mathematicalForm" ⓘ |
| Principles of Topological Psychology | B = f(P, E) via predicate surface "centralFormula" ⓘ |
| Lagrange interpolation polynomial | P(x) = Σ_{j=0}^n y_j L_j(x) via predicate surface "formula" ⓘ |
| Archimedes' principle | F_b = ρ · V · g via predicate surface "hasFormula" ⓘ |
| Coulomb's law | F = k q1 q2 / r^2 via predicate surface "hasFormula" ⓘ |
| Coulomb's law | F = (1 / 4πϵ0) q1 q2 / r^2 via predicate surface "hasFormula" ⓘ |
| Coulomb's law | scalar and vector forms via predicate surface "mathematicalForm" ⓘ |
| i | i^2 = -1 via predicate surface "satisfiesEquation" ⓘ |
| arithmetic–geometric mean identities | K(k) = \frac{\pi}{2\,\operatorname{AGM}(1,\sqrt{1-k^{2}})} via predicate surface "hasKeyFormula" ⓘ |
| arithmetic–geometric mean identities | \operatorname{AGM}(a,b) = \frac{\pi}{4}\,\frac{a}{K(k)} with k^{2}=1-\left(\frac{b}{a}\right)^{2},\ a\ge b>0 via predicate surface "hasKeyFormula" ⓘ |
| arithmetic–geometric mean identities | \frac{1}{\operatorname{AGM}(1,\sqrt{1-k^{2}})} = \frac{2}{\pi}K(k) via predicate surface "hasKeyFormula" ⓘ |
| arithmetic–geometric mean identities | \pi = 2\,\operatorname{AGM}(1,\sqrt{1-k^{2}})\,K(k) via predicate surface "hasKeyFormula" ⓘ |
| arithmetic–geometric mean identities | \pi = 2\,\operatorname{AGM}(1,1/\sqrt{2})^{2}\,\sum_{n=0}^{\infty}2^{n}(a_{n}^{2}-b_{n}^{2}) (Gauss–Legendre type) via predicate surface "hasKeyFormula" ⓘ |
| arithmetic–geometric mean identities | \operatorname{AGM}(1,1/\sqrt{2}) = \frac{\Gamma(1/4)^{2}}{4\sqrt{\pi^{3}}} via predicate surface "hasKeyFormula" ⓘ |
| arithmetic–geometric mean identities | K(1/\sqrt{2}) = \frac{\Gamma(1/4)^{2}}{4\sqrt{\pi}} via predicate surface "hasKeyFormula" ⓘ |
| arithmetic–geometric mean identities | \operatorname{AGM}(1,\sqrt{1-k^{2}}) = \frac{\pi}{4}\,\frac{1}{K(k)} via predicate surface "hasKeyFormula" ⓘ |
| arithmetic–geometric mean identities | \operatorname{AGM}(1,\sqrt{1-k^{2}})\,\operatorname{AGM}(1,\sqrt{1-k'^{2}}) = \frac{\pi}{2} with k'^{2}=1-k^{2} via predicate surface "hasKeyFormula" ⓘ |
| arithmetic–geometric mean identities | \int_{0}^{\pi/2}\frac{d\theta}{\sqrt{a^{2}\cos^{2}\theta + b^{2}\sin^{2}\theta}} = \frac{\pi}{2\,\operatorname{AGM}(a,b)} via predicate surface "hasKeyFormula" ⓘ |
| arithmetic–geometric mean identities | \int_{0}^{\infty}\frac{dx}{\sqrt{(x^{2}+a^{2})(x^{2}+b^{2})}} = \frac{\pi}{2\,\operatorname{AGM}(a,b)} via predicate surface "hasKeyFormula" ⓘ |
| Cramér–Rao bound | Var(T) ≥ 1 / I(θ) for scalar parameter θ via predicate surface "mathematicalForm" ⓘ |
| Cramér–Rao bound | Cov(T) − I(θ)^{-1} is positive semidefinite for vector parameter θ via predicate surface "mathematicalForm" ⓘ |
| Wiener–Khinchin theorem | S_X(f) = ∫_{-∞}^{∞} R_X(τ) e^{-j2π f τ} dτ via predicate surface "mathematicalForm" ⓘ |
| Ampère's force law | F∝I₁I₂ℓ∕r via predicate surface "mathematicalForm" ⓘ |
| Planck temperature | T_P = (1/k_B)·sqrt(ħ c^5 / G) via predicate surface "hasFormula" ⓘ |
| Josephson constant | K_J = 2e/h via predicate surface "hasFormula" ⓘ |
| Bohr radius | a₀ = 4πϵ₀ħ² / (mₑ e²) via predicate surface "formula" ⓘ |
| Bohr radius | a₀ = ħ / (mₑ c α) via predicate surface "formula" ⓘ |