keyFormula

P2310
predicate

Indicates that a formula serves as the primary or defining expression associated with an entity or relationship.

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All labels observed (35)

Label Occurrences
mathematicalForm 239
hasFormula 74
formula 24

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
Surah At-Tawbah does not begin with "Bismillah ar-Rahman ar-Rahim" via predicate surface "openingFormula" ⓘ
Newtonian fluids
surface form: Newtonian fluid
τ_ij = 2 μ e_ij + λ δ_ij ∇·v via predicate surface "mathematicalForm" ⓘ
Stefan–Boltzmann law j* = σ T^4 via predicate surface "mathematicalForm" ⓘ
Planck time t_P = sqrt(ħ G / c^5) via predicate surface "hasFormula" ⓘ
Brillouin–Wigner perturbation theory series expansion in powers of the perturbation via predicate surface "mathematicalForm" ⓘ
Gell-Mann–Nishijima formula Q = I3 + Y/2 via predicate surface "mathematicalForm" ⓘ
Third Epistle of John The elder to the beloved Gaius via predicate surface "openingFormula" ⓘ
Boltzmann–Gibbs entropy in statistical mechanics
surface form: Boltzmann–Gibbs entropy
S = -k_B \sum_i p_i \ln p_i via predicate surface "standardFormula" ⓘ
Boltzmann–Gibbs entropy in statistical mechanics
surface form: Boltzmann–Gibbs entropy
S = k_B \ln W via predicate surface "standardFormula" ⓘ
general relativity Einstein field equations via predicate surface "coreEquation" ⓘ
Chalcedonian Definition in two natures, without confusion, without change, without division, without separation via predicate surface "hasKeyFormula" ⓘ
Smoluchowski coagulation equation integro-differential equation in time and cluster size via predicate surface "mathematicalForm" ⓘ
Young's modulus E = σ / ε via predicate surface "formula" ⓘ
Second Epistle to Timothy Apostle Paul via predicate surface "openingFormula" ⓘ
surface form: Paul, an apostle of Christ Jesus
Surah As-Saff Bismillah ir-Rahman ir-Rahim via predicate surface "openingFormula" ⓘ
Exsultet “O felix culpa” via predicate surface "containsFormula" ⓘ
Wick’s theorem T(ϕ₁…ϕₙ)=:ϕ₁…ϕₙ:+(all single contractions)+…+(all full contractions) via predicate surface "mathematicalForm" ⓘ
Gross–Pitaevskii equation nonlinear complex-valued partial differential equation via predicate surface "mathematicalForm" ⓘ
Gibbons–Hawking temperature T = \frac{\hbar H}{2\pi k_B} via predicate surface "hasFormula" ⓘ
Eddington limit L_Edd = 4πGMc/κ via predicate surface "mathematicalForm" ⓘ
Steinmetz’s law of hysteresis P = k f B_max^n via predicate surface "hasFormula" ⓘ
Euler’s totient function φ(n) If n = p₁^{a₁}…p_k^{a_k} then φ(n) = n ∏_{i=1}^k (1 − 1/p_i) via predicate surface "formula" ⓘ
Euler’s totient function φ(n) If n = p₁^{a₁}…p_k^{a_k} then φ(n) = ∏_{i=1}^k p_i^{a_i−1}(p_i − 1) via predicate surface "formula" ⓘ
Euler’s totient function φ(n) φ(p) = p − 1 for prime p via predicate surface "primeFormula" ⓘ
Abelian groups
surface form: Abelian group
a + b = b + a for all elements a, b via predicate surface "satisfiesEquation" ⓘ
Birkot HaShachar Baruch Atah Adonai Eloheinu Melech HaOlam via predicate surface "containsFormula" ⓘ
Schwarzschild criterion ∇_rad > ∇_ad implies convective instability via predicate surface "mathematicalForm" ⓘ
Schwarzschild criterion ∇_rad < ∇_ad implies convective stability via predicate surface "mathematicalForm" ⓘ
Lorentz force four-vector form in special relativity via predicate surface "mathematicalForm" ⓘ
Landauer's principle Q ≥ kT ln 2 per erased bit via predicate surface "hasFormula" ⓘ
Epistle to the Romans Apostle Paul via predicate surface "openingFormula" ⓘ
surface form: Paul, a servant of Christ Jesus
Epistle to the Galatians Apostle Paul via predicate surface "openingFormula" ⓘ
surface form: Paul, an apostle
Lemaître–Hubble law linear relation between velocity and distance via predicate surface "mathematicalForm" ⓘ
Compton effect Δλ = (h / (m_e c)) (1 − cos θ) via predicate surface "hasFormulaForShift" ⓘ
Kirchhoff's law of thermal radiation ε(λ,T) = α(λ,T) for a body in thermal equilibrium via predicate surface "mathematicalForm" ⓘ
Wigner surmise P(s) = (π/2) s exp(-π s^2 / 4) via predicate surface "GOEFormula" ⓘ
Wigner surmise P(s) = (32/π^2) s^2 exp(-4 s^2 / π) via predicate surface "GUEFormula" ⓘ
Faraday effect θ = V B L via predicate surface "mathematicalForm" ⓘ
farad 1 F = 1 C / 1 V via predicate surface "formula" ⓘ
farad C = F·V via predicate surface "formula" ⓘ
Curie law of magnetization χ = C / T via predicate surface "formula" ⓘ
Curie law of magnetization χ ∝ 1 / T via predicate surface "mathematicalForm" ⓘ
Boyle's law P ∝ 1/V via predicate surface "mathematicalForm" ⓘ
Boyle's law P1V1 = P2V2 via predicate surface "mathematicalForm" ⓘ
Boyle's law PV = constant via predicate surface "mathematicalForm" ⓘ
Mott variable-range hopping σ(T) = σ0 · exp[-(T0/T)^{1/(d+1)}] via predicate surface "mathematicalForm" ⓘ
Hooke's law F = −k x, where k is spring constant and x is displacement from equilibrium via predicate surface "mathematicalForm" ⓘ
Pauli equation first-order in time via predicate surface "mathematicalForm" ⓘ
Pauli equation second-order in spatial derivatives via predicate surface "mathematicalForm" ⓘ
Euclidean metric d(x,y) = sqrt(∑_{i=1}^n (x_i - y_i)^2) via predicate surface "hasFormula" ⓘ