statement

P4223
predicate

Indicates that an entity makes, issues, or expresses a declarative assertion, claim, or remark about something.

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All labels observed (14)

Label Occurrences
statement canonical 141
statedAs 42
stated 18

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: statement
Generated description
Indicates that an entity makes, issues, or expresses a declarative assertion, claim, or remark about something.

Sample triples (258)

Subject Object
Rydberg–Ritz combination principle wavenumber of a line equals difference of two term values via predicate surface "statedAs" ⓘ
Dirichlet approximation theorem For any real number α and any positive integer N, there exist integers p and q with 1 ≤ q ≤ N such that |α − p/q| < 1/(qN). ⓘ
Birkhoff–von Neumann theorem Every doubly stochastic matrix can be expressed as a convex combination of permutation matrices. ⓘ
General Congress of Bukovina proclaimed the union of Bukovina with the Kingdom of Romania ⓘ
Euler criterion For an odd prime p and integer a with gcd(a,p)=1, a is a quadratic residue modulo p if and only if a^((p-1)/2) ≡ 1 (mod p). ⓘ
Euler criterion For an odd prime p and integer a with gcd(a,p)=1, a is a quadratic non-residue modulo p if and only if a^((p-1)/2) ≡ -1 (mod p). ⓘ
Lusin–Souslin theorem The continuous injective image of a Borel set in a Polish space is a Borel set. ⓘ
Legendre’s formula for valuations of factorials For a prime p and integer n ≥ 1, the exponent v_p(n!) of p in n! is given by v_p(n!) = ∑_{k=1}^{∞} ⌊n/p^k⌋. ⓘ
Legendre’s formula for valuations of factorials For a prime p and integer n ≥ 1, v_p(n!) = ⌊n/p⌋ + ⌊n/p^2⌋ + ⌊n/p^3⌋ + …, where the sum is finite because p^k > n for large k. ⓘ
Zeroth Law of Robotics A robot may not harm humanity, or, by inaction, allow humanity to come to harm. via predicate surface "statedAs" ⓘ
Riesz lemma If X is a normed space, Y is a proper closed subspace of X, and 0 < α < 1, then there exists x in X with ∥x∥ = 1 such that the distance from x to Y is at least α. ⓘ
Graham–Pollak theorem The edges of a complete graph on n vertices cannot be partitioned into fewer than n−1 complete bipartite subgraphs. ⓘ
Turán's theorem Among all n-vertex graphs with no K_r subgraph, the Turán graph T_{r-1}(n) has the maximum number of edges via predicate surface "statementInformal" ⓘ
Third Law of Robotics A robot must protect its own existence as long as such protection does not conflict with the First or Second Law. via predicate surface "statedAs" ⓘ
Black Water Transit Tony Kaye has described the film as heavily re-edited without his approval via predicate surface "directorStatement" NERFINISHED ⓘ
First Law of Robotics A robot may not injure a human being or, through inaction, allow a human being to come to harm. via predicate surface "statedAs" ⓘ
Second Law of Robotics A robot must obey the orders given it by human beings except where such orders would conflict with the First Law. via predicate surface "statedAs" ⓘ
Make It in America: The Case for Re-Inventing the Economy argues that manufacturing is critical to long-term economic strength via predicate surface "positionStatement" ⓘ
Make It in America: The Case for Re-Inventing the Economy argues that the United States needs a coherent industrial strategy via predicate surface "positionStatement" ⓘ
Make It in America: The Case for Re-Inventing the Economy argues that offshoring has weakened U.S. competitiveness via predicate surface "positionStatement" ⓘ
Make It in America: The Case for Re-Inventing the Economy argues that policy should support domestic production of high-value goods via predicate surface "positionStatement" ⓘ
van der Corput inequality gives an upper bound for |∑_{n=1}^N a_n e(f(n))|^2 in terms of sums over shifts h of ∑_{n} a_{n+h} \overline{a_n} via predicate surface "typicalStatement" ⓘ
William Binney targeted surveillance is more effective than bulk collection via predicate surface "stated" ⓘ
Trouton’s rule many non-associated liquids have nearly constant molar entropy of vaporization at their normal boiling points ⓘ
Bolzano–Weierstrass theorem Every bounded infinite sequence in ℝⁿ has a convergent subsequence. ⓘ
Bolzano–Weierstrass theorem Every bounded sequence in ℝ has a convergent subsequence. ⓘ
Sharon Murphy public statements supporting the official coroner’s findings on Brittany Murphy’s death via predicate surface "madeStatement" ⓘ
Shephard’s lemma the derivative of the cost function with respect to an input price equals the conditional demand for that input ⓘ
Shephard’s lemma the derivative of the expenditure function with respect to a good’s price equals the Hicksian demand for that good ⓘ
Chernoff bound P(X ≥ (1+δ)μ) ≤ exp(-μ f(δ)) for δ > 0 via predicate surface "typicalStatement" ⓘ
Chernoff bound P(X ≤ (1-δ)μ) ≤ exp(-μ g(δ)) for δ ∈ (0,1) via predicate surface "typicalStatement" ⓘ
Kesten–Stigum theorem If E(X log⁺ X) < ∞ then Zₙ / mⁿ converges almost surely to a non-degenerate limit via predicate surface "typicalStatement" ⓘ
Kesten–Stigum theorem If E(X log⁺ X) = ∞ then Zₙ / mⁿ converges almost surely to 0 via predicate surface "typicalStatement" ⓘ
Liouville's theorem
surface form: Liouville's theorem (complex analysis)
Every bounded entire function is constant ⓘ
Israel–Egypt General Armistice Agreement of 1949 armistice lines were not to be construed as political or territorial boundaries via predicate surface "stated" ⓘ
Plancherel theorem for locally compact abelian groups the Fourier transform extends to a unitary operator from L2(G) onto L2(Ĝ) ⓘ
Dini's theorem If (f_n) is a monotone sequence of continuous real-valued functions on a compact space K converging pointwise to a continuous function f, then (f_n) converges uniformly to f on K. via predicate surface "typicalStatement" ⓘ
Cartan–Eilenberg spectral sequence there is a spectral sequence with E2-term given by derived functors of one functor applied to derived functors of another via predicate surface "typicalStatement" ⓘ
Edinburgh Agreement that both governments would respect the outcome of the referendum via predicate surface "stated" ⓘ
Malgrange–Ehrenpreis theorem Every linear partial differential operator with constant coefficients admits a fundamental solution in the sense of distributions. ⓘ
Wyandotte Constitution Kansas is a free state via predicate surface "stated" ⓘ
Bieberbach conjecture If f(z)=z+\sum_{n=2}^{\infty} a_n z^n is univalent on the unit disk, then |a_n| \le n for all n \ge 2 ⓘ
Carleson theorem on almost-everywhere convergence the Fourier series of any L^2 function on the circle converges almost everywhere to the function itself ⓘ
Galois correspondence there is a bijection between intermediate fields of a finite Galois extension and subgroups of its Galois group via predicate surface "typicalStatement" ⓘ
Jordan–Chevalley decomposition every linear operator can be written as the sum of a semisimple operator and a nilpotent operator that commute ⓘ
Jordan–Chevalley decomposition every invertible linear operator can be written as the product of a semisimple operator and a unipotent operator that commute ⓘ
Stone representation theorem Every Boolean algebra is isomorphic to a field of sets. ⓘ
Stone representation theorem Every Boolean algebra is isomorphic to an algebra of clopen subsets of a Stone space. ⓘ
Stone representation theorem There is a dual equivalence between the category of Boolean algebras and the category of Stone spaces. ⓘ
L’Hôpital’s rule for indeterminate limits If lim_{x→a} f(x)=0 and lim_{x→a} g(x)=0 and f,g are differentiable near a with g′(x)≠0, then lim_{x→a} f(x)/g(x)=lim_{x→a} f′(x)/g′(x) when the latter limit exists or is infinite. ⓘ