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
Dirichlet conditions function is bounded on the interval via predicate surface "typicalStatement" ⓘ
Hurwitz bound on automorphism groups of curves A compact Riemann surface of genus g ≥ 2 has at most 84(g − 1) automorphisms ⓘ
Lefschetz fixed-point theorem If the Lefschetz number of a continuous self-map is nonzero, then the map has at least one fixed point. ⓘ
Conway's thrackle conjecture in any thrackle drawing of a finite graph, the number of edges is at most the number of vertices ⓘ
monotone convergence theorem If 0 ≤ f_1 ≤ f_2 ≤ … and f_n → f pointwise, then ∫ f_n dμ → ∫ f dμ via predicate surface "typicalStatement" ⓘ
Jordan curve theorem Every simple closed curve in the plane divides the plane into exactly two regions ⓘ
Euler’s theorem If gcd(a,n)=1 then a^{φ(n)} ≡ 1 (mod n) via predicate surface "statedAs" ⓘ
Mertens’ theorems
surface form: Mertens’ first theorem
The sum_{p \le x} (log p)/p = log x + O(1) as x → ∞ ⓘ
Mertens’ theorems
surface form: Mertens’ second theorem
The sum_{p \le x} 1/p = log log x + B + o(1) as x → ∞ for a constant B ⓘ
Mertens’ theorems
surface form: Mertens’ third theorem
The product_{p \le x} (1 − 1/p) ~ e^{−γ}/log x as x → ∞ ⓘ
Sewel Convention the UK Parliament will not normally legislate with regard to devolved matters without the consent of the Scottish Parliament via predicate surface "statedAs" ⓘ
complementarity principle certain physical properties are mutually exclusive yet jointly necessary for a complete description of a system via predicate surface "statedAs" ⓘ
North Carolina’s Halifax Resolves
surface form: Halifax Resolves
called for independence from Great Britain ⓘ
North Carolina’s Halifax Resolves
surface form: Halifax Resolves
supported a complete and final separation from the British Crown ⓘ
Tomiichi Murayama Expressed deep remorse and heartfelt apology for Japan’s colonial rule and aggression via predicate surface "statementContent" ⓘ
Yohei Kono acknowledged involvement of the Imperial Japanese Army in coercing comfort women during World War II ⓘ
Charles's law At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature. ⓘ
Ohm's law for electrical conduction V = I R via predicate surface "statedAs" ⓘ
Stockholm Appeal any government that first uses atomic weapons against any other country would be committing a crime against humanity via predicate surface "statementContent" ⓘ
Stockholm Appeal such a crime should be dealt with as a war crime via predicate surface "statementContent" ⓘ
verum factum principle verum et factum convertuntur via predicate surface "statedAs" ⓘ
Erdős–Szekeres theorem any sufficiently large set of points in the plane in general position contains the vertices of a large convex polygon via predicate surface "statementInformal" ⓘ
Steinhaus theorem If A is a subset of the real numbers with positive Lebesgue measure, then the difference set A − A contains an open interval around 0. ⓘ
Tychonoff theorem for products of compact spaces The product of any family of compact topological spaces is compact in the product topology. ⓘ
Banach–Tarski paradox decomposition of a solid ball in 3-dimensional space via predicate surface "statementAbout" ⓘ
Thales’ theorem Any angle inscribed in a semicircle is a right angle ⓘ
Thales’ theorem If A and B are endpoints of a diameter of a circle and C is any other point on the circle, then angle ACB is a right angle ⓘ
Banach–Alaoglu theorem The closed unit ball of the dual of a normed space is compact in the weak-* topology. ⓘ
Closed Graph Theorem A linear operator between Banach spaces is bounded if its graph is closed in the product space ⓘ
Bennett's logical reversibility every step of a computation can be made logically reversible via predicate surface "statedAs" ⓘ
Five Laws of Library Science
surface form: First Law of Library Science
Books are for use ⓘ
Five Laws of Library Science
surface form: Second Law of Library Science
Every reader his or her book ⓘ
Five Laws of Library Science
surface form: Third Law of Library Science
Every book its reader ⓘ
Five Laws of Library Science
surface form: Fourth Law of Library Science
Save the time of the reader ⓘ
Five Laws of Library Science
surface form: Fifth Law of Library Science
The library is a growing organism ⓘ
Banach–Stone theorem If C(X) and C(Y) are isometrically isomorphic as Banach spaces then X and Y are homeomorphic ⓘ
Banach–Stone theorem Every surjective linear isometry T:C(X)→C(Y) is induced by a homeomorphism between X and Y and a unimodular function ⓘ
Banach–Saks theorem Every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm. ⓘ
pragmatic maxim Consider what effects that might conceivably have practical bearings we conceive the object of our conception to have via predicate surface "statedAs" ⓘ
pragmatic maxim Our conception of these effects is the whole of our conception of the object via predicate surface "statedAs" ⓘ
fundamental theorem of arithmetic Every integer greater than 1 can be written as a product of prime numbers. ⓘ
fundamental theorem of arithmetic This factorization into primes is unique up to the order of the factors. ⓘ
Vinogradov's three-primes theorem Every sufficiently large odd integer can be expressed as the sum of three prime numbers. ⓘ
Lebesgue differentiation theorem For an L^1_loc function on R^n, the averages over balls shrinking to a point converge almost everywhere to the function value at that point ⓘ
Lebesgue differentiation theorem If f is locally integrable on R^n, then for almost every x, the limit as r→0 of (1/|B(x,r)|)∫_{B(x,r)} f(y) dy equals f(x) ⓘ
Lebesgue differentiation theorem The set of points where the differentiation formula fails has Lebesgue measure zero ⓘ
twin prime conjecture there exist infinitely many pairs of prime numbers that differ by 2 ⓘ
Dirichlet's theorem on arithmetic progressions Every arithmetic progression a, a+d, a+2d, ... with gcd(a,d)=1 contains infinitely many prime numbers ⓘ
IRA ceasefire of 1994 complete cessation of military operations via predicate surface "statedAs" ⓘ
Mott minimum metallic conductivity σ_min ≈ 0.03 e²/(ħ a) via predicate surface "statedAs" ⓘ