REFERENCE
The Astra glossary.
The terms that make the ten results legible.
Open problem
A question whose answer, proof, or sharp main result was not previously known.
Theorem
A mathematical statement supported by a proof from stated assumptions.
Conjecture
A claim believed to be true but not yet proved or disproved.
Counterexample
A specific example that shows a universal claim is false.
Asymptotic
Describing how a quantity behaves as its input becomes very large.
Upper bound
A value a quantity cannot exceed under the stated conditions.
Lower bound
A value a quantity cannot fall below under the stated conditions.
Exponential
A rate such as cⁿ, which grows or shrinks by a fixed factor per step.
Polynomial
A rate bounded by a fixed power of the input, such as n³.
Dimension
An independent coordinate needed to describe a position or degree of freedom.
Fourier transform
A way to rewrite a signal or function in terms of its frequency components.
Linear program
An optimization problem with a linear objective and linear constraints.
Binary code
A collection of bit strings designed to stay distinguishable despite errors.
Hamming distance
The number of positions at which two equal-length strings differ.
Spherical code
A set of points on a sphere whose pairwise separation is controlled.
Group
A set of reversible operations with a rule for composing them.
Sofic group
A group that can be approximated locally by finite permutation systems.
Property (T)
A rigidity property that prevents almost-invariant behavior from drifting freely.
von Neumann algebra
An algebra of operators closed under the limits used in functional analysis.
Arithmetic circuit
A network of additions and multiplications that computes a polynomial.
Permanent
A matrix polynomial like the determinant but without alternating signs.
Quantum entanglement
Correlations between quantum systems that cannot be described as independent local choices.
Parallel repetition
Repeating a game independently and requiring success in every copy.
Lattice
A regular, discrete grid formed by integer combinations of basis vectors.
Approximation factor
How much farther an allowed answer may be from the optimum.
Convex body
A compact solid where every line segment joining two points stays inside.
Centroid
The average location of a shape’s mass or points.
Ramsey number
The threshold size forcing a specified monochromatic pattern in every coloring.
Extremal graph
A graph that is as large or dense as possible while avoiding a forbidden pattern.
Degeneracy
The smallest k such that every subgraph has a vertex of degree at most k.
Lean
A proof assistant that mechanically checks formal statements and their logical steps.
Formal verification
Checking a precisely encoded claim with a trusted formal system rather than only reading prose.