A proof net is a concept from the field of linear logic, introduced by the logician Jean-Yves Girard in the 1990s. It serves as a geometric representation of proofs in linear logic, providing an alternative to traditional syntactic representations like sequent calculus or natural deduction. ### Key Features of Proof Nets: 1. **Linear Logic**: Proof nets are specifically tied to linear logic, a branch of logic that emphasizes the use of resources.

Redundant proof, often referred to in the context of mathematics and logic, involves demonstrating a statement or theorem using multiple proofs that reiterate the same underlying principles or reasoning. Essentially, one proof does not provide any new insights or alternative approaches but instead reaffirms what has already been established. In a broader context, redundancy in proofs can serve specific purposes: 1. **Verification**: It can help confirm the validity of a theorem or statement by showing that it can be proven in different ways.

The term "Laves graph" does not refer to a widely recognized concept in mathematics, graph theory, or any other standard academic discipline. However, it may be related to certain concepts in materials science, specifically Laves phases. Laves phases are types of intermetallic compounds that typically have a specific crystal structure and are significant in the study of alloys and solid materials.

A relatively compact subspace (or relatively compact set) is a concept from topology, specifically in the context of metric spaces or more generally in topological spaces. A subset \( A \) of a topological space \( X \) is said to be relatively compact if its closure, denoted by \( \overline{A} \), is compact.

Resolution proof compression by splitting is a technique used in the context of automated theorem proving, particularly in the area of propositional logic. The primary goal of this technique is to reduce the size of a resolution proof without losing the essential information that proves the target theorem. In a resolution proof, one derives a conclusion from a set of premises using the resolution rule, which is a rule of inference that allows the derivation of a clause from two clauses containing complementary literals.

Volterra spaces typically refer to function spaces associated with Volterra integral equations or to function spaces defined in the context of Volterra operators.

In mathematics, particularly in topology, compactness is a property that describes a specific type of space. A topological space is said to be compact if every open cover of the space has a finite subcover.

In topology, a space is called a **collectionwise normal space** if it satisfies a certain separation condition involving collections of closed sets.

"Door space" can refer to different concepts depending on the context. Here are a few possible interpretations: 1. **Architecture and Interior Design**: In this context, door space might refer to the area around a door, including the clearance required for the door to open and close without obstruction. This space is important for both functional and aesthetic reasons, ensuring that doors can operate smoothly and that the space looks cohesive.

An **extremally disconnected space** is a topological space in which the closure of every open set is open.

"Rot-proof" refers to materials or products that are resistant to decay and deterioration caused by mold, fungi, and moisture. This term is often used in the context of construction materials, textiles, and outdoor products. For instance, rot-proof wood is treated or engineered to withstand the effects of moisture and pests, making it suitable for outdoor use in environments where it might be exposed to water or humidity.

Corentin Louis Kervran (1901–1993) was a French biologist and researcher known for his unconventional ideas in the field of biology, particularly regarding the concept of biological transmutation. Kervran proposed that living organisms could transform one element into another through biological processes, challenging traditional views of chemistry and biology that adhere to the laws of conservation of mass. His theories garnered interest and some controversy, as they suggested that transmutation could occur within the context of biological systems.

George Woodward Warder was a significant figure in American history, primarily known for his contributions to the fields of botany and horticulture. He was born on January 29, 1815, and passed away on February 27, 1884. Warder is particularly noted for his work in plant taxonomy and for being a prolific author on topics related to trees and their cultivation.

Korte's third law of apparent motion, also known as Korte's law or the Korte effect, relates to the perception of motion in visual stimuli, particularly in the field of psychology and visual perception. The law suggests that when two stationary objects are presented in close temporal succession, the observer perceives the first object as having moved toward the second object. This phenomenon occurs due to the brain's interpretation of the timing and position of the objects, leading to a misperception of motion.

Tom Van Flandern was an American astronomer known for his work in the field of astrophysics and for his unconventional theories regarding celestial mechanics. He gained some notoriety for his ideas about dark matter and the structure of the universe, particularly in relation to the planets and moons in our solar system. Van Flandern is perhaps best known for proposing the "exploded planet hypothesis," which suggested that certain celestial bodies may have originated from the explosion of larger planets.

Adaptive Comparative Judgment (ACJ) is an assessment method primarily used in education to evaluate and compare student work or performance. It leverages the expertise of judges (such as teachers or industry professionals) who assess multiple pieces of work in relation to one another rather than against a fixed standard or rubric.

A "Donkey sentence" is a term used in linguistics to refer to a specific type of sentence that involves an indefinite pronoun and a specific reference that relies on context. The most famous example is the sentence: "Every farmer who owns a donkey beats it." In this example, "it" refers back to "a donkey," which is introduced by the indefinite article "a.

The basic hypergeometric series, also known as the \( q \)-hypergeometric series, is a generalization of the classical hypergeometric series. It involves parameters and is particularly important in various areas of mathematics, including combinatorics, number theory, and q-series.

Hooke's atom refers to a model in physics that is based on the concept of a particle or an atom interacting through a spring-like potential. The idea is inspired by Hooke's law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position, typically expressed as \( F = -kx \), where \( k \) is the spring constant, and \( x \) is the displacement.