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In number theory, the Pólya conjecture stated that "most" (i.e., 50% or more) of the natural numbers less than any given number have an odd number of prime factors. The conjecture was posited by the Hungarian mathematician George Pólya in 1919, and proved false in 1958 by C. Brian Haselgrove.

The size of the smallest counterexample is often used to show how a conjecture can be true for many cases, and still be false, providing an illustration for the strong law of small numbers.

The Perseids are a prolific meteor shower associated with the comet Swift–Tuttle. The meteors are called the Perseids because the point from which they appear to hail (called the radiant) lies in the constellation Perseus.

Quantum tic-tac-toe is a "quantum generalization" of tic-tac-toe in which the players' moves are "superpositions" of plays in the classical game. The game was invented by Allan Goff of Novatia Labs, who describes it as "a way of introducing quantum physics without mathematics", and offering "a conceptual foundation for understanding the meaning of quantum mechanics".

The Messinian Salinity Crisis (MSC), also referred to as the Messinian Event, and in its latest stage as the Lago Mare event, was a geological event during which the Mediterranean Sea went into a cycle of partly or nearly complete desiccation throughout the latter part of the Messinian age of the Miocene epoch, from 5.96 to 5.33 Ma (million years ago). It ended with the Zanclean flood, when the Atlantic reclaimed the basin.

Sediment samples from below the deep seafloor of the Mediterranean Sea, which include evaporite minerals, soils, and fossil plants, show that the precursor of the Strait of Gibraltar closed tight about 5.96 million years ago, sealing the Mediterranean off from the Atlantic. This resulted in a period of partial desiccation of the Mediterranean Sea, the first of several such periods during the late Miocene. After the strait closed for the last time around 5.6 Ma, the region's generally dry climate at the time dried the Mediterranean basin out nearly completely within a thousand years. This massive desiccation left a deep dry basin, reaching 3 to 5 km (1.9 to 3.1 mi) deep below normal sea level, with a few hypersaline pockets similar to today's Dead Sea. Then, around 5.5 Ma, less dry climatic conditions resulted in the basin receiving more freshwater from rivers, progressively filling and diluting the hypersaline lakes into larger pockets of brackish water (much like today's Caspian Sea). The Messinian Salinity Crisis ended with the Strait of Gibraltar finally reopening 5.33 Ma, when the Atlantic rapidly filled up the Mediterranean basin in what is known as the Zanclean flood.

Even today, the Mediterranean is considerably saltier than the North Atlantic, owing to its near isolation by the Strait of Gibraltar and its high rate of evaporation. If the Strait of Gibraltar closes again (which is likely to happen in the near future on a geological time scale), the Mediterranean would mostly evaporate in about a thousand years, after which continued northward movement of Africa may obliterate the Mediterranean altogether.

Only the inflow of Atlantic water maintains the present Mediterranean level. When that was shut off sometime between 6.5 to 6 MYBP, net evaporative loss set in at the rate of around 3,300 cubic kilometers yearly. At that rate, the 3.7 million cubic kilometres of water in the basin would dry up in scarcely more than a thousand years, leaving an extensive layer of salt some tens of meters thick and raising global sea level about 12 meters.

In economics, a negative income tax (NIT) is a welfare system within an income tax where people earning below a certain amount receive supplemental pay from the government instead of paying taxes to the government.

Such a system has been discussed by economists but never fully implemented. According to surveys however, the consensus view among economists is that the "government should restructure the welfare system along the lines" of one. It was described by British politician Juliet Rhys-Williams in the 1940s and later by American free-market economist Milton Friedman.

Negative income taxes can implement a basic income or supplement a guaranteed minimum income system.

In a negative income tax system, people earning a certain income level would owe no taxes; those earning more than that would pay a proportion of their income above that level; and those below that level would receive a payment of a proportion of their shortfall, which is the amount their income falls below that level.

A physical unclonable function (sometimes also called physically unclonable function, which refers to a weaker security metric), or PUF, is a physical object that for a given input and conditions (challenge), provides a physically-defined "digital fingerprint" output (response) that serves as a unique identifier, most often for a semiconductor device such as a microprocessor. PUFs are most often based on unique physical variations which occur naturally during semiconductor manufacturing. A PUF is a physical entity embodied in a physical structure. Today, PUFs are usually implemented in integrated circuits and are typically used in applications with high security requirements, more specifically cryptography.

Bead sort, also called gravity sort, is a natural sorting algorithm, developed by Joshua J. Arulanandham, Cristian S. Calude and Michael J. Dinneen in 2002, and published in The Bulletin of the European Association for Theoretical Computer Science. Both digital and analog hardware implementations of bead sort can achieve a sorting time of O(n); however, the implementation of this algorithm tends to be significantly slower in software and can only be used to sort lists of positive integers. Also, it would seem that even in the best case, the algorithm requires O(n²) space.