Question: Who is reported in some ancient sources to have been a philosopher who was the earliest Greek to develop the theory of atomism, who had a daughters were sought by he jealous murderer of Castor? 

Context paragraphs:
Atomism (social): Atomism or social atomism is a sociological theory arising from the scientific notion "atomic theory", coined by the ancient Greek philosopher Democritus and the Roman philosopher Lucretius.  In the scientific rendering of the word, atomism refers to the notion that all matter in the universe is composed of basic indivisible components, or atoms.  When placed into the field of sociology, atomism assigns the individual as the basic unit of analysis for all implications of social life.  This theory refers to "the tendecy for society to be made up of a collection of self-interested and largely self-sufficient individuals, operating as separate atoms".  Therefore, all social values, institutions, developments and procedures evolve entirely out of the interests and actions of the individuals who inhabit any particular society.  The individual is the ‘atom’ of society and therefore the only true object of concern and analysis.

Leucippus: Leucippus ( ; Greek: Λεύκιππος , "Leúkippos"; fl.  5th cent.  BCE) is reported in some ancient sources to have been a philosopher who was the earliest Greek to develop the theory of atomism—the idea that everything is composed entirely of various imperishable, indivisible elements called atoms. Leucippus often appears as the master to his pupil Democritus, a philosopher also touted as the originator of the atomic theory.  However, a brief notice in Diogenes Laertius’s life of Epicurus says that on the testimony of Epicurus, Leucippus never existed.  As the philosophical heir of Democritus, Epicurus's word has some weight, and indeed a controversy over this matter raged in German scholarship for many years at the close of the 19th century.  Furthermore, in his "Corpus Democriteum", Thrasyllus of Alexandria, an astrologer and writer living under the emperor Tiberius (14–37 CE), compiled a list of writings on atomism that he attributed to Democritus to the exclusion of Leucippus.  The present consensus among the world's historians of philosophy is that this Leucippus is historical.  The matter must remain moot unless more information is forthcoming from the record.

True History: A True History or A True Story (Ancient Greek: Ἀληθῆ διηγήματα , "Alēthē diēgēmata"; Latin: "Vera Historia" ) is a parody of travel tales, by the Greek-speaking Assyrian author Lucian of Samosata, the earliest known fiction about travelling to outer space, alien life-forms and interplanetary warfare.  Written in the 2nd century, the novel has been referred to as "the first known text that could be called science fiction".  The work was intended by Lucian as a satire against contemporary and ancient sources, which quote fantastic and mythical events as truth.

Pallantides: In Greek mythology, the Pallantidai (Ancient Greek: Παλλαντίδαι ) were the fifty sons of Pallas, nobles of Attica, and rivals of their uncle Aegeus and his son Theseus over the Athenian throne.  Diodorus Siculus related that they once became friends with Androgeos, a son of Minos, and that was why Aegeus had Androgeos assassinated, fearing that Pallas and his sons could use this friendship to get assistance from the powerful Minos against him.  The Pallantidae and their father marched against Theseus and Aegeus because they hoped to gain control over Athens.  According to Plutarch, one half of them under command of Pallas openly marched from Sphettus, while the other half laid an ambush near Gargettus.  Their plan failed though, because Leos, their herald, warned Theseus of their schemes and an ambush they had prepared for him.  Theseus pre-emptively ambushed the Pallantides and killed all those at Gargettus, whereupon the other half retreated.  Other sources state that Theseus killed all the fifty Pallantidae as well as Pallas.  A tradition saying that he spared their sister, Aricia, whom he kept as slave, is followed in Jean Racine's "Phèdre" but is not supported by extant genuinely ancient sources.

Dionysus: Dionysus ( ; Greek: Διόνυσος "Dionysos") is the god of the grape harvest, winemaking and wine, of ritual madness, fertility, theatre and religious ecstasy in ancient Greek religion and myth.  Wine played an important role in Greek culture, and the cult of Dionysus was the main religious focus for its unrestrained consumption.  His worship became firmly established in the seventh century BC.  He may have been worshipped as early as c. 1500–1100 BC by Mycenean Greeks; traces of Dionysian-type cult have also been found in ancient Minoan Crete.  His origins are uncertain, and his cults took many forms; some are described by ancient sources as Thracian, others as Greek.  In some cults, he arrives from the east, as an Asiatic foreigner; in others, from Ethiopia in the South.  He is a god of epiphany, "the god that comes", and his "foreignness" as an arriving outsider-god may be inherent and essential to his cults.  He is a major, popular figure of Greek mythology and religion, becoming increasingly important over time, and included in some lists of the twelve Olympians, as the last of their number, and the only god born from a mortal mother.  His festivals were the driving force behind the development of Greek theatre.

Buddhist atomism: Buddhist atomism is a school of atomistic Buddhist philosophy that flourished on the Indian subcontinent during two major periods .  During the first phase, which began to develop prior to the 4th century BCE, Buddhist atomism had a very qualitative, Aristotelian-style atomic theory.  This form of atomism identifies four kinds of atoms, corresponding to the standard elements.  Each of these elements has a specific property, such as solidity or motion, and performs a specific function in mixtures, such as providing support or causing growth.  Like the Hindus and Jains, the Buddhists were able to integrate a theory of atomism with their logical presuppositions.

Erinna: Erinna ( ; Greek: Ἤριννα ) was an ancient Greek poet.  Biographical details about her life are uncertain.  She is generally thought to have lived in the first half of the fourth century BC, though some ancient traditions have her as a contemporary of Sappho; Telos is generally considered to be her most likely birthplace, but Tenos, Teos, Rhodes, and Lesbos are all also mentioned by ancient sources as her home.  Erinna is best known for her long poem, the "Distaff", a three-hundred line hexameter lament for her childhood friend Baucis, who had died shortly after marriage.  A large fragment of this poem was discovered in 1928 at Behnasa in Egypt.  Along with the "Distaff", three epigrams ascribed to Erinna are known, preserved in the Greek Anthology.

Xenophanes: Xenophanes of Colophon ( ; Ancient Greek: Ξενοφάνης ὁ Κολοφώνιος ] ; c. 570 – c. 475 BC) was a Greek philosopher, theologian, poet, and social and religious critic.  Xenophanes lived a life of travel, having left Ionia at the age of 25 and continuing to travel throughout the Greek world for another 67 years.  Some scholars say he lived in exile in Sicily.  Knowledge of his views comes from fragments of his poetry, surviving as quotations by later Greek writers.  To judge from these, his elegiac and iambic poetry criticized and satirized a wide range of ideas, including Homer and Hesiod, the belief in the pantheon of anthropomorphic gods and the Greeks' veneration of athleticism.  He is the earliest Greek poet who claims explicitly to be writing for future generations, creating ""fame that will reach all of Greece, and never die while the Greek kind of songs survives.""

Brychon: Brychon or Vrychonas (Ancient Greek: Βρύχων, Modern Greek: Βρύχωνας, English translation: "the roaring one") was the name of two different small rivers in Greece.  One of them flows from Mount Pelion in Magnesia, Thessaly into the Pagasetic Gulf.  It has been attested under that name since antiquity, and is today known as the location of Greece's oldest bridge made of fortified concrete, constructed for a train line in 1895.  The other is said by ancient sources to have been in the Sithonia peninsula in Chalcidice, Macedonia (Greece), near Pallini.  According to ancient mythology, the river god of the same name was an ally of the Gigantes in their war against the gods, the Gigantomachy, which according to some sources took place at Pallene.

Lynceus (Argonaut): In Greek mythology, Lynceus or (Ancient Greek: Λυγκεύς ) was the jealous murderer of Castor, along with his brother, Idas.  Idas and Lynceus murdered Castor because they all (along with Polydeuces) sought Phoebe and Hilaeira, daughters of Leucippus (who was also Idas and Lynceus' uncle in some versions).  Lynceus was one of the Argonauts and he participated in the hunt for the Calydonian Boar.  He was a son of Aphareus and Arene and was said to have excellent sight, even able to see through trees, walls and underground.

Supporting paragraphs: Lynceus (Argonaut) Leucippus
Answer: Leucippus