Algorithms of Proa

The Alogrithms of Proa were a heretical cult that inhabited the hive world of Proa during the 41st millenium.

Before the heresy
Proa, with a population in the tens of billions, is a minor manufactorum site in Ultima Segmentum and the recruiting ground for the Proa Targeters, a regiment renowned for the skill of its snipers and artillery personnel. Since not all of the planet is urbanised, with there still being a few open fields, the artillery have a lot of room to practice, while the high towers of the hives are perfect for snipers to hone their skills. This is due to the exceptional mathematical skill instilled in the populace since the War of the Beast and also ensured that the inhabitants were in demand by the Administratum, Adeptus Terra, and the Departmento Munitorum. However, such focus on one subject led to a degree of corruption in 830.M41 that resulted in a cult springing into existence in the lower hives of the northern continent.

The heresy
Containing some of the best snipers in the hive, the cult was able to assassinate key Imperial officials before using the rest of its forces to establish a hold on the northern continent. Several elements of the PDF and Imperial Guard joined the rebellion. The Imperial Governor, Strategos Pythagoras, requested Imperial aid but the nature of the warp meant that help did not arrive until 8 years later.

The aid came not from the Guard or the Space Marines but an unofficial army. A group of zealots referring to themselves as Frateris Militia arrived to cleanse the world in the Emperor's name. At the head was one of the Ecclesiarchy's most violent Priests, Marcia Hrodberht. The Militia had been well armed for the attack, taking surplus tanks and armoured personnel carriers with them to protect themselves against the Algorithms' snipers. It also happened to be composed mostly of ex-Guardsmen and women, many of whom had kept their equipment from their time in the galaxy's largest army. Reinforced by loyalist Proa forces, the Militia entered the northern hives under air cover.

While loyalist and traitor snipers traded shots and artillery bombarded each other, Marcia herself went on a search of the hive for clues to the cult's motives. She expected to find signs of Chaotic infiltration, especially as she had to deal with a copycat Chaos rebellion on her first few missions after her liberation from her homeworld. However, she found no signs of worshippers of the Blood God, the Dark Prince, Nurgle, or Tzeentch. Indeed, there was not even a sign of Chaos Undivided or a minor Chaos God. However, Marcia found images of a skeletal figure in a black hood wielding a scythe and a golden giant with green energy wrapped around it. It was not clear whether these were objects of worship or something else altogether, so Marcia kept them and destroyed them after they proved to be of no use.

The end
Marcia managed to stumble upon the inner sanctum of the cult, where several of the leaders were willing to talk with her. Realising that this would distract the cult's commanders from managing the battle outside, Marcia agreed. One of the key topics of discussion was quadratic equations. The questions included, "As such algebraic puzzles have two answers, is it possible that every question has two answers?" The cult and Marcia also discussed the value of non-decimal counting systems, such as nonary, ternary, sexagesimal, and octodecimal. By the time the conversation had run its course, the militia and Proa loyalists had defeated the Algorithms.

Once the militia had finished, Marcia burnt all the leaders to death on the spot with her inferno pistol. A few commanders tried to fight back, but Marcia had spent the conversation preparing for an Act of Faith. She was able to Divide by Zero and make x=0 through her faith in the Emperor. Pistols, armour, blood, and even a whole person vanished into nothingness as the Act cancelled them out of existence. The rest were easy prey for Strategos Pythagoras. The Governor had joined the battle and was the first to break into the inner sanctum after Marcia. Eager to prove his faith and to get vengeance for the taint on his record, Pythagoras put several hellpistol blasts into the remaining leaders before they could strike back at Marcia.

Afterwards, Marcia supervised a purge of all heretical elements on Proa. All remaining Algorithm members were dealt with. Some suspects claimed to be innocent but Marcia decided that anyone brought to her must have been guilty of something. This success was Marcia's final mission as a Priest. Afterwards, she was a Confessor of the Ecclesiarchy.

The Proa Heresy was mostly forgotten until the discovery of the Necrons. Since the images of the hooded figure with a scythe and the golden giant matched that of the C'tan beings known at Nightbringer and the Deceiver, the Algorithms became a subject of interest once more. Marcia's statement said that she did not find anything about the images beyond the images themselves and it is clear that there was no obvious Necron or C'tan influence on the cult. Even if the images were of the two most well-known C'tan, that still raises a few questions. How did the cult know of the C'tan before the Imperium and what focus did the beings have for the cult? Were they objects of worship or objects of fear?

Doctrine
The version of the Imperial Cult on Proa placed a value on music as an expression of harmonious mathematics. The Emperor was believed to be the supreme mathematician of the universe, a fact that the Ecclesiarchy did not dispute. In fact, several individuals who knew the Emperor such as Bjorn the Fell-Handed of the Space Wolves said that was not too far from the truth. Certainly, it is said that the Emperor was wise and skilled at whatever he put his mind to. For this reason, Proa always had strong links with the Adeptus Mechanicus, seeing them as kindred spirits. However, the Algorithms believed that the Emperor's divinity and wisdom was much exagerrated, perhaps false. Somehow, a few their leaders had obtained details of the Horus Heresy and believed that somebody so wise could not have alienated his sons so much that they turned to Dark Powers in retaliation. Believing that the Emperor may not be so harmonious, the Algorithms decided that a proper debate was needed. However, the Imperium leaves no room for debating the Emperor's godhood, so rebellion was the only option.

The Algorithms (and even the loyal population of Proa) had mathematical ideas even on human nature. They believed men to be odd numbers and women to be even numbers, that true love required the numbers 220 and 284, and that imaginary numbers were a necessary evil. Sanctioned psykers and mutants were believed to be imaginary numbers- they look human but they aren't really. This reflects the nature of imaginary numbers- while they exist, they do not fit onto a normal number line.

Despite this, the Algorithms appeared to fail to realise that even if they had succeeded in seizing all of Proa, the hive world's lack of sufficient food production would have killed it. The Imperium could quite simply have starved it into surrender. The Algorithms did not think about this because they were benefiting from food imports that the loyalists needed. Such a grave error was not noticed, which Marcia used against them in the final mathematical confrontation.

Superior mathematical skill is not necessarily a prerequisite for a leadership, management, or command position in loyalist society. Many of those skilled at arithmetic, trigonometry, or geometry enlist in the military, so traditional qualities of the aforementioned positions are the main focus, with mathematical skill. However, the Algorithms insisted that only the most numerate could possibly preserve the harmony of society and so excluded those who struggled with quartic equations, mental trigonometry, or long division.

Military
Just like Proa in general, the Algorithms' military strength rested in its snipers and artillery.

A Proa Targeter force can easily take out key figures in any enemy army whilst also blowing them to pieces with unnervingly accurate barrages. In the Targeters, most specialist regiments are either light infantry, artillery, or siege. The command structure is heavily decentralised to ensure that the enemy cannot use similar tactics back on them. Also, everyone receives training in the skills of their immediate superior to allow seamless replacements in the chain of command. Outsiders are rarely tolerated as they are perceived to be disruptive to the musical harmony of the regiment. All small arms of the Targeters are produced on Proa itself.

The Proa Planetary Defence Force is more varied, as not everyone has the mathematical skills needed for sniping or artillery work, at least by that hive world's standards. Such individuals find themselves in more conventional roles, such as infantry and vehicle crew.

The Algorithms copied this formula exactly. However, while they were able to put up a decent fight against the Frateris Militia, killing a large chunk of them without hassle and holding their own in conventional fights, they were not able to stand up to the loyalists, who were just as skilled as them, if not better. Neither side had any qualm about shelling the other side's  hives, though the loyalists retained the majority of the air force, so had superior air cover.