The Final Singularity

The Final Singularity is the current stage of the Homelanders' development.

It had increased their abilities to an incalculable level, allowing them to change the fabric of reality in almost (within the laws of quantum mechanics) any way with ease.

Brief overview
One of the main goals the Homelanders pursue ever since they'd become sapient is a constant development and gain of new technologies and abilities. So it's not surprising that they decided to go through the final singularity, that changed their lives and minds once and for all.

After the Final Singularity, all the projects that were currently running instantly became obsolete because the Homelanders gained an ability to work directly with reality, bypassing all intermediate stages of production and development.

The SC (stellar cycle) of 1,000 AI was proclaimed as the cycle when the 'Final Singularity project' started.

Energy
The Homelanders had used their star as the main source of energy. It produces more energy than the Sun, but the exact numbers are yet to be known.

Before that, they were using orbital power stations and nuclear power to supply themselves and their technologies. That was one of the main reason why the star sphere construction had taken so many SCs to finish.

At the next point of their history, after constructing the first stellar sphere and getting all the energy from their home star, along with steady and regular asteroid capture and swarms of bionanobots at the Homelanders' service, they were able to cut the time needed for the stellar spheres' production dramatically.

To address the problem of speed, limited by the laws of physics that prohibit faster than light travels, the Homelanders used an original type of engine which, given enough energy and constructed properly, lets them reach distant stars in hours, rather than SCs and dozens of SCs.

The principle of functioning of this drive lies in the usage of cosmic expansion phenomenon. With a lot of energy and negative mass, this drive is contracting space in front of it and expanding space behind it, resulting in speeds that are as many time faster than light as much 'fuel' is used.

Black rifts in form of wormholes were also used to cover great distances.

Considering the stellar energy being the major faster than light traveler, along with possible replacement of solid walls of the accumulators that capture SSP with those functioning on principles of quantum teleportation, the Homelanders literally conquered 60,034,123 + 1 stars in a thousand SCs, ensuring that each of them had the power of the star in their disposal.

The speed of stellar power capture had grown exponentially with more and more energy available, eventually resulting in currently having the energy of the whole Supercluster in the full disposal of the Homelanders.

Molecules, atoms and particles
With enough energy supplies and further technological progress, more advanced particle accelerators and nuclear transmutation centers had arisen. It resulted in total control of molecules, atoms and particles, with quarks being the further goal, and obsolescence of nanomachines as the tools of matter manipulation.

By manipulating atoms, the Homelanders create any allotropes or substances without using chemical processes to, for example, make a tungsten disulfide. Instead of a complex chemical reaction they just unite two atoms of sulfur and one atom of tungsten in a required order, ensuring faster and more reliable creation of required substance.

Particles manipulation has even vaster potential, for they make any resources' requirements obsolete. By using hydrogen -- the most abundant chemical substance in the Universe -- as a starting point (and the second most abundant chemical substance in the Universe, helium, as a source of neutrons), the Homelanders are able to create any chemical element in form of any isotope by breaking hydrogen and helium atoms in electrons, protons and neutrons and uniting them in any order.

Quark manipulation remains the last matter manipulation section of the Final Singularity project that isn't fully used. Potentially, it will give the Homelanders abilities way beyond their current understanding, but for now only limited manipulation is available.

Processing power

Quantum CPUs, the major part of the Homelanders' minds, are extremely efficient and powerful data processing devices that worked flawlessly for many stellar cycles, so it was logical to save and upgrade them over the course of the Singularity.

Nowadays, each Homelander has its personal star as a source of energy, used solely for their mind, in form of a giant stellar quantum computer.

Thanks to the melding of their minds, Homelanders can increase their already vast processing power to truly incalculable levels.

This power is used mostly in explanding beyond their supercluster and conquering the total energy and matter in the Universe.

Expansion
The full potential of this Singularity remains unclear because it is not known currently if the Universe is endless or not, or if there are other Universes and Multiverses. What's clear is that the Homelanders have no intentions to stop at conquering their supercluster, explicitly planning to have the whole observable and non-observable Universe to control.

Current level
The current level of Final Singularity is letting Homelanders to control the total energy of their Local Supercluster. Their total power output equals 1.14x1039watts. Given current energy efficiency and energy logistics, the total power output for free usage is aproximately 80% of this number, or 9.12x1038watts.

The recent quasar taming project added roughly the same energy output as the whole supercluster, effectively doubling the power of the Homelanders. Because of its relatively compact size compared to dozens of galaxies and thus, much higher energy density, energy transfer and security increased dramatically.

As for computation power, it went way beyond 1x1040 FLOPS for a single Homelander. By using CPU melding, this amount increases even further.

The ultimate goal
The ultimate goal of the Final Singularity is to prevent any ultimate fate of the Universe, such as Big Rip, Big Crunch, Big Bounce, Heat death and so on, to prolong Homelanders' existence indefinitely.

To get a chance for that, they will need to utilize the full energy of the Universe. Because they only had one star as an energy source in their disposal in the beginning, it took 10,000 years to 'conquer' just one supercluster.

But with its power output, the Homelanders can cut the time from 10,000 years to 1,000 years per supercluster. The speed of conquering increases twofold with each supercluster they start to use as an energy source. With approximately 10 million superclusters in the observable Universe, the first stage of Final Singularity will be over in 25,000 years.

The second stage of Final Singularity is harnessing the elusive energy and matter of the Universe, which are currently known as dark energy and dark matter. Learning their functions, usage potential and origin will lead to utilizing them just as stars' energy is being utilized.