Singularity
"But HBM, a manifold with an undefined state of spacetime? How is this possible?"
Long answer short:
"I have no idea!"
A singularity (specifically, a gravitational or spacetime singularity) as described by general relativity, is a region in spacetime where gravity and density are so high, the laws of physics "break down" and is not fully understood, it is a single point in space. As stated, the laws of normal spacetime break down here.
Despite being impossible to contain in real life, singularities in the mod can be contained using specific materials like 
euphemium. This presents a danger; when dropped, singularities will break containment and destroy blocks temporarily (however, the minature black hole lasts indefinitely).
Creation and Variants
Singularities are fairly expensive and are upgrade based, starting with the base singularity, simply called "singularity".
Anticlimactically, they are all created in the basic crafting table:
Base Singularity
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Superheated Resonating Singularity
Continuously heats up matter by resonating every planck second. Tends to catch fire or create small plasma arcs.
(Note: Does not actually set fire to anything or create plasma arcs.)
   |
Contained Counter-Resonant Singularity
Nullifies the resonance of objects in non-euclidean space, creates variable gravity well. Spontaneously spawns tesseracts. If a tesseract happens to appear near you, do not look directly at it.
(Note: Neither "nullifies the resonance of objects in non-euclidean space", creates any noticeable gravity, nor spawns any tesseracts that can't looked at directly.)
   |
Miniature Black Hole
Contains regular singularity in the center. Large enough to stay stable. It's not the end of the world as we know it, and I don't feel fine.
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Spark Singularity
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Dangers
Singularities, with the exception of the singularity screwdriver (possibly because it is contained better), will break containment and turn into a black hole if dropped. These black holes can destroy all blocks, including bedrock and the barrier block, which makes it extremely dangerous. The singularities are temporary, which means they're not as dangerous as they could be.
However, the miniature black hole lasts indefinitely. It can only be destroyed when the antimatter cluster is dropped on it. It can be crafted as follows:
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A list of their estimated strength level and duration:
| Singularity Type | Strength | Duration (Seconds) | Notes |
|---|---|---|---|
| Base | Weak | 30 | |
| Superheated Resonating | Strong | 50 | |
| Contained Counter-Resonant | Strong | 50 | |
| Miniature Black Hole | Strong | N/A | Infinite duration |
| Screwdriver | N/A | N/A | Harmless if dropped |
| Spark | Very Strong | 160 |
Uses
Singularities have little use, however they can be used to craft these items:
Dark Fusion Core Items
The 
dark fusion core can be crafted in the 
plasma forge using the spark singularity.
12,000mB
Additional items to operate the 
DFC crafted using singularities are:
Trivia
- Despite all of them forming small black holes when losing containment, the miniature black hole is the only one stated to be, naturally, in a black hole state.
- The spark singularity is the only one without a comment in its tooltip.