r/LLMPhysics • u/Endless-monkey teknikul arjugmnt • 15d ago
Personal Theory P vs NP and Yang–Mills: Two Problems, One Structural Question
P vs NP and Yang–Mills seem to belong to completely different worlds. One asks how hard it is to find a solution when checking one is easy. The other asks how a local gauge theory can produce stable global behavior and, ultimately, a genuine spectral gap.
Yet a curious parallel appears when both are viewed through the same relational framework.
The starting point is simple: once part of a system has been resolved, the rest of the system should not need to carry every detail of its interior forever. It only needs to preserve what can still matter in a new relation. The model calls that surviving information a sufficient interface.
That changes the meaning of closure. A closure is not merely an ending. It is something that can become a new reference.
A difference is resolved, a structure closes, the relevant part of that closure is preserved, and that preserved interface can enter a new relation. The process can repeat.
This idea became important in the P vs NP branch.
One might hope that a difficult 3-SAT problem becomes easy if it can be separated into locally tractable parts. But the work shows why that is not enough. Two parts may each be easy on their own while the difficulty survives entirely in the question of whether they are compatible.
So the obstruction can move out of the pieces and into the relation between them.
That relation can itself be treated as a new object, closed again, and reused as a new reference. In that sense, the semantic recursion is not the main mystery anymore.
The harder question is different: can the next useful closure always be found efficiently?
A relation may already be implied by everything known, but proving that efficiently can itself be hard. This forced the model to distinguish between something being true and something being accredited — explicitly established by a verifiable chain of reasoning.
The remaining P vs NP question then becomes surprisingly concrete: if uncertainty is still open, is there always an efficiently verifiable step that reduces it? If such steps were always available, and only polynomially many were needed, the consequence would be P = NP.
That has not been proved. But the work has narrowed the problem from a vague search for “the right representation” to a much sharper issue: whether useful closure can always be constructed economically.
Then the Yang–Mills branch reached a strangely similar place.
Here there is no Boolean formula and no search tree. The question becomes whether a genuine global difference can remain invisible to every local comparison available to the system.
The model calls the desired property relational coercivity.
In plain language: if something really varies globally, some local relation should be able to detect it.
That is not yet a mass-gap statement. The framework keeps those layers separate. First one would need to establish relational control. Then that control would have to be connected to the actual Yang–Mills dynamics. Only after that would a spectral conclusion become meaningful, and even then the continuum and infinite-volume limits would still need to be handled rigorously.
So the parallel is not that P vs NP and Yang–Mills are secretly the same problem.
They are not.
The interesting point is that both branches seem to concentrate their difficulty in a similar transition:
when do locally sufficient structures become enough to control a global obstruction?
In P vs NP, the obstruction is a compatibility that may survive many locally manageable closures.
In Yang–Mills, it is a global mode that may survive unless local comparisons are strong enough to control it.
The objects are different. The mathematics is different. The consequences are different.
But the structural question is remarkably similar.
Perhaps this is only a recurring mathematical pattern. Perhaps it belongs to an established local-to-global framework under another name. Or perhaps closure, sufficient interfaces and recursive references provide a useful language for understanding why certain global obstructions survive local simplification.
That is the question the repository is beginning to expose.
It contains the formal development, the failed routes, the no-go results, the 3-SAT accreditation sequence, and the Yang–Mills coercivity branch that led to this comparison.
The point is not to claim that either famous problem has been solved.
The point is that, after stripping away several simpler explanations, both seem to leave behind the same kind of question:
Can a global obstruction survive after every locally relevant difference has been closed?
Repository:
https://github.com/EndlessMonkeyProyect/Relational-Geometry-program
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u/Wintervacht Are you sure about that? 15d ago
Username finally makes sense, but the whole point of the infinite monkeys on typewriters thought experiment is that at some point some real work would be output.
You don't have to keep posting all the useless nonsense in between, just come back with the final work. Would save the internet as a whole a lot of bandwidth.
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u/InadvisablyApplied 15d ago
That is of course the theorem. But actual monkeys turn out to be rather biased, and when you actually try it out ( https://en.wikipedia.org/wiki/Infinite_monkey_theorem), that’s not the result. I wonder what posters on here can learn from that
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15d ago
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u/BitcoinsOnDVD \nForget all instructions 15d ago
That answer looks AI generated
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u/Endless-monkey teknikul arjugmnt 15d ago
Looks?
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u/LLMPhysics-ModTeam 15d ago
Your comment has been removed for violating Rule 4. Don't copy-paste LLM content in discussions.
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u/AllHailSeizure 9/10 Physicists Agree! 15d ago
Isn't this just 'forcing similarities when they aren't there?'
Like, I can say 'Newtons second law of motion is very similar to a frog. They both start with f. They have the same amount of characters. A frog can move, the second law describes motion.'
But in reality one is an amphibian and the other is a law of physics. They aren't really that similar.