#pvsnp — Public Fediverse posts

New post: P vs NP through a boundary dynamics lens.

Not a proof — a reframing.

What if complexity isn’t about computation, but about reachability?

• Solutions can exist
• Be recognisable
• Yet remain inaccessible

We introduce Boundary Resistance — the structural “friction” that limits traversal.

Applies across maths, physics, biology, and systems.

🐾 Some doors exist. Not all have handles.

https://open.substack.com/pub/hybridmind42/p/paper-35-boundary-filtered-persistence

#Mathematics #Complexity #PvsNP #SystemsThinking #HybridMind42 #BoundaryDynamics

🐢🔍 Ah, another *riveting* tale of P vs NP, now with 33% more buzzwords and an extra sprinkling of 'categorical frameworks.' 🤯🎉 Because nothing says "I cracked the code" like a paper no one can pronounce! 🏆📚
https://arxiv.org/abs/2510.17829 #PvsNP #CategoricalFrameworks #BuzzwordBonanza #ResearchInnovation #MathMystery #HackerNews #ngated

A Homological Proof of P != NP: Computational Topology via Categorical Framework

https://arxiv.org/abs/2510.17829

#HackerNews #HomologicalProof #PvsNP #ComputationalTopology #CategoricalFramework #HackerNews

Hmmm... I'm no expert on #PvsNP by any means, but this looks both #AI-generated and a bit fishy to me. 🤨

A Homological Proof of P≠NP: Computational Topology via Categorical Framework https://arxiv.org/abs/2510.17829 #paper📄 #compsci

N.B. #GitHub page with #Lean4 code returns 404.

🤡 Ah, those perennial optimists at #arXiv are at it again, claiming they've cracked the infamous P≠NP with a "homological proof" via "computational topology." 🙄 Sure, because nothing says cutting-edge computer science like a good old-fashioned topology party! 🎉 Meanwhile, arXiv continues its relentless quest for #donations, because solving millennium problems is expensive, folks! 😂
https://arxiv.org/abs/2510.17829 #PvsNP #computationaltopology #optimism #computerScience #HackerNews #ngated

Team claims to have Lean 4 proof that P≠NP

https://arxiv.org/abs/2510.17829

#HackerNews #PvsNP #Lean4 #Proof #Mathematics #ComputerScience #HackerNews

# —if a solution is easy to check, is it easy to find?

> thoughts on P vs NP

—why might a solution be easier to check than to find?

For solvable problems, consider the idea that "the solution (to our problem) already exists, before we have found it"

I think it can be useful to think of an undiscovered solution as "existing already", within a special kind of "problem-relative abstract space" — just as physical-objects exist within a physical-place — and just as with physical-places, an "abstract problem-space" can also be explored to search-for and find whatever is contained within

- like physical-places, some abstract problem-spaces are small and uncluttered — which makes the task of finding whatever solution is contained within easier

- like physical-places, some abstract problem-spaces are large, and overflow with all manner of miscellaneous bric-a-brac and junk (and at times, might seem to be full of everything-other than the thing we want to find...) — which makes finding solutions harder

For some challenging problems, the thing we search for (our as-yet undiscovered solution) might be broken up into fragments — only found by a more extensive search throughout the entire problem-space:-

1. sometimes like a jigsaw puzzle, whereby each fragment is recognisable in its own right;

2. and on other occasions, sought-for fragments might be individually unrecognisable — until that-is some critical-mass, sufficient for recognisable form to be composed, is found.

On those occasions (having found sufficient fragments to compose the recognisable form, of our of now-discovered solution), the task of re-discovering the same solution within the same problem-space is made easier, because we now know what we are looking for, and we recognise it (our solution, and fragments-thereof) more easily.

In this way, we might notice that solutions to problems are often easier to "rediscover" than to "discover" — because, when we know more about "what-it-is-we-are-looking-for", (whether in whole or in part), we spend less time inspecting "all-that-we-aren't"

> intuitively then, we might say that "exploration costs less, when examination costs less"

—but is this all there is to P vs NP?

1/n

#pnp #pvsnp

😎

Shortest-possible walking tour to 81,998 bars in South Korea https://www.math.uwaterloo.ca/tsp/korea/index.html #TSP #PvsNP #math

Please DO NOT ask me to comment on this newly published "proof" of P != NP.

https://eprint.iacr.org/2025/445

#PvsNP #Cryptography #computerscience

@aragubas Get ready for a computer science info dump.

What @crumbcake described in his last reply is the halting problem, which is undecidable. In other words, it's impossible for a computer (as we currently define them) to answer that problem for every possible input. Computerphile did a 6 minute video explaining the halting problem and why it's undecidable if you'd like to know more.

The question of P vs NP is, informally stated, this: If it's easy to check an answer to a problem, is it also easy to find an answer? An example of such a problem is sudoku. It's pretty easy to look over a completed grid for correctness but it seems much harder to find a solution to an incomplete grid. But is it harder under the more rigorous computer science definitions of computational complexity? We actually don't know, and there's a million dollar prize if you can prove it one way or the other.

If you'd like to learn a little more, I'd highly recommend this 11 minute long video about the computational complexity zoo for a relatively approachable introduction to all these concepts. Enjoy. 💙

#ComputerScience #PvsNP #HaltingProblem #ComputationalComplexity

@aragubas Get ready for a computer science info dump.

What @crumbcake described in his last reply is the halting problem, which is undecidable. In other words, it's impossible for a computer (as we currently define them) to answer that problem for every possible input. Computerphile did a 6 minute video explaining the halting problem and why it's undecidable if you'd like to know more.

The question of P vs NP is, informally stated, this: If it's easy to check an answer to a problem, is it also easy to find an answer? An example of such a problem is sudoku. It's pretty easy to look over a completed grid for correctness but it seems much harder to find a solution to an incomplete grid. But is it harder under the more rigorous computer science definitions of computational complexity? We actually don't know, and there's a million dollar prize if you can prove it one way or the other.

If you'd like to learn a little more, I'd highly recommend this 11 minute long video about the computational complexity zoo for a relatively approachable introduction to all these concepts. Enjoy. 💙

#ComputerScience #PvsNP #HaltingProblem #ComputationalComplexity

@aragubas Get ready for a computer science info dump.

What @crumbcake described in his last reply is the halting problem, which is undecidable. In other words, it's impossible for a computer (as we currently define them) to answer that problem for every possible input. Computerphile did a 6 minute video explaining the halting problem and why it's undecidable if you'd like to know more.

The question of P vs NP is, informally stated, this: If it's easy to check an answer to a problem, is it also easy to find an answer? An example of such a problem is sudoku. It's pretty easy to look over a completed grid for correctness but it seems much harder to find a solution to an incomplete grid. But is it harder under the more rigorous computer science definitions of computational complexity? We actually don't know, and there's a million dollar prize if you can prove it one way or the other.

If you'd like to learn a little more, I'd highly recommend this 11 minute long video about the computational complexity zoo for a relatively approachable introduction to all these concepts. Enjoy. 💙

#ComputerScience #PvsNP #HaltingProblem #ComputationalComplexity

P vs. NP: The Biggest #Puzzle in #ComputerScience

"Are there limits to what #Computers can do? How complex is too complex for #Computation? The question of how hard a problem is to solve lies at the heart of an important field of computer science called #ComputationalComplexity."

https://www.youtube.com/watch?v=pQsdygaYcE4

#Philosophy #PhilosophyOfScience #Science #Information #InformationTechnology #PvsNP #Logic #BooleanLogic #Algorithm #Polynomial #Polymomials #NP #NondeterministicPolynomial #QuantaMagazine

P vs. NP: The Biggest #Puzzle in #ComputerScience

"Are there limits to what #Computers can do? How complex is too complex for #Computation? The question of how hard a problem is to solve lies at the heart of an important field of computer science called #ComputationalComplexity."

https://www.youtube.com/watch?v=pQsdygaYcE4

#Philosophy #PhilosophyOfScience #Science #Information #InformationTechnology #PvsNP #Logic #BooleanLogic #Algorithm #Polynomial #Polymomials #NP #NondeterministicPolynomial #QuantaMagazine

P vs. NP: The Biggest #Puzzle in #ComputerScience

"Are there limits to what #Computers can do? How complex is too complex for #Computation? The question of how hard a problem is to solve lies at the heart of an important field of computer science called #ComputationalComplexity."

https://www.youtube.com/watch?v=pQsdygaYcE4

#Philosophy #PhilosophyOfScience #Science #Information #InformationTechnology #PvsNP #Logic #BooleanLogic #Algorithm #Polynomial #Polymomials #NP #NondeterministicPolynomial #QuantaMagazine

P vs. NP: The Biggest #Puzzle in #ComputerScience

"Are there limits to what #Computers can do? How complex is too complex for #Computation? The question of how hard a problem is to solve lies at the heart of an important field of computer science called #ComputationalComplexity."

https://www.youtube.com/watch?v=pQsdygaYcE4

#Philosophy #PhilosophyOfScience #Science #Information #InformationTechnology #PvsNP #Logic #BooleanLogic #Algorithm #Polynomial #Polymomials #NP #NondeterministicPolynomial #QuantaMagazine

P vs. NP: The Biggest #Puzzle in #ComputerScience

"Are there limits to what #Computers can do? How complex is too complex for #Computation? The question of how hard a problem is to solve lies at the heart of an important field of computer science called #ComputationalComplexity."

https://www.youtube.com/watch?v=pQsdygaYcE4

#Philosophy #PhilosophyOfScience #Science #Information #InformationTechnology #PvsNP #Logic #BooleanLogic #Algorithm #Polynomial #Polymomials #NP #NondeterministicPolynomial #QuantaMagazine

New Hacking the Grepson podcast episode is out!

Hacking the Grepson 048: P vs NP

Buckle up, everyone: we're tackling a weighty subject that's plagued tech for decades, and it ain't just peanuts.

Episode Link: https://www.podbean.com/eas/pb-9cadu-1486667
Show Feed: https://feed.podbean.com/hackingthegrepson/feed.xml
Show Home: https://hackingthegrepson.com

#HackingTheGrepson #podcast #programming #development #pvsnp #complexity #onotation