### Improving NP-complete algorithms

Suppose we have an (efficient) NP-complete algorithm. I remind that proving a provable theorem isn’t an NP problem, because there are theorems whose shortest proof is of super-exponential length. However, finding a proof that is below a given “threshold” length is an…

### [ERRONEOUS] A proof of P=NP using a Merkle tree

I denote s(X) the size of data X (in bits). I denote execution time of an algorithm A as t(A,X). Using a Merkle tree technology similar to one of the Cartesi crypto (but with a true random number generator, and possibly the…

### I’ve Proved Constructivity of P=NP

I’ve found (and proved) an algorithm that is NP-complete in the assumption that P=NP. In other words, if P=NP has a positive solution, my algorithm is its solution. I was kinda afraid if I already have almost solved P=NP as an easy…

### An infinitely big structure in the center of a black hole?

I remind that I defined generalized limit of arbitrary function. The limit may be an infinitely big value. It allows to define derivative and integral of an arbitrary function. I also defined what are solutions of partial differential equations where such infinities…

### Some Conjectures About Generalized Limits

Continuing my research from general topology monograph Algebraic General Topology, the following new open problems arose: I remind that I define generalized limit of arbitrary function. This limit is defined in terms of funcoids. As I show in the Book 3, Algebra,…

### Monograph “Algebraic General Topology. Volume 1” sent for publication

I’ve sent the final version of the first edition of my research monograph Algebraic General Topology. Volume 1 to Russian publisher INFRA-M and signed the publication contract. They are going to publish my book electronically. They also asked to send them a…

### Math volunteer job

I welcome you to the following math research volunteer job: Participate in writing my math research book (volumes 1 and 2), a groundbreaking general topology research published in the form of a freely downloadable book: implement existing ideas, propose new ideas develop…

### A step forward to solve an open problem

I am attempting to find the value of the node “other” in a diagram currently located at this file, chapter “Extending Galois connections between funcoids and reloids”. By definition $latex \mathrm{other} = \Phi_{\ast}(\mathsf{RLD})_{\mathrm{out}}$. A few minutes ago I’ve proved $latex (\Phi_{\ast}(\mathsf{RLD})_{\mathrm{out}})\bot = \Omega^{\mathsf{FCD}}$, that…

### A conjecture proved

I have proved the conjecture that $latex S^{\ast}(\mu)\circ S^{\ast}(\mu)=S^{\ast}(\mu)$ for every endoreloid $latex \mu$. The easy proof is currently available in this file.

### New conjecture about funcoids

Conjecture $latex \langle f \rangle \bigsqcup S = \bigsqcup_{\mathcal{X} \in S} \langle f \rangle \mathcal{X}$ if $latex S$ is a totally ordered (generalize for a filter base) set of filters (or at least set of sets).