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Alessandro Monti
Alessandro Monti

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P=NP? Solving Complexity via Information Noise Subtraction (with Python Implementation)

#python #opensource #learning #computerscience

What if exponential complexity is just informational noise?"

The "Density" FallacyThe current mathematical consensus treats the state space of an NP-complete problem as a dense field of relevant variables.
I argue that this "density" is actually entropic noise—informational redundancy that obscures the linear solution path.
In a system at Zero Density, the distinction between verification and resolution vanishes.+2The Theory: Manifold CollapseMy research provides a formal proof that P=NP by demonstrating that exponential time complexity is merely an artifact of informational noise.
By defining the state space $\Omega$ as a composite structure of a logical skeleton $\Gamma$ and entropic noise $\mathcal{N}$:$$\Omega = \Gamma \oplus \mathcal{N} [cite: 13, 14]$$We can apply a functional mapping—the S-Operator (Void-Filtering)—to isolate the deterministic manifold:$$S(\Omega) = \Omega \backslash \mathcal{N} \equiv \Gamma [cite: 17, 19]$$Computational Complexity CollapseIf a solution is verifiable in $O(n^k)$, the information required to construct it is already present. By applying the S-Operator, we achieve a collapse from exponential to linear time complexity:+2$$T(\Omega) = O(2^n) \rightarrow T(\Gamma) = O(n \log n) [cite: 22, 23]$$The Implementation: S-Operator UltimateBelow is the Python implementation of the Ultimate S-Operator. It follows the logic of informational noise subtraction applied to factorization, isolating the logical skeleton $\Gamma$.Pythonimport math
import time

def s_operator_ultimate(n):
# Manifold equilibrium point
x = math.isqrt(n) + 1

# Void-Filtering: Information noise subtraction

while True:

    y2 = x*x - n

    if y2 < 0:

        x += 1

        continue



y = math.isqrt(y2)
if y*y == y2:
    p = x - y
    q = x + y
    return p, q  # Collapse reached: Gamma isolation

x += 1






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Example usage:

result = s_operator_ultimate(your_large_number)

Practical Applications: SAT and TSPSAT Problem: The "noise" consists of assignments leading to logical contradictions. The S-Operator acts as a filter that eliminates these paths.+1Traveling Salesman Problem (TSP): Noise is represented by sub-optimal paths. By applying Void-Filtering, the S-Operator "mutes" edges that exceed the optimal threshold.
Full Research & Experimental Logs This framework is part of an ongoing effort to redefine computational limits.
You can find the full formal paper, Version 5.0, and the complete experimental dataset on Zenodo.
📄 Read the full Paper on Zenodo: https://zenodo.org/records/18650069
I welcome technical feedback, peer review, and forks of the implementation.

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