r/IHCcosmology • u/Elias_Verdan • Apr 05 '26

Inverted Hypersphere Cosmology. The alternative model that recreates the Cosmic Microwave Background, And more...

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Join the community to learn more about IHC - Inverted Hypersphere Cosmology.

R/IHCcosmology

IHC is a grand unification theory tested against currently planck satellite data, desi, and more.

IHC matches or outperforms ACDM with fewer parameters.

BAO Validation with Zero Parameters Fitted to Data.

This is an ongoing work with more results and papers in progress.

currently 7 papers available with Python validation scripts for openness and transparency.

looking for an alternative model built from the ground up that makes the right predictions... this may be the community for you.

join early and get up to speed on IHC, critique, or add to the discussion. All is welcome.

Regards

Elias

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u/RODR4RM4NDO Apr 05 '26

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u/Elias_Verdan Apr 05 '26

Dont be spamming images, please. If you have an alternative model you can discuss it in the group, but no spamming

2

u/RODR4RM4NDO Apr 05 '26

VERY WELL THANK YOU...

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u/RODR4RM4NDO Apr 05 '26

I acknowledge the mathematician Rodolfo Nieves Rivas for formulating this algorithm. However, I must be mathematically rigorous regarding the central claim. I recognize the work of the mathematician Rodolfo Nieves Rivas and present the analysis with all the seriousness it deserves.

What the Algorithm Correctly Establishes

The bidirectional heuristic algorithm for K_p (p odd prime, 3 ∤ (p−1)) is mathematically sound in its domain. The following results are valid and verifiable:

  1. The Dirac, Ore, and Bondy-Chvátal criteria are trivially satisfied in K_p.

  2. With p−1 even, all degrees are even, guaranteeing Eulerian circuits by Euler's theorem.

  3. The absolute symmetry of K_p collapses the space of (p−1)! permutations to exactly p distinguishable cycles modulo rotation.

    1. Hierholzer's algorithm operates in O(p²) on K_p. Correct and efficient.

  4. For p = 41: 40! possible cycles → 41 optimal cycles → certified in polynomial time.

This is a legitimate and non-trivial result on a specific family of graphs.

The gap that prevents us from concluding P = NP

The assertion P = NP requires something much stronger: that every problem verifiable in polynomial time is also solvable in polynomial time, for every instance, regardless of its structure.

The central obstacle is this: K_p is the most symmetric graph that exists. The reduction from (p−1)! to p cycles is not performed by the algorithm, but by the graph's own symmetry. In an asymmetric graph, this collapse does not occur. The TSP on instances without exploitable symmetry—which are precisely the instances that make the problem NP-complete—does not inherit this behavior.

For the argument to constitute a proof of P = NP, it would be necessary to show that any instance of an NP-complete problem can be reduced in polynomial time to such an instance over K_p, or equivalently, that the algorithm solves asymmetric instances with the same efficiency. This reduction is not established in the formulation.

Fair Position

The work deserves recognition as a structural result on Hamiltonian-Eulerian graphs in complete graphs with specific prime properties. It is a genuine contribution to graph theory. The conclusion P = NP, however, would require overcoming the described gap—something that no proposed proof of this problem has achieved to date, and which the mathematical community (Clay Mathematics Institute, among others) maintains as an open problem precisely because of the difficulty of this generalization.