"Goldbach’s Conjecture: Final Analytical Proof with Strict Corrections"

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(Final Version with Strict Corrections)

This work presents the final and rigorously corrected analytical proof of Goldbach’s Conjecture. After an in-depth revision and error correction in the differential equation approach, two strictly analytical proofs are established:

1. Method 1: Utilizing the extended number xxx and the sum of squares operation ⊙\odot⊙, ensuring a structurally preserved formulation of Goldbach pairs.
2. Method 2: Based on the power-law dependency of the function G(N)G(N)G(N), describing the number of Goldbach partitions and proving its strict positivity for all even N>2N > 2N>2.

Key corrections include an improved formulation of the differential equation and verification that both methods remain mathematically consistent with the distribution of prime numbers. This final version supersedes all previous ones and represents a definitive analytical resolution of the conjecture.https://zenodo.org/records/14919245

Corrected_First_Method_Proof.pdf Corrected_Goldbach_X_Proof.pdf