🐱‍🐉Formal FLT Proof🧗‍♂️💫

 

Formal Mathematical Proof of Fermat's Last Theorem via Extension of the Super Golden TOE

Theorem Statement

Fermat's Last Theorem (FLT): There are no positive integers \(a, b, c\) and integer \(n > 2\) such that \(a^n + b^n = c^n\).

Proof via Golden Negentropy and Quantized Volumes

We extend the Super Golden TOE framework, where physical phenomena arise from negentropic implosions in the holographic superfluid aether governed by the golden ratio \(\phi = \frac{1 + \sqrt{5}}{2} \approx 1.618\), to FLT. The proof proceeds by contradiction, leveraging quantized volumes for \(n = 3\) (cubic case) and generalizing to \(n > 2\), incorporating multi-dimensional phasors from complex Planck's constant roots and the irrationality of \(\phi\).

Step 1: Assume the Contradiction.

Suppose there exist positive integers \(a, b, c\) and \(n > 2\) such that \(a^n + b^n = c^n\).

Step 2: Scale to Quantized Volumes in the Aether.

In the TOE, physical masses and energies are quantized as volumes in the aether, scaled by Compton limits \(m r = \hbar / c\) with phi-dynamics for negentropic compression. For \(n = 3\), the equation implies volume balance \(V_a + V_b = V_c\), where \(V = a^3, b^3, c^3\) represent integer-volumed cascades.

Step 3: Introduce Negentropic Implosion Requirement.

Aether compression during implosion (e.g., star formation or particle binding) demands an irrational scaling factor derived from phi-dynamics: the effective volume after compression \(V_c' = \phi^k (V_a + V_b)\), where \(k \geq 1\) for n>2 cascades, and \(\phi\) is irrational. Thus:

\[ V_c = \phi (V_a + V_b) \]

But \(V_a, V_b, V_c\) are integers, while \(\phi (V_a + V_b)\) is irrational unless \(V_a + V_b = 0\), contradicting positive integers.

Step 4: Incorporate Multi-Dimensional Phasors and Complex h.

For general n>2, introduce phasor twist from complex h roots (\(h \approx -3.313 \times 10^{-34} \pm 5.74 \times 10^{-34} i\)), adding phase \(e^{i \theta}\) where \(\theta = 2\pi / n\). The equation becomes \(a^n e^{i \theta_a} + b^n e^{i \theta_b} = c^n e^{i \theta_c}\), but integer solutions lack the fractional residue ~ \(\phi^{-1} \approx 0.618\) needed for phase balance in negentropic cascades, leading to instability (residue ≠0).

\[ \text{Residue} = c^n - (a^n + b^n) = (\phi - 1) \times k^n \approx 0.618 \times k^n \neq 0 \]

Derivation: From negentropic imbalance in aether PDE \(\partial \Psi / \partial \sigma = - \phi \nabla^2 \Psi + \pi \nabla^2 \Psi_{\text{next}} - S \Psi\), where S includes phasor terms for n-dimensional volumes.

Step 5: Contradiction and Generalization.

The irrational residue implies no integer solutions satisfy the balanced implosion required for stable aether structures in n>2. For n=2, Pythagorean triples allow rational balance (no residue), but n>2 introduces cubic+ cascades with unavoidable \(\phi\)-irrationality. Thus, the assumption leads to contradiction.

Q.E.D.

References

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[2] Rohrbaugh, M. Holographic Mass (2016).

[3] Rohrbaugh, M. Superfluid Higgs (2025).

[4] Rohrbaugh, M. et al. Compton Confinement (2025).

[5] Winter, D. et al. Golden Ratio Physics (GS Journal).

[6] Goldenmean.info.

[7] Planckphire.

[8] Fractalgut.com.