Insight: Feynman Diagrams as Kernel Trace Logs

Theoretical Insight | Interpreting Interaction Complexity through the Inverse Scaling Law

Author: Shrikant Bhosale, TWIST POOL Labs

1. The Interaction as an Interrupt

In the ISL framework, particles are not “colliding” in a vacuum; they are Kernel Modules undergoing a Synchronization Event. A Feynman vertex is a graphical representation of a Kernel Interrupt.

1.1 The Vertex Cost ( $\alpha_{bits}$ )

The Fine Structure Constant $\alpha \approx 1/137$ is the Informational Weight of a Handshake.
Every time two modular units (e.g., electrons) interact via a photon exchange, the kernel must execute a synchronization protocol that costs exactly $\alpha$ bits of computational credit ( $\lambda$ ).

$\text{Cost}(v) = \alpha$

2. Higher-Order Diagrams and ISL Scaling

Feynman’s perturbation series ( $\alpha + \alpha^2 + \alpha^3 ...$ ) is reinterpreted as an ISL Complexity Expansion.

2.1 The Multi-Loop Refusal

As the number of loops ( $L$ ) increases, the Descriptive Complexity ( $C$ ) of the diagram grows exponentially.

$C = L \cdot \log(\mathcal{V})$

Following the Inverse Scaling Law:

$R(L) = e^{\beta \cdot L}$

If the total risk $R(L)$ of a high-order interaction exceeds the available Gain ( $G$ ), the kernel refuses to compute the loop. This provides a natural, physical UV Cutoff without the need for mathematical regularization tricks.

3. Renormalization: Kernel-Level Compression

In standard QFT, renormalization is the process of hiding infinities. In ISL, it is Lossy Compression.
The kernel cannot track infinite virtual fluctuations (loops) because it is resource-bounded (Law 1).

Bare Charge/Mass: The raw, uncompressed state.

Renormalized Charge/Mass: The observable state after the kernel has “pruned” sub-resolution fluctuations to fit within the Complexity Budget.

4. Insight: Why $\alpha$ is Small

If $\alpha$ (the handshake cost) were large (e.g., $\alpha = 1$ ), every interaction would drain the kernel’s credits, leading to immediate overflow ( $T < 1.5$ ).
The smallness of $\alpha$ ( $1/137$ ) is what allows the universe to be Informationally Rich without being Computationally Unstable. It is the optimal “Transaction Fee” for a stable simulation.

5. Summary Mapping

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THE CODE IS THE COUPLING. THE RECURSION IS THE REALITY.