Infinite Stabilization Formula (ISF)

Public Status Boundary. The Infinite Stabilization Formula (ISF) is an original theoretical construct within the Science of Fabric Reality (SFR). It models recursive field stabilization across multiscale discrete boundaries. This page presents theoretical formulations and Lean 4 target structures, not experimentally verified physical constants.

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1. Conceptual Framework

The Infinite Stabilization Formula (ISF) addresses the open question of how discrete topological lattices achieve macroscopic stability without introducing arbitrary cutoff parameters.

In classical field theories, continuous scaling leads to ultraviolet divergences. Within the SFR framework, ISF formalizes a recursive feedback operator that bounds energy densities through topological invariance:

$${\mathcal{S}}_{\mathrm{\infty }}(\mathrm{\Phi })=\underset{n\to \mathrm{\infty }}{lim}{\mathcal{R}}^n({\mathrm{\Phi }}_0)\text{such that}\parallel \mathrm{\nabla }{\mathcal{S}}_{\mathrm{\infty }}\parallel \le K_{\text{bound}}$$

Where:

• ${\mathrm{\Phi }}_0$ represents the initial relational field configuration.
• $\mathcal{R}$ denotes the recursive stabilization operator enforcing topological conservation laws.
• $K_{\text{bound}}$ is the invariant curvature ceiling preventing point-like singularities.

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2. Structural Coupling to KP-Field Dynamics

ISF provides the formal boundary condition for the KP-Field equation:

• At micro scales ($\ell \to {\ell }_P$), ISF prevents lattice collapse through discrete knot topology.
• At macro scales ($\ell \gg {\ell }_P$), ISF smoothly recovers continuous differential geometry and standard relativistic invariance.

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3. Formalization & Lean 4 Objectives

Within our formalization pipeline, ISF is tracked under Gate M2 (Internally Derivable):

1. Lemma ISF-01 (Convergence): Proof that ${\mathcal{R}}^n$ converges uniformly on compact topological manifolds.
2. Lemma ISF-02 (Invariance): Proof of Noether-like charge conservation under the recursive transformation $\mathcal{R}$.

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Direct Navigation

• Inspect KP-Field Dynamics →
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