The Infinite Digital Structure Theorem (IDST), formerly referenced as the pi-DST Framework, extends the recursive stabilization problem into the digital domain. It establishes the structural conditions under which digital orders can extend indefinitely across layers without forfeiting operational integrity.

Institutional Specifications

ProgramInfinite Digital Structure Theorem (IDST)

StatusFORMAL THEOREM — CANONICAL

Core InvariantCoherent Extensibility

Archive IDGILC-ARCH-IDST-2024

Original Theory

Canonical

Original Authorial Theory

This manuscript represents original theoretical research authored by Ivan Pasev. It introduces candidate models, axioms, and conceptual formalisms.

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Epistemic Boundary:Authorial work is designed for peer and scholarly audit. It represents a candidate scientific model under active investigation.

I. Notation & Definitions

The following formal objects govern the IDST logic:

• $D_n,D_{n+1}$: The successive Digitally Structured Layers in the computational manifold.
• $\mathrm{\Psi }$: The Admissible Digital Operator, governing valid inclusions and inclusions logic.
• Coherent Extensibility: The capacity of digital strata to remain unified under repeated self-similar layering.

II. Structural Extensibility Theorem

IDST reframes digital architecture from an ad hoc engineering discipline into a structural science. The core theorem states that infinite digital structure is not mere accumulation, but coherent extensibility governed by:

$$\underset{n\to \mathrm{\infty }}{lim}{D}_n\subseteq \text{CoherentManifold}$$

Where each discrete layer transition satisfies the inclusion relation:

$$D_{n+1}=\text{Include}(D_n,\mathrm{\Psi })$$

This transition relation ensures that scale produces structured growth rather than fragmentation, preventing "ghost states" or logic-drift as layers multiply.

Traversal Node Situation

This page occupies a dedicated coordinate slot in the program—s global knowledge graph:

External Academic Grounding

SCIENTIFIC LADDER: CORE TRANSITIONS

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Step 5: Invariant Eng.

Operational engineering principles.

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Step 6: IDST

Infinite Digital Structure Theorem.

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Step 7: Fabricon Theory

The minimal compositional atomic unit.

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**Status**: Canonical Formal Framework — **Version**: 6.0.0 **Reference**: PIDST_v6.0.0-CANONICAL *Maintained under the GILC public corpus architecture.*

Position in the Theory Spine

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