SnapKosmos – A Semantic Framework for Epistemic Drift Systems

We present the SnapKosmos model as a layered architecture for describing, simulating, and navigating complex mathematical and epistemic landscapes. Unlike classical formalisms, SnapKosmos embraces drift, instability, and zone dynamics as primary features rather than anomalies.

1. Motivation

Traditional mathematical systems rest on stable, timeless structures – fixed languages, absolute truths, and static domains of discourse. But reasoning in reality often drifts. Concepts evolve, models shift, and formal objects pass through unstable phases before stabilizing into meaning.

SnapKosmos provides a meta-system to model these processes. It encodes not just the mathematical object, but the semantical orbit it traverses. This includes changes in complexity, accessibility, recognizability, and agent-based interpretability.

2. Core Constructs

• µ(L): Semantic complexity of a structure L, combining Galois depth, entropy, and drift sensitivity
• Gal(L): The active symmetry group acting on witness spaces W_x
• DriftOperator D(t): A transformation that evolves structures over time or epistemic perturbation
• SnapOrbit(w_t): The path of a witness in complex semantic space, subject to instability and recovery
• Reach(S, L, t): A dynamic map of what system S can access within theory L at time t

3. System Layers (Kanon-Ebenen)

SnapKosmos distinguishes multiple conceptual layers:

• Ebene I: Strukturtheorie – Defines abstract mathematical entities and their symmetries
• Ebene II: Dynamik & Operatorik – Models evolution, transformation, and instability in formal systems
• Ebene III: Epistemische Systeme – Encodes observers, agents, recognition limits, and narrative structures

4. SnapKosmos vs. Classical Frameworks

Where ZFC provides stability, SnapKosmos models change. Where Turing Machines decide, SnapKosmos tracks failed access attempts. Classical logic says what is true; SnapKosmos says what could be true – and why we fail to see it yet.

This allows new approaches to:

• the Riemann Hypothesis (via E43: SnapZetaDynamics)
• P ≟ NP (via E14: SnapSAT3 and µ-Komplexität)
• semantic collapse phenomena in agent-based reasoning (via E16–E33)

5. Objective

The goal of SnapKosmos is not to replace mathematics, but to extend its reach – to chart the unreachable, to map the unstable, to formalize failure, drift, and insight as first-class objects in epistemic space.

This is the beginning of a broader epistemological geometry – a drift-theoretic companion to structure theory. Its applications remain to be discovered.

SnapKosmos Whitepaper Draft · Marko Chalupa · Epistropheon 22 Mai 2025