Virtual Invasion Dynamics: Mutual Invasion of Self-Organizing Attribute Clusters — From Boundary Generation to Actual Condensation: A Formal Outline of an Interdisciplinary Meta-Framework

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-21
DOI
https://doi.org/10.5281/zenodo.22870047
Primary Topic
Complex Systems and Dynamics
Type
preprint
Controls
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preprint

Virtual Invasion Dynamics: Mutual Invasion of Self-Organizing Attribute Clusters — From Boundary Generation to Actual Condensation: A Formal Outline of an Interdisciplinary Meta-Framework

Trace Drift
Zenodo (CERN European Organization for Nuclear Research)
Complex Systems and Dynamics
preprint

Virtual Invasion Dynamics: Mutual Invasion of Self-Organizing Attribute Clusters — From Boundary Generation to Actual Condensation: A Formal Outline of an Interdisciplinary Meta-Framework

Trace Drift
preprint en

Abstract

This paper presents the Virtual Invasion Dynamics (VID) framework, a meta-theory describing "how interaction is possible." The framework's core claims are: interaction precedes entities; entities are emergent products of interaction processes reaching condensation thresholds; time is not a background parameter but the accumulation of irreversible marks left by invasion; boundaries are products of condensation rather than prerequisites. The framework comprises a global constraint layer (attribute lattice L, partial order ≼, Möbius ring field theory, time projection, self-referential structure, dynamic category Inv) and a local dynamics layer (virtual invasion process operator I, phase transition criterion Ψ, condensation operator G, invasion-response function H). This paper provides eight closure clauses and validates the framework's operability on three instances: the chicken-egg problem (pure logical demonstration), Marin d2048 training (real data validation, condensation moment n* ≈ 5%), and the N-S proof event (qualitative analysis). The framework is at the formal outline stage; unclosed items are marked. Version v1.2 update: Three additional structural elements are formalized: the generation mechanism of the observation cross-section, the directionality of invasion, and the distinction between phase transition and condensation maintenance. Nine technical clarifications are incorporated, and a fourth instance is added. Remaining unclosed items: constructive proof of Fix(F), and full vector definition of ∇Φ_I in metric-free regions. In this version (v1.3), two structural elements are newly resolved: the constructive proof of Fix(F) existence via the Lawvere fixed-point theorem on the category of categories, and the formalization of the dynamic category Inv as a parameterized structure. A finite-section fixed-point theorem is also introduced, demonstrating that fixpoints exist on any finite observation cross-section. The remaining boundary conditions—terminal object existence on the full lattice and directed completeness of the parameter space—are inherent to the framework's finite-section nature.

Zenodo (CERN European Organization for Nuclear Research)
Complex Systems and Dynamics
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