Theory of Structural Instability as the Source of Irreducible Emergence

DESONA (Dynamically Emergent Structure from Openness, Non-Closure, and Axiomlessness) is a fully constructive, axiom-free framework that explains how form/structure can arise from the absence of prior assumptions. The system introduces no external arithmetic, no discrete time, and no imported rules; instead it uses a minimal grammar and witnessed transformations to derive dynamics intrinsically. DESONA Part I — Axiom-Free Structural Emergence and the Authenticated Kernel DESONA (Dynamically Emergent Structure from Openness, Non-Closure, and Axiomlessness) is a constructive, axiom-free framework that explains how structure, logic, and dynamics can arise from the absence of prior assumptions. It introduces no external arithmetic, no discrete time, and no imported logical operators. Instead, DESONA derives all structural behaviour from three emergent principles — Event-Freeness (EF), Irreversibility (IR), and Transcontextual Reproducibility (TR) — each proven as an intrinsic constraint within its generative kernel. Part I provides the formal base of the framework. It includes: The Generative Core Kernel (DCK), which expresses EF, IR, TR as emergent structural necessities of unfolding traces. The Deep-Intrinsic Kernel (DIK), which proves EF and IR constructively from the acyclicity of the compelled-step relation (K⁺). Unavoidability is represented as the transitive closure of witnessed repairs (Redex → K → K⁺), and the saturation state Kipp appears as the internal fixed-point of NoRedex. DESONA is fully number-free and time-independent: all directedness and well-foundedness emerge from internal structural constraints rather than external time. The result is a necessity-driven theory of emergence where structure, time-as-irreversibility, and reproducibility are not postulated but compelled by the framework’s own logic. This release (Zenodo v5) is the authenticated, signed publication corresponding to DESONA Part I v 1.2 (Oct 2025), verified by detached GPG signatures and a DCL Conformance Seal. The complete verification set (PDF, ASC signatures, SRH, public key, and seal manifest) is included under DOI 10.5281/zenodo.17390422. Supersession and Withdrawal Notice All earlier releases, drafts, or exploratory distributions of DESONA — including any text, Coq code, or documentation formerly made available under Creative Commons (CC BY-NC or related) terms — are hereby formally withdrawn and fully superseded by this edition. Only this version, identified by DOI 10.5281/zenodo.17390422 onstitutes the official and authorized release. All prior materials are obsolete and may not be copied, modified, or redistributed under any previous license or permission statement. This supersession explicitly includes DOI 10.5281/zenodo.17296031 and any other earlier DESONA publications released under CC BY-NC terms. Holders of earlier BY-NC versions are requested to delete local copies and cease further distribution to comply with the withdrawal notice.