The Dynamics of Constraint Networks: Formation, Meltdown, and the Dual Engines of Physical Existence

Energy-Efficiency Theory rests on a single irreducible dynamical engine: the constraint network. Every change in any physical system---the flow of time, the increase of entropy, the creation of order, the resistance of inertia, the sliding of Ben and Se, the onset of meltdown---is governed by the formation and meltdown of constraints, and by the spontaneous evolution of the basal differences that precede and surround them. Version 4. 0 establishes this unified dynamical authority as Constraint Network Dynamics (CND). CND v4. 0 is a comprehensive architectural upgrade from Constraint Dynamics v3. 2. Its central innovation is the dual-engine architecture: Part~II-A (Difference Dynamics) governs the spontaneous evolution of the substrate---diffusion, fluctuation-dissipation, the difference continuity equation, and the vacuum (N=0) limit---while Part~II-B (Constraint Dynamics) governs the five operations that select, sustain, and release specific substrate configurations as persistent Beings. The two engines are coupled through shared source-sink terms and the Template Condition. Jointly they constitute the complete physics of how Existence changes. Three fatal corrections are applied from v3. 2. (i) The cooperative capacity is restored to its authoritative form () =4/ (+1) ² with (1) =1, replacing the superseded Cₘ²+Cᵣ²=1 normalization inherited from pre-v6. 0 conventions. (ii) S₁ and S₂ state numbering is unified with Constraint Ontology v3. 3: S₁= (1, 1) designates the persistent Being (constraint exists, maintenance active), and S₂= (1, 0) designates the unmaintained constraint (constraint exists, maintenance absent). (iii) All occurrences of ``Constraint + Difference'' as the product of Distinction are corrected to ``Constraint + Being'': under the v6. 1 constitutional framework, Difference precedes Constraint as the basal inhomogeneity of the substrate; Distinction simultaneously produces Constraint (the boundary face) and Being (the maintained entity). Eight rounds of constitutional excavation structure the v4. 0 architecture. Part~I is rebuilt with ten new framework elements: L0 Sole Meta-Axiom anchoring, Existence/Being/non-Being constitutional distinction, the Difference Precedes Constraint annotation, the dual-engine declaration, the unified T₄₅₅ treatment, the vacuum--causality--CND constitutional triangle, constraint network metabolism, and the physical-engine cognitive-engine isomorphism. Part~II-A receives the ten-section Difference Dynamics migration from Difference Ontology v3. 3 Part~III, augmented with twenty-five structural extensions including three-layer spectral decomposition, the complex amplitude form, the two-quadrature rotation generator, two-channel transport, decoherence morphology, collective excitations (constraint phonons), localization-delocalization phase transitions, the holographic entropy bound, and the constraint/CFT correspondence conjecture. Part~II-B preserves the complete operational grammar of the five constraint operations---Formation, Meltdown, Maintenance, Transient Event, and Capture---with the three fatal corrections applied and new constitutional joint registration declarations. Part~III-A establishes the six-asymmetry unified framework with Being-as-Resistance as the single constitutional root. Part~III-B consolidates the Being lifecycle theorems, including the Template Condition as a new constitutional theorem. Part~III-C introduces the complete constraint thermodynamics: the single-Being thermodynamic cycle and the five-channel complete constraint Second Law. Part~III-D expands the degeneration dynamics with two-channel decoherence morphology (0 scrambling-dominated) and the Poincar\'e No-Go Theorem. Part~III-E consolidates competition and optimization: Physical Selection, the Full Coupling Theorem with three independent derivation paths to the golden ratio, and the Fourth Law candidate. The document is organized as follows. Part~I establishes the constitutional foundations. Part~II presents the core ontology---the dual engines of physical existence. Part~III develops the structural realization: theorems, dynamics, and thermodynamics. Part~IV provides the interface and bridge declarations. Part~V delivers operational signatures and cross-domain instantiation. Part~VI concludes with governance, falsifiable predictions, and deep insights. Fifty-nine bridge declarations, ten falsifiable predictions with full PM-9 statistical specification, thirty-plus deep insights, and a complete symbol table complete the constitutional architecture. Keywords: constraint network dynamics; difference dynamics; barrier asymmetry; creative asymmetry; Being lifecycle; constraint thermodynamics; degeneration corridor; decoherence morphology; dual-engine architecture; Energy-Efficiency Theory.