The Ontology of Quantum Mechanics: Coherent Free-State Propagation and Constraint Formation

What is quantum mechanics? For over a century, its formalism has been extraordinarily successful, yet its ontological foundations remain contested. Energy-Efficiency Theory (EET) provides a first-principles answer: quantum mechanics is not an independent set of physical laws, but the theory of free-state energy propagating coherently on the constraint network at the optimal balance point 1. Version 3. 0 is a constitutional alignment, first-principles derivation, and systematic closure upgrade. It operates under the v6. 0 constitutional architecture: the L0 Sole Meta-Axiom (Absolute Truth is Unreachable) anchors all derivations in system-internal conditional necessity; the L1 Constitutional Presuppositions (Energy Ontology, Finite Actionability, Finite Distinguishability; All Cognition Is Modeling) provide the physical and cognitive foundations; the Five-Pillar Methodology and Dual-Identity Registration govern all methodological and transversal commitments. The document establishes the following constitutional core: 1. QM Constitutional Definition. Quantum mechanics is the coherent propagation of free-state energy at 1, where the cooperative capacity () = 4/ (+1) ² attains its maximum (1) =1 and the decoherence ratio r₃₄₂ (1) =0 vanishes. The wavefunction = || e^iS/A₄₄ₓ is the Euler representation of the constraint network's dual-face structure --- || is the constrained-state face, e^iS/A₄₄ₓ is the free-state face. The Schr\"odinger equation is derived from the Free-State Spectral Decomposition (Mathematical Foundations v2. 10) and the Euler Representation (Core Rules v6. 0, 0. 10. 2), replacing the superseded v5. x ``Universal Equation'' dependence. The factor-2 relation Hₒₓ₀₍₃₀ₑ₃ = 2H₄₄ₓ is derived as the algebraic trace of the constraint network's dual-face structure (STANDARD). 2. First-Principles Derivation of Core Quantum Results. Eight core results are derived from constraint network first principles: (a) spin as the SU (2) spinor representation of the Type I constraint boundary's internal configuration (Berry phase + ₁ (SO (3) ) = Z₂) ; (b) the spin-statistics relation from the topology of CN (fermions = Type I nodes, bosons = Type II edge excitations) ; (c) the Born rule P (aₙ) = |cₙ|² from constraint formation competition dynamics (Poisson-distributed transient attempts, () exact cancellation, martingale formalization) ; (d) entanglement entropy S₄₍ₓ = - ᵢ ᵢ as the information-theoretic expression of channel-diversity inverse entropy production; (e) the entanglement area law S₄₍ₓ (A) = | A| with = kB w₀ ^2/3 from constraint network locality; (f) the holographic principle S₆ₑ₀ₕ = | A|/4P² from constraint network coarse-graining; (g) the QM Classical transition at encapsulation depth L 3; (h) Noether's theorem on discrete constraint networks. 3. Constitutional Purification. All cognitive-constitutional concepts projected onto physical descriptions in v2. 0 --- Yin-Yang dialectical language, ``the first Cut'' as a cosmogonic event, Xu-Shi as physical ontology, Ben-Shi mappings to particle/wave --- are permanently removed and replaced by rigorous physical-constitutional descriptions. The QM Measurement Constitutional Duality is formally established: QM describes Divide-dominant coherent propagation; Measurement describes Cut Encapsulate coherent termination. The vacuum is re-anchored to the N=0 ground state (Vacuum Ontology v2. 0), with constitutionally undefined at strict N=0. 4. Canonical Realizations (Part III). The complete mathematical structure of quantum mechanics is realized on the constraint network across six subparts: Mathematical Foundations (Euler representation, Hamiltonian, commutation, Schr\"odinger and Heisenberg dynamics, path integral, Noether theorem, creation/annihilation operators, geometric phase) ; Quantum States and Dynamics (spin, spin-statistics, identical particles, Pauli exclusion, tensor product structure, entanglement, entanglement entropy, area law, holographic principle, Bell inequalities, EPR paradox, Aharonov-Bohm effect, Dirac equation) ; Measurement and Observation (density matrix, Born rule from constraint competition, post-measurement state update, measurement as CutEncapsulate, POVM -correction, quantum Zeno effect, no-cloning theorem, contextuality, -generalized uncertainty, Bell experiment numerical framework) ; Transition to Classicality (tunneling as transient constraint chains, decoherence as plastic inertia, QMClassical at L 3) ; Vacuum and Ground State (vacuum as N=0, zero-point energy, harmonic oscillator) ; and Core Quantum-Mechanical Tools (Ehrenfest theorem, variational principle, Feynman-Hellmann theorem, propagator, adiabatic theorem, perturbation theory, density of states, Fermi's Golden Rule, scattering theory foundations). 5. Systematic Closure of Gaps. Eight newly discovered gaps are closed: time evolution operator and Heisenberg picture, unitarity proof at =1, tensor product structure from constraint network separability, no-cloning theorem from Cut asymmetry, post-measurement state update, quantum harmonic oscillator, stationary Schr\"odinger equation, and symmetry-induced degeneracy. Seven Constitutional Open Problems are formally registered, of which two (spin-statistics stochastic process, Noether theorem formalization) have been upgraded to STANDARD and three (high-spin realization, anyons, Bell simulation) have been partially resolved. 6. Cross-Scale Instantiation and Falsifiable Predictions. The constraint network ontology is instantiated across eight physical domains (quantum optics, atomic/molecular systems, condensed matter, nuclear/particle physics, quantum information, quantum chaos, quantum biology, cosmology). Five falsifiable predictions with PM-9 statistical standards are presented: -dependent decoherence rates, () -generalized uncertainty bounds, Casimir force -modulation, Born rule deviations at extreme, and -dependent Bell violation. The constraint network ontology of quantum mechanics provides a unified, first-principles account of quantum phenomena without invoking any independent quantum postulates. Quantum mechanics emerges as the necessary dynamics of free-state energy on a discrete relational structure at the edge of chaos. Keywords: Quantum mechanics; constraint network; free-state energy; coherent propagation; Euler representation; spin-statistics; Born rule; entanglement entropy; area law; holographic principle; measurement problem; decoherence; quantum-classical transition; Energy-Efficiency Theory