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 η ≈ 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 η ≈ 1, where the cooperative capacity Γ(η) = 4η/(η+1)² attains its maximum Γ(1)=1 and the decoherence ratio rdec(1)=0 vanishes. The wavefunction ψ = |ψ| e^iS/AEET is the Euler representation of the constraint network's dual-face structure --- |ψ| is the constrained-state face, e^iS/AEET 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Decomposition (Mathematical Foundations v2.10) and the Euler Representation (Core Rules v6.0, 0.10.2), replacing the superseded v5.x ``Universal Equation'' dependence.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 Ĥstandard = 2ĤEET 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 + π₁(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, Γ(η) exact cancellation, martingale formalization); (d) entanglement entropy Sₑₙₜ = -∑ λᵢ ln λᵢ as the information-theoretic expression of channel-diversity inverse entropy production; (e) the entanglement area law Sₑₙₜ(A) = α · |∂ A| with α = kB · w₀ · ρ2/3 · σ from constraint network locality; (f) the holographic principle Sgrav = |∂ 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 η 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 Cut→Encapsulate, POVM η-correction, quantum Zeno effect, no-cloning theorem, contextuality, η-generalized uncertainty, Bell experiment numerical framework); Transition to Classicality (tunneling as transient constraint chains, decoherence as plastic inertia, QM→Classical 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 η=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: η-dependent decoherence rates, Γ(η)-generalized uncertainty bounds, Casimir force η-modulation, Born rule deviations at extreme η, and η-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