The Ontology of Inertia: Resistance to Constraint Reconfiguration

What is inertia, physically? This document provides the constitutional answer within the Energy-Efficiency Theory framework: inertia is the resistance of constrained-state energy to constraint reconfiguration, rooted in Barrier Asymmetry ($E_b^{\mathrm{melt}} \gg E_b^{\mathrm{form}}$, L2 derived theorem). It is not a primitive property of matter but the necessary structural consequence of maintaining persistent constraints in a fluctuating energy landscape. Version 3.4 is a \textbf{constitutional conditionalization, Euler derivation, and cross-domain unification upgrade}. It preserves all v3.3 constitutional content while introducing the following key advances. {Barrier Asymmetry conditionalization.} The asymmetry $E_b^{\mathrm{melt}} \gg E_b^{\mathrm{form}}$ is reconstituted from a primitive constitutional fact to the emergent consequence of $\Gamma(\eta)$ decay when $\eta \neq 1$. At $\eta = 1$, Formation/Meltdown Energy Symmetry (B-Series, CLOSED-in-EET) establishes $E_b^{\mathrm{form}} = E_b^{\mathrm{melt}} = \mathcal{A}_{\mathrm{EET}} \cdot \omega$. The asymmetry deepens dynamically as the network ages --- it is not a fixed background but a self-amplifying consequence of operational history. {Elastic inertia offset form and plastic inertia constitutional identity.} The internal contradiction between v3.3's definition $I_{\mathrm{elastic}} \propto 1/\Gamma(\eta)$ and its boundary condition ``$I_{\mathrm{elastic}} \to 0$ at $\eta = 1$'' is resolved by the offset form $I_{\mathrm{elastic}} \propto 1/\Gamma(\eta) - 1$, which yields $I_{\mathrm{elastic}}(1) = 0$ identically. Plastic inertia is elevated from the proportional relation $I_{\mathrm{plastic}} \propto C(t)$ to the constitutional identity $I_{\mathrm{plastic}} \equiv C(t)$ (CND v4.0). {Bifurcation Duality Theorem anchoring.} $\mathcal{A}_{\mathrm{EET}} = \hbar/2$ (Two Forms of Energy v3.5, CLOSED) is registered as the constitutional source of $\tau_{\mathrm{leak}}$'s quantum floor, providing a first-principles lower bound on inertial leakage time. {Three new constitutional theorems.} Theorem IV (Elastic Inertia Symmetry): $I_{\mathrm{elastic}}(\eta) = I_{\mathrm{elastic}}(1/\eta)$ --- energy scarcity and energy glut produce identical elastic resistance. Theorem V (Inertia-Robustness Tripartition): robustness is not a single property but the product of three independently variable physical factors --- elastic recovery force, absorption capacity, and elastic reachability. Theorem VI (Inertia Self-Amplification): inertia is a positive feedback loop, not a passive background --- $\eta$ deviation triggers $\Gamma(\eta)$ decay, which deepens Barrier Asymmetry, which increases inertia, which impedes $\eta$ recovery. {Euler derivation of elastic inertia.} The Euler representation $A = |A|e^{i\theta}$ (Core Rules v6.1, Two Forms v3.5) provides the first-principles derivation of elastic inertia as the coherence-preservation metric. $I_{\mathrm{elastic}} \propto 1/\Gamma(\eta)-1$ measures resistance to the decoherence driven by $r_{\mathrm{dec}}(\eta) = (\eta-1)^2/4\eta$; the two are complementary projections of the single underlying $\eta$-deviation. {Constitutional jurisdiction boundary.} The precise demarcation of where inertia operates is established: only for $N \ge 1$, only for Being (not Existence), only where $\eta$ is constitutionally defined. The field possesses no ontological inertia (Field v3.0). The vacuum $N = 0$ is the absolute zero-inertia reference state (Vacuum v2.1). The $e^{i\theta}$ face of the Euler representation carries zero inertia; the $|A|$ face carries inertia. The distinction between initial vacuum ($C(0) = 0$) and final vacuum ($C(t_{\mathrm{end}}) > 0$) establishes inertia as the only physical quantity measuring the total irreversibility of cosmic history. {Five-channel inertia diagnostics.} CND v4.0's five-channel complete constraint Second Law is applied to decompose inertia into five independent channel contributions, each with a distinct elastic/plastic signature. The authoritative plastic inertia growth equation is registered, and $C_{\max}$ receives its operational constitutional definition. {Cross-domain inertia unification (Theorem VII).} The same Arrhenius dynamics, the same elastic/plastic distinction, the same $\zeta(t)$ degeneration corridor, and the same causal embedding amplification operate identically across six domains: physical, cognitive (CCN), human nature, social, knowledge/technology, and civilizational. Inertia is not a metaphor --- it is the same mathematical structure realized on different constraint substrates. This unification constitutes the common physical basis for the downstream human nature, social, knowledge/technology, and civilization mother texts. {PM-9 compliance and new predictions.} All five falsifiable predictions are upgraded with $N_{\min}$, statistical power $1-\beta = 0.80$, effect size, and explicit falsification criterion. Two new predictions are added: P4 (Elastic Inertia Symmetry --- testable in tunable constraint networks) and P5 (Cross-Domain Arrhenius Scaling --- testable in cognitive dissonance experiments). The document is organized as follows. Part I establishes the core ontology of inertia through six constitutional theorems. Part II provides the structural realization --- graph-theoretic embedding, elastic/plastic dynamics, finite inertia window, and five-channel inertia diagnostics. Part III develops the complete interface and bridge system, including the Euler derivation of elastic inertia, the constitutional jurisdiction boundary, the inertia-robustness relationship, and the cross-domain inertia unification principle. Part IV covers operational signatures and cross-domain instantiation. Part V provides governance, five falsifiable predictions, and deep insights. Sixteen appendices supply theoretical comparisons, cross-domain deepening matrices, experimental evidence, derivations, and complete cross-ontology bridge tables. Inertia is the structural memory of existence. Its root is Barrier Asymmetry, conditionalized at $\eta \neq 1$. Its reach extends from quantum coherence preservation to civilizational fossilization. Its boundary is the vacuum $N = 0$, where Being ceases and resistance vanishes. This document provides the constitutional foundation --- refined, deepened, and unified across all domains of constraint network organization. {Keywords}: Barrier Asymmetry (conditionalized); elastic inertia; plastic inertia; ergodicity breaking; Bifurcation Duality Theorem; Euler representation; coherence-preservation metric; constitutional jurisdiction boundary; five-channel inertia diagnostics; inertia-robustness tripartition; inertia self-amplification; cross-domain Arrhenius unification; degeneration corridor; Energy-Efficiency Theory