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 (Eb^melt Eb^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 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 Eb^melt Eb^form is reconstituted from a primitive constitutional fact to the emergent consequence of () decay when 1. At = 1, Formation/Meltdown Energy Symmetry (B-Series, CLOSED-in-EET) establishes Eb^form = Eb^melt = A₄₄ₓ. 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 I₄₋₀ₒₓ₈₂ 1/ () and its boundary condition ``I₄₋₀ₒₓ₈₂ 0 at = 1'' is resolved by the offset form I₄₋₀ₒₓ₈₂ 1/ () - 1, which yields I₄₋₀ₒₓ₈₂ (1) = 0 identically. Plastic inertia is elevated from the proportional relation I₏₋₀ₒₓ₈₂ C (t) to the constitutional identity I₏₋₀ₒₓ₈₂ C (t) (CND v4. 0). Bifurcation Duality Theorem anchoring. A₄₄ₓ = /2 (Two Forms of Energy v3. 5, CLOSED) is registered as the constitutional source of ₋₄₀₊'s quantum floor, providing a first-principles lower bound on inertial leakage time. Three new constitutional theorems. Theorem IV (Elastic Inertia Symmetry): I₄₋₀ₒₓ₈₂ () = I₄₋₀ₒₓ₈₂ (1/) --- 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 --- deviation triggers () decay, which deepens Barrier Asymmetry, which increases inertia, which impedes recovery. Euler derivation of elastic inertia. The Euler representation A = |A|e^i (Core Rules v6. 1, Two Forms v3. 5) provides the first-principles derivation of elastic inertia as the coherence-preservation metric. I₄₋₀ₒₓ₈₂ 1/ () -1 measures resistance to the decoherence driven by r₃₄₂ () = (-1) ²/4; the two are complementary projections of the single underlying -deviation. Constitutional jurisdiction boundary. The precise demarcation of where inertia operates is established: only for N 1, only for Being (not Existence), only where 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 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 (t₄₍₃) > 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_ receives its operational constitutional definition. Cross-domain inertia unification (Theorem VII). The same Arrhenius dynamics, the same elastic/plastic distinction, the same (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_, statistical power 1- = 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 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