Building on canonical decomposition, this work develops an intrinsic stability theory for variational functionals S, splitting the second variation as δ²S (x) = Aₛym, x - Kₓ, where Aₛym, x drives dissipation and Kₓ induces distortion. The dimensionless stability index Θₓ = ||Kₓ||ₛym, x / λₘin (Aₛym, x) governs nonlinear regimes: Θₓ 1 enables transient amplification. A geometric foliation Tₓ X = E^ (-) ₓ ⊕ E^ (0) ₓ ⊕ E^ (+) ₓ organizes global dynamics, producing irreversibility and hysteresis without stochasticity. The theory unifies linear/nonlinear behaviors across manifolds, treating phenomena like geometric flows and phase transitions geometrically.
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