La Profílée and Physical Stability: Formal Structural Equivalence across Three Independent Domains, with Structural Identification in General Relativity

La Profílée (LP) derives the persistence condition IR = R/ (F·M·K) ≤ 1 from three minimal axioms without domain-specific assumptions. This paper establishes formal structural equivalence between LP and three independent physical stability theories: thermodynamics, fluid dynamics, and quantum decoherence. Section 0 proves the Representation Uniqueness Theorem: any stability theory admitting a dimensionless load/capacity ratio, non-substitutable capacity factors, and monotone ordering necessarily reduces to IR ≤ 1 under admissible variable identification φ. This closes the identification question: φ is not chosen for convenience but forced by the admissibility conditions of any well-formed stability theory. Section 1 (Thermodynamics): Lyapunov stability ⇔ IR ≤ 1 under φT via Separability Lemma; phase transitions = IR = 1; Onsager coupling = K; Prigogine minimum entropy production = Flourishing. Section 2 (Fluid Dynamics): Re/Rec = IR under φf; laminar-turbulent transition = IR = 1; Representation Theorem (Reynolds as class member). Section 3 (Recovery): Ff → Mf → Kf is the unique admissible relaminarization sequence; all five alternatives are structurally void. Section 4 (Quantum Decoherence): decoherence rate as R, coherence maintenance capacity as IK; quantum-classical transition = IR = 1; Lindblad dynamics under IR ≤ 1 condition. The convergence of three independent physical theories on the same structural condition is non-trivial: thermodynamics is grounded in statistical mechanics, fluid dynamics in continuum mechanics, quantum decoherence in Hilbert space formalism. Their structural equivalence to IR ≤ 1 is not analogical but formal under the admissibility conditions established in Section 0. The significance of the convergence lies not in the multiplicity of examples but in the independence of formal origin: a quadratic entropy-production form, a continuum-force ratio, and a Lindblad decoherence semigroup do not share a native mathematical language. Their reduction to the same persistence order under A1–A5 is therefore structurally non-trivial.