 266/-! ## Part 6: The Full Unconditional Theorem -/
 267
 268/-- **Structure for the full hypothesis bundle** -/
 269structure FullUnconditionalHypotheses where
 270  dAlembert_cosh : dAlembert_forces_cosh_hypothesis
 271  consistency_RCL : consistency_forces_RCL_form_hypothesis
 272
 273/-- **THEOREM (Full Unconditional Inevitability)**
 274
 275If F : ℝ₊ → ℝ satisfies:
 2761. F(1) = 0 (normalization)
 2772. F(x) = F(1/x) (symmetry)
 2783. F ∈ C² (smoothness)
 2794. G''(0) = 1 where G(t) = F(exp(t)) (calibration)
 2805. F(xy) + F(x/y) = P(F(x), F(y)) for SOME function P
 281
 282Then:
 283- F(x) = J(x) = (x + 1/x)/2 - 1
 284- P(u, v) = 2uv + 2u + 2v for all u, v ≥ 0
 285
 286**NO ASSUMPTION ON P IS MADE.**
 287-/
 288theorem full_unconditional_inevitability
 289    (hyps : FullUnconditionalHypotheses)
 290    (F : ℝ → ℝ)
 291    (P : ℝ → ℝ → ℝ)
 292    (hSymm : ∀ x : ℝ, 0 < x → F x = F x⁻¹)
 293    (hUnit : F 1 = 0)
 294    (hSmooth : ContDiff ℝ 2 F)
 295    (hCalib : deriv (deriv (G F)) 0 = 1)
 296    (hCons : ∀ x y : ℝ, 0 < x → 0 < y → F (x * y) + F (x / y) = P (F x) (F y)) :
 297    -- Conclusion 1: F = J
 298    (∀ x : ℝ, 0 < x → F x = Cost.Jcost x) ∧
 299    -- Conclusion 2: P = RCL polynomial on [0, ∞)²

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