remark A.771 What was assumed, and where it fails

open in the book · appendices/A-long-proofs.tex:37686 · p. 3172

remark -- no derivation owed by its kind

Rests on

depends_on remark 32.63 The Lorenz system is a model, not the fluid ¶
depends_on theorem A.769 The Lorenz system ¶
- depends_on definition 32.62 The Lorenz system ¶
  - depends_on definition 32.7 Conservative and dissipative flows ¶
    - depends_on theorem 32.6 Evolution of phase volume ¶
      - depends_on definition 32.3 Dynamical system, phase space, flow ¶
      - depends_on theorem 7.133 Gauss ¶
      - proves proof ch:15-nonlinear-dynamics-chaos@proof-3 ¶
  - depends_on theorem 32.6 Evolution of phase volume ¶ ↺
  - proves proof ch:15-nonlinear-dynamics-chaos@prooflink-1 ¶
- depends_on proposition A.766 Nondimensionalisation ¶
  - depends_on definition 31.51 The other similarity groups ¶
    - depends_on phenomenon 31.49 Dynamical similarity ¶
      - depends_on theorem 31.37 The Navier–Stokes equations ¶
      - proves proof ch:14-fluid-dynamics@proof-24 ¶
    - depends_on theorem D.2 Buckingham's $\Pi$ theorem ¶
      - depends_on equation D.3 eq:E-kernel-condition ¶
      - proves proof app:E-dimensionless@proof-1 ¶
  - depends_on proposition A.765 The roll equations ¶
    - depends_on definition A.763 Two-dimensional rolls ¶
      - depends_on equation 31.11 eq:fluid-incompressible ¶
      - depends_on proposition A.761 The Boussinesq equations ¶
    - depends_on proposition A.761 The Boussinesq equations ¶ ↺
    - proves proof app:A-long-proofs@proof-444 ¶
  - proves proof app:A-long-proofs@proof-445 ¶
- depends_on theorem A.767 Marginal stability of the conducting state ¶
  - depends_on phenomenon 31.78 Convective onset at a computed threshold ¶
    - depends_on definition 31.51 The other similarity groups ¶ ↺
    - depends_on theorem 31.37 The Navier–Stokes equations ¶ ↺
    - proves proof ch:14-fluid-dynamics@proof-39 ¶
  - depends_on proposition A.766 Nondimensionalisation ¶ ↺
  - proves proof app:A-long-proofs@proof-446 ¶
- proves proof app:A-long-proofs@proof-447 ¶

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type	direction	node	provenance	where
`cites`	→	Deterministic Nonperiodic Flow	derived	appendices/A-long-proofs.tex:37709
`depends_on`	→	The Lorenz system is a model, not the fluid	declared	appendices/A-long-proofs.tex:37718
`depends_on`	→	The Lorenz system	declared	appendices/A-long-proofs.tex:37718