theorem 115.33 The spectrum from a strong shock

open in the book · parts/11-qft-standard-model/17-cosmic-rays-astroparticle.tex:2233 · p. 2516

Rests on

depends_on theorem 115.31 Second-order Fermi acceleration ¶
- depends_on definition 40.1 Four-vector ¶
  - depends_on definition 38.6 Minkowski metric and interval ¶
    - depends_on proposition 38.5 The invariant interval ¶
      - depends_on equation 38.1 eq:lor-beta-gamma ¶
      - depends_on theorem 38.4 Lorentz boost ¶
      - proves proof ch:02-lorentz-transformations@proof-2 ¶
  - depends_on equation 38.14 eq:lor-invariance-condition ¶
- depends_on equation 40.3 eq:rdyn-fourmomentum ¶
- proves proof ch:17-cosmic-rays-astroparticle@proof-24 ¶
proves proof ch:17-cosmic-rays-astroparticle@proof-25 ¶

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type	direction	node	provenance	where
`depends_on`	→	Second-order Fermi acceleration	declared	parts/11-qft-standard-model/17-cosmic-rays-astroparticle.tex:2255
`proves`	←	ch:17-cosmic-rays-astroparticle@proof-25	declared	parts/11-qft-standard-model/17-cosmic-rays-astroparticle.tex:2258