proposition A.639 The first two brackets

open in the book · appendices/A-long-proofs.tex:31115 · p. 3102

Rests on

depends_on equation A.1008 eq:app-hypersurface-deformation-commutator ¶
depends_on equation 26.84 eq:cd-adm-hamiltonian-constraint ¶
depends_on lemma A.638 Naturality ¶
- depends_on equation A.1005 eq:app-hypersurface-deformation-bracket ¶
- depends_on lemma A.637 Closed form of $H_{\parallel}$, and what it generates ¶
  - depends_on equation A.1005 eq:app-hypersurface-deformation-bracket ¶ ↺
  - depends_on equation 26.85 eq:cd-adm-momentum-constraint ¶
  - depends_on notation A.636 Densities and smearing ¶
    - depends_on equation 26.82 eq:cd-adm-momentum ¶
    - depends_on notation 26.28 Field systems ¶
      - depends_on definition 22.29 Poisson bracket ¶
      - depends_on notation 26.1 Weak and strong equality ¶
    - depends_on theorem 26.42 The Hamiltonian structure of general relativity ¶
      - depends_on proposition 26.41 The ADM form of the Einstein–Hilbert Lagrangian ¶
      - depends_on proposition 26.10 The four outcomes ¶
      - depends_on theorem 26.17 Counting the physical degrees of freedom ¶
      - proves proof ch:09-constrained-hamiltonian-dynamics@proof-16 ¶
  - proves proof app:A-long-proofs@proof-383 ¶
- proves proof app:A-long-proofs@proof-384 ¶
proves proof app:A-long-proofs@proof-385 ¶

Supports

depends_on corollary A.642 The constraints are first class ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	eq:app-hypersurface-deformation-commutator	declared	appendices/A-long-proofs.tex:31124
`depends_on`	→	eq:cd-adm-hamiltonian-constraint	declared	appendices/A-long-proofs.tex:31124
`depends_on`	→	Naturality	declared	appendices/A-long-proofs.tex:31124
`depends_on`	←	The constraints are first class	declared	appendices/A-long-proofs.tex:31367
`proves`	←	app:A-long-proofs@proof-385	declared	appendices/A-long-proofs.tex:31129