Manuscript III-B@1 · III-B-v1.tex · section · d2c98f62

The four classical rows

Introduction: descent before operational interpretation › The four classical rows · lines 274–312

Equation space	Identification tested	Result here
Vacuum metric and unchanged free scalar	Only $h$ is quotiented	One exhibited Poisson symbol fails to descend.
Unchanged massive free scalar shell	Proposed scalar variation $X_{ξ} ϕ$	Local tangency for every admitted solution is equivalent to local Killing symmetry.
First-order scalar jet	$(h, ϕ_{0}, ϕ_{1}) \mapsto (h + K ξ, ϕ_{0}, ϕ_{1} + X_{ξ} ϕ_{0})$	A past-trivial harmonic section gives descent.
Fixed-background triangular model $C_{1}$	Constrained harmonic data modulo residual waves	A Hausdorff Cauchy quotient and nonzero compact coupled Ward observables.

The second row is not a quotient by arbitrary compact gauges: the proposed transformations generally fail to preserve its equation space.

The notation $C_{1}$ names a model. It does not mean that the fields have only $C^{1}$ regularity. All classical fields in this paper are smooth.