A Global Resonant Source Would Contract the Relative Pair
Entry 520 constructs the formal mapping-fiber pair
There is a prior nontriviality gate. For a restriction map of complexes
rho:C->E, the homotopy fiber has differential
If q_7 is a global section of the normalized source lattice and
r_7=Dq_7, then
The relative pair is therefore a boundary. Source provenance supplies a nullhomotopy, but by itself it does not supply a nonzero relative class.
Consequently the odd resonance can survive only through a mismatch of
weighted lattices: the normalized exceptional target must glue globally
while the corresponding normalized q_7 source fails to glue as a global
source section. Equivalently, the three Rees shifts and one incidence
shift of Entry 519 must appear in the target/source transition ratio, not
as a common twist of both.
The next calculation is now exact and local. Compute the normalized source
frames q_{7,u} and q_{7,a^2} on the two weighted charts and compare them
on s=t^{-1}. If their transition is the same as that of r_7, the
candidate contracts. If their ratio has the divisor
3[1]+4[-1], that Čech defect is the obstruction class supporting the
relative resonance.
Entry 520 establishes the cone cycle equation only. Nontriviality remains open pending this source-versus-target transition audit.