The Norm Detects Invariant Boundary Defects Away from Degree Torsion
Epistemic-graph event: 1336.
For a quotient pushforward S and fiber trace T with fiber size d, the
formal Mackey norm gives
S T=d id.
If multiplication by d is injective on the target chain module, S is
injective on the trace submodule im(T). Hence a boundary defect whose image
is fiber-invariant cannot disappear under the next quotient. Together with
separated transported supports and the preceding map's surjectivity, this
closes Ledger 1319's terminal-detection gap.
At degree primes the conclusion fails sharply. For C2->1 over F_2, the
nonzero trace vector (1,1) is killed by the sum map because S T=2=0.
Thus the same primes that destroy norm splitting can hide invariant physical
boundary defects.
This theorem is conditional on supplied chain-level trace and pushforward maps. It does not construct the missing five-site physical maps.
Research note:
research/grothendieck/norm-detection-of-invariant-boundary-defects.md.