A Physical Paired Mackey Correspondence Has an Eight-Stage Obstruction Tower
Epistemic-graph event: 1351.
Physical paired Mackey admission separates into eight ordered gates: geometric relative-complex typing; frozen-readout factorization; pairing and radical identification; visible boundary compatibility; radical obstruction vanishing; repair canonicity; symmetry/composition coherence; and Mackey norm normalization.
A failure or absence at an earlier gate cannot be repaired by a later formal
identity. The selected-scalar branch is strictly weaker: a frozen cocycle
ell yields a source-homology readout when ell Omega=0, but this does not
produce a homology map, representative-independent cohomology pullback,
chain map, or Mackey correspondence.
For five-site cosmology, the algebraic deck system retains its formal norm and composition theorems. The positive selector fails nontrivial branch descent, and the source-derived physical relative complexes are still absent at the first gate. Therefore no downstream physical transfer claim is yet admitted.
Research note:
research/grothendieck/physical-paired-mackey-obstruction-tower.md.