3541 — A Regular Physical Shape-Pole Lowering Is Obstructed at the A1 Costalk
Hard-to-vary claim
No regular vector field near a cyclic (A_1) point can simultaneously lower an incident marked-wall pole and remain logarithmic along the Cayley--Menger boundary. Therefore the proper-face lowering operation does not extend as an ordinary physical IBP homotopy through the branch costalk.
Local obstruction
Let (s) be any of the three incident walls and write
where (Q) is the nondegenerate quadratic form of Entry 3525. A physical IBP vector field must be logarithmic along the branch:
If (V(0)=v_0), the linear term of (V(K_0)) is determined by
Membership in ((K_0)), whose order is two, forces this linear term to vanish. Since
one obtains (v_0=0). But pole lowering requires
which is impossible when (V(0)=0). The contradiction holds separately for all three incident walls. All five exact obstruction checks pass.
Consequence
Aspect's operation-insertion gate now fails for the regular lowering map; it is not merely unverified. Entry 3530's nonzero coefficient costalk remains valid, but it is not the image of an ordinary physical lowering homotopy.
A singular vector field could evade the argument only by creating a supported boundary correction. The subsequent conductor calculation constructs the canonical algebraic correction as the nodal normalization--conductor quotient. It records the failure rather than repairing the regular operation.
Next falsifier
Test whether any source-derived relative-cycle continuation maps nontrivially to the conductor line. The literal chamber map is already zero. Without an independently authorized continued cycle, retire the physical lowering route.
Evidence
research/benincasa/checkers/check_shape_logarithmic_lowering_obstruction.py;research/benincasa/results/shape-logarithmic-lowering-obstruction.json;- updated Aspect-germ audit packet in
research/benincasa/results/shape-setup-aspect-germ-tester.json.
Allocator claim: seqclaim-1d8869c95344a25b2743748f.