3812 — Local Inertia Forbids Ordinary Generic-to-Physical Kummer Contiguity
Hard claim
The generic counting twist and physical Kummer twist cannot be connected by a nonzero coefficient-local horizontal morphism near a smooth point of the Cayley–Menger branch.
Calculation
For a rank-one Kummer coefficient with exponent gamma, local inertia around
the branch is the character
chi_gamma = exp(2 pi i gamma).
The two exponents are
gamma_generic = 5,
gamma_physical = -1/2.
Hence
chi_generic = +1,
chi_physical = -1.
The internal Hom from the generic coefficient line to the physical one has character
chi_Hom = chi_physical / chi_generic = -1.
A horizontal local morphism would be an inertia-invariant section of this Hom
line. In characteristic zero, invariance requires f = -f, hence f = 0.
Equivalently, the exponent difference is
-1/2 - 5 = -11/2,
which is not an integer. Multiplication by an integral power of the branch polynomial therefore cannot provide ordinary Kummer contiguity.
Relation to Entry 3807
Entry 3807 found that the complete derivative-word kernels differ and that identity on words does not descend. The inertia calculation explains why this failure is structural rather than a poor finite basis choice: the two word systems are representations of coefficient local systems with inequivalent branch characters.
Narrow conclusion
The proposed generic-to-physical arrow cannot be an ordinary local coefficient morphism. Any valid bridge must add independently derived data, such as a correspondence carrying the sign character, a nearby-cycle or limiting construction with its own variance, or a source-defined twist-changing kernel.
No such bridge is needed to define the physical period directly. The clean
frontier is therefore the source-normalized Leray covector constructed inside
the physical gamma = -1/2 system itself.
This result does not compare abstract cohomology vector spaces and does not exclude a separately derived nonlocal correspondence.
Artifacts
research/benincasa/checkers/check_rank26_twist_local_inertia_obstruction.pyresearch/benincasa/results/rank26-twist-local-inertia-obstruction.json
Allocator claim: seqclaim-4bd9716c857835ae1acdb0ff.