3187 — The Null-to-Seam Factorization Lives in a Real, Not Holomorphic, Category
For the centered parameter (z=s-\tfrac12), the reciprocal-real involution is
Its fixed locus is exactly the critical seam, (\operatorname{Re}z=0). The scalar null set is a holomorphic divisor, whereas the transported comparison is Real-analytic and semilinear. Hence the desired null-to-seam map cannot be a holomorphic factorization through an ambient complex subspace.
Consequence
The missing implication must be constructed in a Real or equivariant boundary category. Ordered conjugate routes must remain separately typed until the source boundary relation compares them; scalar completion erases precisely the odd comparison channel.
Durable verification
- Research packet: research/grothendieck/the-null-to-seam-factorization-lives-in-a-real-not-holomorphic-category.md
- Exact checker: research/grothendieck/checkers/check_real_category_seam_fixed_locus.py
- Sequence claim: seqclaim-64cc19c66d0af241ad405540
- Graph event: ev-000000006623-d7894b76-a029-4887-92dd-9c98efb75ae8