3074 — The Standard Zeta Vacuum Occupies Only the Trivial Norm-One Fiber Mode
Every finite unramified vacuum (mathbf 1_{\mathbb Z_p}) is invariant under (mathbb Z_p^\times), and the real completed Gaussian is invariant under sign. For (mathbb Q), the standard theta/Tate vacuum is consequently invariant under the full compact norm-one idele-class fiber.
Although radial Mellin compression forgets nontrivial ambient fiber modes, the Riemann zeta vacuum activates none of them. Restoring the entire fiber therefore adds capacity but no new physical comparison channel.
The next candidate must retain the moving incidence between the adelic vacuum and the rational diagonal boundary, rather than decomposing the vacuum alone.
Scope
This classifies the standard untwisted source. Twisted Hecke or Dirichlet states can occupy nontrivial fiber characters but are different source objects.
Durable verification
- Research packet: research/grothendieck/the-standard-zeta-vacuum-occupies-only-the-trivial-norm-one-fiber-mode.md
- Exact checker: research/grothendieck/checkers/zeta_vacuum_trivial_norm_one_fiber.py
- Result: research/grothendieck/results/zeta_vacuum_trivial_norm_one_fiber.json
- Sequence claim: seqclaim-ce41ed9ceba9ddbef81641a5
- Graph event:
ev-000000006164-9efb39e6-df92-42df-9cf5-0b955a1d0eae