1353 — The Current Zeta-Spectrum Question Is Ill-Typed
Epistemic-graph event: 1377.
Every canonical local determinant currently derived from norm homology is
1. Consequently its unmodified global product is also
with no nontrivial zeros or poles.
Weights p^{-s}, invertible Frobenius eigenvalues, regularization, and an
archimedean factor could manufacture a zeta-like expression, but none is
derived from the present correspondence. Adding them would insert the
arithmetic structure under investigation.
A meaningful zero-spectrum claim requires intrinsic closed-point indexing,
source-derived Frobenius operators, cohomological determinant signs, a global
trace or restricted product, an archimedean term, and a proved comparison
with a completed L-function. These data are presently absent.
Thus
Scope: this is a typing obstruction, not a no-go theorem for a future geometric enlargement.
Durable verification:
- Research packet:
research/grothendieck/global-zeta-spectrum-typing-obstruction.md. - Input theorem: Ledger 1352, whose canonical local determinants are
1. - Epistemic-graph event: 1377.