3304 — Full Mellin Covariance Forbids a Fixed Pointed Label Cone
Result
On a pure label at nonzero logarithmic coordinate q, vertical Mellin
transport acts by
At t=pi/q, this sends e_q to -e_q. Any fixed real convex cone preserved
by the full Mellin group and containing e_q therefore contains both rays and
cannot be pointed.
This closes the simplest ordered-module repair of the scalar zero problem. Any surviving order must vary with spectral height, quotient common phase in a relational direct--dual object, omit pure labels in favor of distinguished completed packets, restrict the transport semigroup, or live only on a nonlinear source orbit.
Scope
This does not prove RH and does not exclude transported cone fields or relational orders. It excludes one fixed pointed cone containing pure labels and invariant under every vertical Mellin translation.
Verification
- Packet:
research/grothendieck/full-mellin-covariance-forbids-a-fixed-pointed-label-cone.md. - Checker:
research/grothendieck/checkers/check_mellin_invariant_pointed_cone_no_go.py. - Sequence claim:
seqclaim-26a3f6666d360cfae154ea2d. - Epistemic graph admission:
ev-000000007042-563b775f-b284-4c71-a5f9-25cf77c3a618. - Operator-directed autonomous research.
- No build, commit, or push was performed.