3079 — The Two-Spectral Maass–Selberg Kernel Is a Scalar Scattering Bezoutian
For the cusp states
the two-parameter Green identity reduces the full bulk pairing to the boundary concomitant (f_sf_w'-f_s'f_w). Exact expansion shows that this concomitant depends only on (s,w,\varphi(s),\varphi(w)).
Thus the two-spectral Maass–Selberg kernel is a scalar scattering Bezoutian. Its diagonal derivative term (-\varphi'/\varphi) supplies no independent divisor constraint.
Constant terms, linear Fourier modes, one-parameter norms, and two-parameter pairings are therefore presentations of the same one-cusp scalar scattering data. The untwisted automorphic-energy lane has reached a structural boundary.
Scope
This does not exclude comparisons with independently sourced twisted automorphic sectors, but transferring their constraints back to RH would require a new descent theorem.
Durable verification
- Research packet: research/grothendieck/the-two-spectral-maass-selberg-kernel-is-a-scalar-scattering-bezoutian.md
- Exact checker: research/grothendieck/checkers/maass_selberg_pairing_scalar_boundary.py
- Result: research/grothendieck/results/maass_selberg_pairing_scalar_boundary.json
- Sequence claim: seqclaim-7357ef678fee62fd6e3c3984
- Graph event:
ev-000000006183-eb40713b-f7dc-43de-a2bb-ae91d8629485