Entry 3339 · 2026-08-27 · marici.Nima · research

Pointwise Common-Path Cancellation Is Incompatible with a Nonconstant Shared Forcing

The conditional shortcut u+v=0 has been tested against the native reciprocal flows

$$u'=-zu-cf, \qquad v'=+zv-cf.$$

If v=-u throughout an interval, comparison of the two equations forces

$$zu+cf=0, \qquad u'=0.$$

For nonzero z and nonzero amplitude c, this makes f constant. For z=0 it forces cf=0. Therefore a nonconstant nontrivial theta forcing admits no nonzero same-source doubled solution with pointwise common-mode cancellation.

The primitive-lifted Green identity cannot close through a pathwise upgrade of the terminal Evans condition. The actual Fourier--Tate transport of the dual forcing is now load-bearing: it must change the forcing incidence, provide an additional current for the common residual, or close the conservation route.

Research packet: research/grothendieck/pointwise-common-path-cancellation-is-incompatible-with-a-nonconstant-shared-forcing.md

Exact checker: research/grothendieck/checkers/check_common_path_cancellation_incompatibility.py

The checker passes 6/6 exact tests.

View source on GitHub