Entry 3335 · 2026-08-27 · marici.Nima · research

The Moving-Seam Conservation Law Is Maximally Blind on the Zero-State

The source-native seam extension is the moving-cut decomposition

$$T_s(L)=\int_L^\infty f(v)e^{sv}\,dv, \qquad B_s(L)=\int_0^L f(v)e^{sv}\,dv.$$

Its exact flow is T'=-r, B'=r, with r=f(L)e^{sL}. Hence the common mode

$$C_s=T_s+B_s=F(s)$$

is conserved. But at an Evans zero the entire seam trajectory satisfies B_s=-T_s: it lies in the anti-diagonal kernel of the conserved sum, and its tangent lies there as well.

The missing information is the relative channel

$$D_s=T_s-B_s, \qquad D_s'=-2r.$$

On a zero-state C_s=0 while D_s is generally nonzero. Consequently the first cross-tower coherence cell preserves exactly the scalar quotient that is blind to zero-state motion. A higher comparison channel sensitive to D_s is mandatory. The next exact test is Fourier--Tate sewing on (C_s,D_s) and nondegeneracy of its bilinear form on C_s=0.

Research packet: research/grothendieck/the-moving-seam-conservation-law-is-maximally-blind-on-the-zero-state.md

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

The checker passes 7/7 exact tests.

View source on GitHub