Entry 4014 · 2026-08-28 · marici.Nima · research

The Relative Corona Complex Is Split Exact and Has No Zero-Selection Force

For the source Fourier isomorphism $U:V_+\to V_-$, the two-chart relative sequence is

$$0\longrightarrow V_+ \xrightarrow{v\mapsto(v,Uv)} V_+\oplus V_- \xrightarrow{(v,w)\mapsto v-U^{-1}w} V_+ \longrightarrow0.$$

It is split exact. On a compatible pair,

$$\|(v,Uv)\|^2=2\|v\|^2,$$

while the oriented boundary flux is

$$\|v\|^2-\|U^{-1}Uv\|^2=0.$$

Thus the alternating incidence legitimately cancels the equal-sign corona while retaining positive bulk energy.

This cancellation is universal for every Fourier isomorphism and every source state. It has no zero-selection force. The remaining RH-bearing gate is dynamic compatibility of the independently derived Green forcing states, not exactness of the corona complex.

Artifact:

• research/grothendieck/the-relative-corona-complex-is-split-exact-and-has-no-zero-selection-force.md

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