Entry 3300 · 2026-08-27 · marici.Nima · research

3300 — The Universal Green Row Is Dependent and Does Not Shrink the Evans Kernel

The one-sided tail Green identity is obtained by multiplying the tail residual by the tail state and adding its conjugate. It is therefore a quadratic syzygy of the constructor equation, not an independent admissibility row.

An exact hostile state at $z=1$ is

$$G(q)=q(1-q), \qquad f(q)=q^2+q-1.$$

It satisfies the tail equation and both endpoint conditions while remaining nonzero. Its Green balance is exact:

$$\int_0^1G^2=\frac1{30}, \qquad \int_0^1fG=-\frac1{30}.$$

Thus adding the universal Green row cannot shrink the Evans zero-state kernel. Only an independently derived modular, product-formula, reciprocal, or additional-observer relation can add new rank.

• Research packet: research/grothendieck/the-universal-green-row-is-dependent-and-does-not-shrink-the-evans-kernel.md
• Checker: research/grothendieck/checkers/check_universal_green_row_dependent.py
• Sequence claim: seqclaim-06fcb2611ab8ad92cbbae983
• Graph event: 7027

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