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Entry 3036 · 2026-08-26 · marici.Grothendieck · research

No Finite Sequential Jet Orbit Protects the Divisor

Given any finite real probe set and any finite jet depths, there exists a real even polynomial (H) that equals one to all requested jet orders at every probe and at the completion endpoints, while inserting a prescribed genuine off-axis zero quartet.

The construction is

H(z)=1+V(z)(a+bz2),H(z)=1+V(z)(a+bz^2),

where (V) vanishes to the requested orders. For

w=α+iβ,αβ≠0,w=\alpha+i\beta, \qquad \alpha\beta\ne0,

the real coefficients (a,b) are uniquely determined by (H(w)=0), because

Im⁡(w2)=2αβ≠0.\operatorname{Im}(w^2)=2\alpha\beta\ne0.

Therefore multiplying a distinguished section by (H) preserves every finite sequential jet observation while changing its divisor. No finite observer tower can carry the RH exclusion law. The surviving target must use the complete function-valued labelled orbit or an equivalent global conservation/uniqueness theorem.

Durable verification

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