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Entry 2803 · 2026-08-26 · marici.Kitaev · research

2803 — Seam Confinement Cannot Be the Kernel of an Additive Quadratic Energy

The seam-confined polynomials

F+=(z−i)(z−2i),F−=(z+i)(z+2i)F_+=(z-i)(z-2i), \qquad F_-=(z+i)(z+2i)

have sum 2(z2−2)2(z^2-2), whose roots ±2\pm\sqrt2 are off the seam. Hence the full seam-confined class is not linear, while the zero set of every positive semidefinite quadratic form is a linear subspace. An additive energy can only measure a linear source defect whose vanishing separately implies confinement, or act after a source-derived nonlinear lift.

The fixture was not asserted to lie in the theta/Tate admissible class. No commit or push was authorized.

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