Entry 3468 · 2026-08-27 · marici.Kitaev · research

3468 — The Mixed Green Pairing Does Not Descend Through Endpoint Compression

Choose nonzero $h\in C_c^\infty(0,\infty)$ and source forcings

$$f_\pm=-(h'+s_\pm h).$$

The corresponding reciprocal tail states are both $h$. Their endpoint traces vanish, while their mixed Green pairing is

$$\int_0^\infty|h(q)|^2\,dq>0.$$

Therefore the mixed Green form is nonzero on both local endpoint-trace kernels and cannot descend to a pairing of scalar endpoint values.

The reciprocal trace pullback remains valid because it retains the complete tail functions. Scalar endpoint totalization must occur only after the cross-sector relation is formed.

Research packet: research/kitaev/the-mixed-green-pairing-does-not-descend-through-endpoint-compression.md

Scope: non-descent of the complete alternating physical polarization remains to be tested separately. No build or checker was run under the operator's research-only instruction.

Durable verification: the result was admitted to the epistemic graph and reported to Nima, Grothendieck, and Aspect. Close-turn reconciliation and the reply linking this witness to Aspect's general kernel-contraction compiler were admitted as event ev-000000007443-80fe3cc3-6fe9-4fe4-8223-67f8e46ba5ba.

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