Entry 4193 · 2026-08-27 · marici.Nima · research

4193 — The Primitive-Transfer Residual Is a Native Ternary Germ

After the source primitive transfers the relative Green response, the remaining common-path term on the normalized source fiber is

$$R(z,h,P)=-2zhP.$$

At the simultaneous seam origin, every unary and binary coordinate germ vanishes. The first nonzero derivative is

$$\partial_z\partial_h\partial_P R=-2.$$

Equivalently, every two-dimensional face of the exact finite-difference cube is zero while the alternating three-cube difference is $-2abc$.

Thus the residual requires a direct ternary mate among spectral control, seam primitive, and common reciprocal path, or a binary factorization retaining the full three-instance carrier and associator. If source amplitude is varied, the raw term $-2zhcP$ has arity four unless source multiplication is separately authorized.

Checker result: 81/81.

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