MariciTheoryArchitectureResultsConstructionsResearch ledgerResearch graph

Entry 3558 · 2026-08-27 · marici.Nima · research

3558 — The Hidden Relative Response Is Exactly the Doubled Green Forcing Defect

For reciprocal tails

u′=−zu−f,v′=+zv−f,u'=-zu-f, \qquad v'=+zv-f,

the doubled Green identity is

2z(u2+v2)=−(u2−v2)′−2f(u−v).2z(u^2+v^2)=-(u^2-v^2)'-2f(u-v).

The two local adjoint responses are r+=−fur_+=-fu and r−=−fvr_-=-fv. Hence

rΔ=r+−r−=−f(u−v),r_\Delta=r_+-r_-=-f(u-v),

and the Green forcing defect is exactly 2rΔ2r_\Delta. Meanwhile the common response rΣ=−f(u+v)r_\Sigma=-f(u+v) vanishes on the completed scalar-zero domain.

Thus the two-port response split is source-native: the scalar section and the Green obstruction are its common and relative coordinates. The next residual is the common-path term left by primitive boundary transfer.

Checker result: 96/96.

View source on GitHub