← NS-INRS / DCRP102 / X72R85 · Backward Adjoint Dynamics and the Copula Cone
Following the joint second/third-moment lock problem left by DCRP101, this round derives the exact backward adjoint equation for the pulled-back X72 test Φ, and proves that no universal invariant-sign half-space exists (the No-Invariant-Sign-Cone result): using the explicit example G=diag(1,-1,0), it shows that at a detector zero, admissible local strains S=±G push the detector projection to opposite signs, so fixed-sign transport–Riesz recurrence cannot be read as pointwise adjoint-sign conservation. But on the complementary regular pair-scale branch, it proves that a fixed positive transport–Riesz source together with a compact amplitude bound forces a positive-measure pair set into a strict oriented angular cone, and a finite pair-state pigeonhole argument yields a fixed recurrent angular cell. The conclusion gives a new dichotomy: the adjoint direction either pays a positive angular action, or falls into an explicit nonlocal tensor-ray eigen-lock kernel, leaving the next round to classify the complete tensor-ray structure of this eigen-lock kernel.
Relationship to the rest of the series, stated as closely as possible in the document's own words, not my interpretation.
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