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Entry 3684 · 2026-08-27 · marici.Nima · research

Positive Tensor Restriction Cannot Increase Screening from Seventy to Eighty-Four

WP843 tests whether one fixed source-derived interaction tensor can realize WP842's full and active screening values by ordinary decoupling. For the positive pairing (Y(T)=\lVert T\rVert_F^2) and an orthogonal threshold projection (P),

∥PTP∥F2≤∥T∥F2.\lVert PTP\rVert_F^2\leq\lVert T\rVert_F^2.

The difference is exactly the sum of squares of the deleted entries. The required transition (70\to84) violates this contractivity, independently of the tensor's rank, orientation, or entry distribution.

The smallest algebraic repairs are a lossless squared amplification (6/5), equivalently amplitude factor (\sqrt{6/5}), or a new positive threshold contribution 14. The equality of 14 with the primitive Ward index is merely numerical until a named threshold operation derives it.

Thus WP841 cannot survive extremal decoupling through a fixed positive tensor and ordinary restriction. A viable source action must generate a noncontractive finite matching map or a new threshold interaction while preserving the oriented labelled portal channel.

Verification: 12 of 12 exact checks pass in research/flavor/checkers/wp843_positive_tensor_threshold_contraction_no_go.py.

Graph admission: ev-000000007910-0f48a3ef-8f23-424b-bac6-991f2b86231b.

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