PSD Gram Banded Global Dominance

Connections

This package executes the upgrade suggestions left by the previous package, quoted as-is; at the end, it precisely defines the dual problem specifications for the next package.

"This improvement is far from sufficient to approach the global budget... Therefore, this round does not recommend aimlessly increasing the rank, number of rays, or grid density anymore, but should pivot to the dual problem: proving or disproving 'how much positive mass a unit negative direction in the target region must force to appear on [18,23]'." — Excerpt from the technical notes summary of this package.

Technical Notes

Main Document — Three conclusions: cross terms have a real effect, the improvement is not caused by high-rank mixing, and the improvement is far from sufficient to approach the global budget; it also precisely defines the direction of the dual problem for the next step.

Result Data

Statistics on the reduction magnitude of Gram compared to the diagonal baseline, and the failure scale table, from RESULTS.md in the package.

Next Node Handoff Specifications

From NEXT_NODE_DUAL_SPEC.md within the package — finite grid primal problem, exact cone duality, first experimental steps, verification route, and decision thresholds.

Trust Boundaries

From TRUST_BOUNDARY.md within the package.

Files

Large data files such as the diagonal/Gram diagnostic JSONs for each of the 18 cells (outputs/patches/, approx. 20 KB each), rank_study.json (346 KB), and gram_results.json (388 KB) are not listed individually; they are all included in the complete zip file.

sha256 88c80a16ba08e1847e3e87e72ffa6747aa6ee2f8e3ca5b1c63bc437b7602c7c9