Axis Suppression and Full-Window Leakage-Aware Optimizer

Axis-Suppressed Global-Window Optimizer v0.1 — After adding the finite critical line cancellation condition, the arithmetic positive direction dimension rapidly collapsed from 12 to 0; the target rectangle negativity was preserved, but no feasible solution was found for the non-positivization of the full control window.

RH_CLAIM = False — The selected_candidate_summary.json in the package self-reports status="target-negative and arithmetic-positive, but finite control-window nonpositivity failed", reproduced here as-is. This is a finite-dimensional floating-point diagnostic prototype, not an interval certificate, and not a proof of RH.

Connections

The summary of this package explicitly states from the beginning that it is responding to the questions left by the previous package, quoted exactly as is.

"The previous round has already quantified: the negative margin of the existing local negative certificate is far smaller than the positive mass generated by the critical line zeros. Therefore, this round no longer solely maximizes the negativity of a single target rectangle, but establishes a joint optimization prototype that simultaneously features finite critical line sampling elimination, arithmetic quadratic lower bound, target rectangle negativity, and finite off-axis control window exchange limits." — Excerpt from the technical notes summary in this package.

Previous Package · v0.1Zero-Side Leakage Budget

Integration Node · v1.0Equivariant Arithmetic Obstruction Integration Overview

Corresponding TheorySequence ③ · Equivariant Arithmetic Separation §12

Technical Notes

Main Document — Identity theorem argument for why the control window cannot stick to the critical line, paired-bump basis modification, arithmetic positive direction collapse scanning, target rectangle and full-window exchange method, selection of the q=12 candidate, geometric interpretation, and next step recommendations.

Result Data

Collapse table of arithmetic positive direction dimensions with respect to the elimination number q, from RESULTS.md within the package.

Trust Boundaries

From TRUST_BOUNDARY.md within the package.

Figures

Three out of five images from outputs/ in the package, reproduced exactly as is, without post-processing.

Arithmetic-positive dimension under axis constraints — The number of arithmetic-positive eigen-directions decreases linearly to zero as the number of eliminated critical line samples q increases. — Arithmetic positive direction collapse: as q increases from 0 to 15, the positive characteristic directions drop from 12 to 0.

Target negativity versus residual axis leakage — Logarithmic coordinate comparison between target negative margin (blue) and residual axis mass (orange); the gap between the two maintains several orders of magnitude under all q. — Target negative margin (blue) vs. residual on-axis mass (orange): The gap is maintained by several orders of magnitude across all q.

Selected q=12 paired-bump test function — Graph of the selected candidate test function psi(t), composed of 24 real even paired-bump bases. — Test function ψ(t) for the selected q=12 candidate: composed of 24 real-even paired-bump bases.

Files

The complete dense grid data for the control window/target rectangle (selected_control_grid.csv 593 KB, selected_target_grid.csv 731 KB) are not listed individually, but are all included in the complete zip.

Download Full Package (766.3 KB)

sha256 496474dedba4d922f33ddf9614e9653f04487ca5ad3c93d186f60818908c4881