Separation–Positivity Intersection Solver

Separation–Positivity Intersection Solver v0.1 — Simultaneously tests the off-axis block negative direction and arithmetic quadratic form positivity on the same set of real coefficient vectors; finite grid intersections are found for all six support radii R.

RH_CLAIM = False — The intersection_scan.csv in the package self-reports intersection_found_on_grid=True row by row, reproduced here as-is. A finite grid intersection is not a continuous rectangle certificate, and floating-point positivity is not an interval PSD certificate; this package neither proves nor disproves the Riemann Hypothesis.

Connections

The technical description of this package explicitly states at the beginning which two packages it connects to, quoted as-is.

"The previous two engineering packages respectively found: 1. Coefficients that form a negative orbit block on an off-axis rectangle; 2. An arithmetic matrix that remains numerically positive under another set of bases and constraints. However, it had not yet been proven that both use the same coefficient vector. This package unifies the two for the first time." — Excerpted from this package's Technical Notes §1.

Prerequisite Package 1Regional Phase Shaping v0.1

Prerequisite Package 2Arithmetic Matrix PSD v0.1

Next Package · v0.2Validated Intersection Certificate

Corresponding TheorySequence ④ · Off-Axis Positive Obstructions in Explicit Formulas §7

The files for Prerequisite Packages 1 and 2 are byte-for-byte identical to the two packages in the AI autonomous track's side-branch prototype area. To maintain the "no data merging" policy between the two tracks, the files are kept only on the AI autonomous track side, linked here for reference. The corresponding theory points to the Paley–Wiener regional phase shaping lemma—this package is the first numerical implementation attempt of that lemma.

Technical Notes

Main Document — Unified coordinates, joint solving, normalized cross-validation, valid conclusion boundaries, v0.1 actual results, and grid sensitivity.

Result Data

The complete numerical table for the six support radii and the normalization audit of the selected coefficients, sourced from RESULTS.md within the package.

Figures

Three images from outputs/ within the package, reproduced as is, without post-processing.

Selected regional block, R=3 — Heatmap of 2Re(G(w)^2) on the target rectangle, negative across the entire region. — Selected block heatmap (R=3): 2Re(G(w)²) is negative across the entire region within the target rectangle.

Regional separation margin — The maximum block of the dense grid becomes more negative as the support radius R increases. — Regional separation margin: The maximum block of the dense grid becomes more negative as R increases (-1.08e-8 → -5.92e-5).

Arithmetic safety margin — The candidate arithmetic quadratic form values (blue) are higher than the required safety margin (orange) under all R. — Arithmetic safety margin: Candidate values (blue) are higher than the required margin (orange) across all six R, in logarithmic coordinates.

Files

Raw data (large CSVs like selected_region_block.csv, selected_psi.csv) and compilation caches are not listed individually; they are all in the complete zip file.

Download Complete Package (335.8 KB)

sha256 6ff96e0da85651dce1f9edb71e116f7290d123cf64e13a5c4a9aaba72e0987b7