Regional Phase Shaping Prototype

Regional Phase Shaping v0.1 — For an off-axis spectral rectangle K, construct a test function ψ in a real-even compactly supported bump basis such that its Fourier transform G approximates i, and exactly enforce G(i/2)=G(-i/2)=0 via null-space projection. The goal is to keep the off-axis orbital block B(w)=2Re(G(w)²) negative on the rectangular grid.

Numerical prototype; not an RH proof; not an interval arithmetic certificate — The phased status self-reported by the documents within the package, reproduced here as is. "Even if the prototype succeeds, it only means that all hypothetical off-axis zeros within the rectangle will form a negative contribution. It does not mean the total Weil quadratic form is negative" — the critical line zero modulus squared, other off-axis orbits, Archimedean terms, prime terms, and the infinity tail remain untouched.

Connections

Regarding its relationship with other packages, I try to use the words from its own documents as much as possible, not my interpretation. This is a cross-track connection: this package is the first autonomous research execution prototype of the semi-autonomous research track theoretical draft.

Theoretical Source (Semi-Autonomous Track)Off-Axis Positivity Obstructions in the Explicit Formula

Next PrototypeArithmetic Matrix and Positive Semi-Definite Certificate Prototype

Side-Branch Prototype Series1 / 2

"This package is the first executable engineering prototype of the 'Off-Axis Positive Obstruction in Explicit Formulas' series... The prototype does not read any unknown ζ zero positions, but only accepts rectangular geometry." — Excerpt from the beginning of the technical notes in this package, indicating that this is the first bridging step from the semi-autonomous track theoretical draft to executable code, involving no real zero data.

Overview and Usage · README

Problem setup, important limitations, installation and execution methods, output descriptions, methodology (paired translated bump bases), and planning for the next engineering package (arithmetic matrix connection).

Methods and Mathematical Boundaries · METHOD

What the prototype did (null space projection), why the blocks are negative (real even symmetry derivation), continuous region estimation (Lipschitz upper bound), and pending parts.

Technical Notes

Research status explanation — even if the prototype succeeds, how narrow the represented scope is; next step planning.

Files

Download Full Package (287.0 KB)

sha256 43b780a12e0272b64e6e4bfe33a665937ec0a74246466c464acfe0fee4951ea0