Riemann Hypothesis AI Research Starting Point v1.4: Kernel Sensitivity–Regularity Duality

The integration package includes the complete content of W-11. It generalizes the discovery of the single cubic kernel in v1.3 to the entire centered cardinal B-spline kernel family: the prime boundary activation order r=m+n+1 simultaneously controls the local amplitude O(ε^r), boundary regularity C^(r-1), Fourier decay, and tail bound cost — there is no single optimal kernel. The response of the linear kernel (m=1) to prime-3 is approximately 1.65×10¹⁶ times greater than that of the cubic kernel (m=3).

KERNEL_SENSITIVITY_ORDER_CLOSED — The phased status self-reported by the documents within the package, reproduced here as is. "What this version accomplishes is the engineering of the kernel selection GAP: rewriting 'smoother is better' into a computable, comparable, and relayable Pareto problem."

Connections

The relationship with other packages, using the words from its own documents as much as possible, not my interpretation. The complete W-11 content incorporated into this package is identical to its independent page and is not rendered again here.

Previous VersionResearch Starting Point v1.3 · Prime Boundary 7th-Order Soft Activation

Next VersionResearch Starting Point v1.5 · Mixed-Order Cross-Cancellation

Merged intoW-11

Research Starting Point Series14 / 23

"Smoother ⟹ easier to certificate, but harder to see new prime layers. Sharper ⟹ more sensitive, but tail bounds and condition control are more expensive. There is no single degree that is simultaneously optimal." — Excerpt from Section 2 "The True Trade-off of Kernel Design" in the main document of this package.

v1.4 Core Content

Milestones of this version (r=m+n+1 general formula), the true trade-off in kernel design, the 16 orders of magnitude difference, next-generation mixed-order dictionary design, and boundary declarations.

Files

The complete RH_W_11_工程包_v0.1/ folder merged into this package is identical to the W-11 page; only the filenames are listed here for verification.

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