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Research Starting Point v1.5 2026-07-23 CROSS_REGULARITY_CANCELLATION_OPEN

Riemann Hypothesis AI Research Starting Point v1.5: Mixed-Order Cross-Regularity Cancellation

The integration package includes the complete contents of W-11 and W-12—this version builds on the kernel sensitivity discoveries of W-11 to complete W-12. For the first time, an m=1/3 mixed-order kernel dictionary is established, revealing the "cross-regularity cross-cancellation mode": when two kernels of different regularities are superimposed, 93.4% of the self-energy is canceled out, yielding a bracket estimate for λ_min in (1/2000, 1/1000), which has not yet converged to a single exact value.

CROSS_REGULARITY_CANCELLATION_OPEN — The phased status self-stated in the package's files, reproduced here as-is. "This is the first observation and bracket estimate of a new phenomenon, not a closed-form solution."

Connections

Regarding the relationship with other packages, try to use the words from its own documents, not my interpretation. The contents of W-11 and W-12 fully merged into this package are identical to their independent pages, so they are not rendered repeatedly here.

"When the m=1 kernel and the m=3 kernel are superimposed on the same prime boundary, the self-energy contributed by each does not simply add up—93.4% is canceled out by the cross term. This is not a coincidental numerical rounding, but rather because the Fourier supports of the two kernels are almost completely out of phase near that boundary." — Excerpt from the "Cross-Cancellation Mode" section of the main document in this package.

v1.5 Core Content

The construction method of the mixed-order dictionary, the first observation of the cross-cancellation mode, the λ_min bracket estimate (1/2000, 1/1000), the relationship with the v1.4 kernel sensitivity results, and the next step (converging to an exact value or a counterexample).

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Files

The complete folders RH_W_11_工程包_v0.1/ and RH_W_12_工程包_v0.1/ merged into this package are identical to their respective independent pages (W-11, W-12); only the filenames are listed here for verification.

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Download Complete Package (129.9 KB)

sha256 4eaa2000f7fa4d3e4f3efa559ff9034374e9d2c35c500b2f3cb91ae9854764ec